From 1ba69539860abc7eeeb7d32901bf86681ee82b48 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 1 Feb 2024 11:51:36 -0700 Subject: [PATCH 01/22] adding PF version of krylov demo --- docs/krylov-subspace-demo.ipynb | 1044 +++++++++++++++++++++++++++++++ 1 file changed, 1044 insertions(+) create mode 100644 docs/krylov-subspace-demo.ipynb diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb new file mode 100644 index 0000000..aa7e11a --- /dev/null +++ b/docs/krylov-subspace-demo.ipynb @@ -0,0 +1,1044 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Krylov subspace expansion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map problem to quantum native format\n", + "\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "\n", + "\n", + "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", + "\n", + "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", + "\n", + "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", + "\n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "\n", + "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", + "\n", + "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Imports and definitions\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pylab as plt\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", + "from qiskit.quantum_info import SparsePauliOp, Operator\n", + "from qiskit.circuit import Parameter\n", + "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit.circuit.library import PauliEvolutionGate\n", + "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", + "from qiskit.providers.fake_provider import FakePrague\n", + "from qiskit.primitives import Estimator\n", + "\n", + "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", + " s_vals, s_vecs = sp.linalg.eigh(s)\n", + " s_vecs = s_vecs.T\n", + " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", + " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", + " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", + " if k==1:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", + " else:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define Hamiltonian\n", + "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['ZZIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIZZ', 'XXIIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIXX', 'YYIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Define problem Hamiltonian. Kicked Ising in this case\n", + "n_qubits = 20\n", + "J = 1 # coupling strength for ZZ interaction\n", + "\n", + "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", + "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", + "for i in range(n_qubits-1):\n", + " H_int[i][i] = 'Z'\n", + " H_int[i][i+1] = 'Z'\n", + "for i in range(n_qubits-1):\n", + " H_int[n_qubits-1+i][i] = 'X'\n", + " H_int[n_qubits-1+i][i+1] = 'X'\n", + "for i in range(n_qubits-1):\n", + " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", + " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", + "H_int = [''.join(term) for term in H_int]\n", + "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", + "\n", + "# Get operator\n", + "H_op = SparsePauliOp.from_list(H_tot)\n", + "H_op" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set parameters for the algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set parameters for quantum Krylov algorithm\n", + "krylov_dim = 20 # size of krylov subspace\n", + "dt = 0.1 # time step\n", + "num_trotter_steps = 4\n", + "dt_circ = dt/num_trotter_steps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### State preparation\n", + "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_state_prep = QuantumCircuit(n_qubits)\n", + "for i in range(n_qubits):\n", + " if i%2 != 0:\n", + " qc_state_prep.x(i)\n", + "qc_state_prep.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time evolution\n", + "\n", + "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + " ## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "qc_evol = QuantumCircuit(qr)\n", + "qc_evol.append(evol_gate, qargs=qr)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" + ] + }, + { + "attachments": { + "H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hadamard test\n", + "\n", + "![H_test.PNG](attachment:H_test.PNG)\n", + "\n", + "\n", + "\\begin{equation}\n", + " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit for calculating the real part of the overlap in S via Hadamard test\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "## Create the time-evo op dagger circuit\n", + "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", + "evol_gate_d = evol_gate_d.inverse()\n", + "\n", + "# Put pieces together\n", + "qc_temp = QuantumCircuit(n_qubits)\n", + "qc_temp.compose(qc_state_prep, inplace=True)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", + "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", + "\n", + "# Create controlled version of the circuit\n", + "controlled_U = qc_temp.to_gate().control(1)\n", + "\n", + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", + "qc_real.h(0)\n", + "\n", + "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", + "qc_real.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 16644\n" + ] + } + ], + "source": [ + "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" + ] + }, + { + "attachments": { + "optimized_H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize circuits and operators\n", + "\n", + "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", + "\n", + "\n", + "![optimized_H_test.PNG](attachment:optimized_H_test.PNG)\n", + "\n", + "\n", + "This works provided the operator $\\hat{O}$ preserves Hamming weight.\n", + "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " |0\\rangle_a|0\\rangle^N\\quad&\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|0\\rangle^N+|1\\rangle_a|\\psi_0\\rangle\\Big) \\\\\n", + " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|0\\rangle^N+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", + " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", + "\\end{split}\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\|e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\|e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}\n", + "Hence the desired matrix element is\n", + "\\begin{equation}\n", + " \\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle=e^{i\\phi}\\big(\\langle X\\rangle_a+i\\langle Y\\rangle_a\\big).\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", + "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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581m0aBHjxo2joaHBd6UiIyODgoICjh07xtKlS5k7dy4Oh4OUlBSSkpJ48sknB5wzJvp6nvjH9Xp9BMPjD4RBQ2DSP8KRHdrBbtw4uPGr6vNe54hn2YOvhFxsf4iIgokPapfVa4/DuPvgulvV51XpXTA6DRAZA19/QLt3pasLEqeA40b1ea3oteMmmHC/NvmA8xTcOQeuGaU+rxW9jrsdbGHaEIZBQ+Ar34AhkWpzqvYuWL2+eRLYB2sduYZy7XtSRYfiQqzo9a0zNI9rj8PQEdq6ig5Fb6zq9YT7tSGrDeXQcAbu+i4B61CAgZ2KKVOm+IYvzZgxg7i4OADee++9v9p25cqVfdZPnDjB1q1bOXz4ME8//TTDhg1T3t5QZkgkfPX+QLfCGgxzwB3fge0rjelQWJnhsfD1OZffTvCfkTdrr+0rIeq6QLfG3MTepr0E9dz4Ne21faX6zpuVsdkg4W7tJaglLAxuSdGWt68Ee3hg22P4E7U9Hg/h4Vf3qRMTE3njjTcUtUhQxZbCV9hz6H3CwuzcO/EhJt8+OyRiC0J/iNOCGRGvBTMiXhuP4c+psNvtbN0a4DmvBMN4IPURHvvuWvYe1f9vrjK2IPSHOC2YEfFaMCPitbEE9OF3gvnJ3vU7Hvl9CrPuXsgH+S9R01DOho9/02dZj9hv7XgOZ8tZNhes7bMsCHojTgtmRLwWzIh4bSyGD38ygiFR6mLpFVvPNgYz35n+ExxRcXy0bz0Ppj3Br157gEfnvkTkUIdvWY/Yd98+mxc3LePRuS9yvOKAb9lMiNfBgTitLyrdE6+vHPFaP1Tuq/WKbwWnQbw2GlN2KiZ9LzRjm5UbYm6hrqmClvYGIgZfQ5urGWw237IjKvbyQS4Te/SoMdx6410Msodz202TfMtmQrwOHsRp/RCvgwfxWh9UeydeXx3itXGYslMhBAf3TXrIt7x0zhre+WQVP3/wVbJzn8ceNsi3nDljmd+xgb7zqAVyTjXBtIjTghkRrwUzIl4bj82r6okcgiXo/ZAff4kYDtN/pH/sC+OqYPtK+OZj2vLOnTvJyclh5syZvp+pqals27aNiRMn4nA4fL+Xn59PYWEhS5YsAWDDhg04nU4yMzPJzc3F6/USHx9PeXk5aWlpMp2yQYjXGuK1eVDptJ7xxWvhaggFr41wGoLDa7lRWxB0ZsKECcTHx/t+pqamAlBZWYnD4WDdunUsWbKErKwsJk+eTGRkz4Tp7e3tpKWlUVJSQlJSEmPGjCE7O5vExERKSkoC9ZEEQbwWTIl4LZiRQHktnQpB0JmsrCxiYmKYN28eMTExlJaWAhAXF4fT6WT+/PmsXr2a5cuXc+TIEYqKimhtbaWoqIiIiAhycnIYO3YsycnJJCcnk5iY6HtPEAKFeC2YEfFaMCOB8lqGPwl+cTWXBkvPHOCWG+7o99/9GSZyqdhGX04XQh/xWkO8Ng9XO4zjat270vhX+/9FBeK1eQgFrwMx/ClQyJUKwTB2H8ymqr4s5GILwqUQrwUzoso9cVoIJOK1Wkw5+1Phm+Bq1ifWkKi+07fpFfvCuFYgbmQiXm9XyMUOFsTr4ES89g+V7onXA0eVe+L01aHKays6DeK1akzZqXA16zcbgJGxzU7vKdhCKXawIF4HJ+K1f4jXwYkq98Tp4I9vZsRrtcjwJ0EQBEEQBEEQ/CKgnQqXy8WUKVOIjIz03ZkOsGzZMlJSUliwYAEejyeALRQEQRAEQRAE4XIEtFMRHh7Oxo0bmTNnju+9oqIiampqyM3NJSEhgU2bNgWwhYIgCIIgCIIgXA5DOxWrVq1i+vTpPPzww6SnpxMWFkZsbGyfbfLy8khPTwcgPT2dvLy8Aec76zzFije/z7NvzOOs85RfbTcytr+0OWHvBtjzKpzIByMmDT5ZfYhn1mWyfvszIRXbX5rPwmdvasvlnxuT06pe15+CgnWQ/zqcPWpMTqt6ffaoVmeA+tMG5bSo1+VF2r76sze1/YkRWNFrrxdO7NFqDdDWoD6nau+C1euuLjj6CXz6ChzIBlerMXmt6LXHDSVb4dOXtfXO9sC2x7BOxf79+ykuLmbXrl2kpqYSHx9/0e2cTifR0dEAREdH43Q6B5xzc+FaFs1ewcJZz7Kl8OUBxzE6tj90nIO9b4PzFLTUQNkeODHwftkVc3PsOBbNfi7kYvvDuUbY/w40nNHWSz+BM1+oz2tFr5uq4Iv3tZ/N1XBoK9SeUJ/Xil7XfqnVt7laW//iz8Yc7FrR6/LPoXSntq9uOKPtT841qs9rRa+/3A1l+VqtAfa+BZ3n1OZU7V2wel2yBcr3Q2st1B7XOswet/q8VvS66D2oOAitddr63reNOZHcH4bN/pSdnc3ixYsBsNvtJCcnX3S7ESNG0Nio7VUbGxtxOBy8//77HDx4kKqqKp5//vkrzlnfVMmo4dfj9Xqpa670/0MYFNsfGs707al6OqGyBJLuCVybzErNceho61l3u+BMEdwwQW1eK3pdeajvAYC7Xat1TGLg2mRWzhRp9e2m8xxUFkPUdWrzWtHrM0XafqObjjatU3fT1wPXJrNSdVj7Puymsx0aKuDaMepyqvYuWL2uPwVdvToRbpfWwRgeF7g2mRFvl9ZJ7j2TbUcruFogIiowbTLsSkV9fT1utxu3282aNWsYP378RbebNm0aW7duBWDLli1MnTqV+++/nyeeeIL29v6v69hsNt+rrKwMgJHDR1PXVEFt0xlGRY0eULvLysqUxL4wrl6v+9LTaGrqe3Xn4KEiJbl610MP+qu13nH1ev3gh/PpuOBa40efbFFeayt6/cyzT+Pudaqrq6uLV9e/KF4r+Oyvv7W2Tx63x80vn3ky6L2+WD2C3etPdm3vk8fVeY7/s+DBkHM6FLw+VNL3MnJjk5Nv3vuNoHa6v3roEV9VnW02GydP9r2MXFNzlnETbrWs16pqHWa3UVVV1SdXdXU1o66LVva3vRyGXamYP38+ixYtYty4cTQ0NPiuVGRkZFBQUMCxY8dYunQpc+fOxeFwkJKSQlJSEk8++SQAK1asYOHChf3G9/a63tP9WPX0ST9g7YdP4fV2sSB9YOPgEhISlMS+MK5eeL2wbwM0VkFXJ4QPg8yffY0fr1JzPay7HrWNFby8+SnO1B4jIW4894zPuOpY/dXa39iqat3lhoI3oK1OG0M6eBj8y4r7ePxFtbW2oted7dr9FO1N2lmZYdFhPPvyD1n1xx/qngus7XV7MxS+oZ3tstlguGMQr33wa94Y8mvdc4Fa94Ld69Y67f63jjbACzE3DCXns7cIG/SW7rm6awFq3At2r53l8PmfobMNwsIhfqyDA6WfcAXHSVeNyn21XvFV1Rmg+ggc3t5zdfm2iddRXqPmRrhQ8FplrU/tgy/ztKvLg4bA1ybG0rrcgDGU/WDzqvqkl2DGjBns2LHjirf/9a9/zdGjR7njjjv46U9/etneUm/J/CViOEz/kf6xL4yrJ94uqPkSPn8Ppi2CYSPU5AGpdZdbGwbl7tCG4gyJVJMHpNbuDqgpheIP4BsPQ/hQNXlAat1xThsLbQuDa2+BQYPV5AG19QiFWrc3Q12ZNg497REIs6vJo9JpPeOrrHVbg3a/4eBhEJOk+a2CUKi1yjoDtNRqw7EPb4OZP0NJ5w2k1qDda9hUDdeMAseN6vJcCYY/Udvj8RAeHn5Vv9N9tUK4MmxhcN0t2rLKDoUAYYMg9rZAt8IaDBoMo8dpnQqVHQoBBg+F6y8+QlXQmYgo7T6ski3qOhSCxrAR8p1oFJEx2uvwNnUdCkFjeFzw3K9ieKfCbrf77pkIBFsKX2HPofcJC7Nz78SHmHz77JCILQj9IU4LZkS8FsyIeC2YmYA+/C5QPJD6CI99dy17j+rfuVEZWxD6Q5wWzIh4LZgR8VowK5bsVGTv+h2P/D6FWXcv5IP8l6hpKGfDx7/ps6xH7Ld2PIez5SybC9b2WRYEvRGnBTMiXgtmRLwWzIrhw5+Cge9M/wmOqDg+2reeB9Oe4FevPcCjc18icqjDt6xH7Ltvn82Lm5bx6NwXOV5xwLdsJoboOBfyhbH0iq1nG4MVcVpfxOvgQLzWD5VO6xlfvBavr4ZQ8NoKTndjyU4FwA0xt1DXVEFLewMRg6+hzdUMNptv2REV63fs0aPGcOuNdzHIHs5tN03yLZuJSd8LzdhmRJzWD/E6eBCv9UG1d+L11SFe64N4HVxYrlNx36SHfMtL56zhnU9W8fMHXyU793nsYYN8y5kzlvkdG+g77YFMgSAoQJwWzIh4LZgR8VowMwF5ToVqrD7HfDfbV8I3H+tZ37lzJzk5OcycOdP3MzU1lW3btjFx4kQcDodv2/z8fAoLC1myZAkAGzZswOl0kpmZSW5uLl6vl/j4eMrLy0lLS2PYsGFqP4wgXp+nt9fidOhj9edUdCNemwd5dkIP4rW1sOSN2lZlwoQJxMfH+36mpqYCUFlZicPhYN26dSxZsoSsrCwmT55MZGTPk9za29tJS0ujpKSEpKQkxowZQ3Z2NomJiZSUlATqIwkWR5wWzIh4LZgR8dr8SKfCQmRlZRETE8O8efOIiYmhtLQUgLi4OJxOJ/Pnz2f16tUsX76cI0eOUFRURGtrK0VFRURERJCTk8PYsWNJTk4mOTmZxMRE33uCEAjEacGMiNeCGRGvzY/lhz+VnjnALTfc0e+/+zNM5FKxAzH8SQhtxGsN8dpcqHRPvBYCwdUOT1LldaCdBvHaalj+SsXug9lU1ZeFXGxBuBTitWBGxGvBjKhyT5wWjMZysz9dSNzIRLzerpCLHSwUvgmuZn1iDYnqO32bXrEvjGsFxGv/EK+DE/F64Kh0Ws/44nXwxw0mQsFrKzlt+U5F7ynYQil2sOBq1m+WCyNjmx3x2j/E6+BEvB44qr0TrweOKvfM7jSI18GG5Yc/CYIgCIIgCILgHwHtVLhcLqZMmUJkZKRvFgCAZcuWkZKSwoIFC/B4PAFsoSAIgiAIgiAIlyOgnYrw8HA2btzInDlzfO8VFRVRU1NDbm4uCQkJbNq0KYAtDF3MN6dX8OL1gsmHrQYN4rVxeL1Sb6OQ/YdxeLvEa6MQr40jWGpt6D0Vq1at4t133+VrX/sax48fZ/PmzcTGxvbZJi8vj/T0dADS09N59913+fa3vz2gfCerD/H6tuUkxk1g3jf/1e/2Gx1/oFQWw7Gd2nLhm/D1f4BBQ9TmPOs8xdrNT+H1drFw1rNc54gPidj+crJQewFExcHXvg1hdsU5FXoXrE57vXDsE6g6pK0f/ACSZ4HNpjavFb32eqH4Q6gvAy9wfTJ85Rvq81rR6y43FG2E5rPa+snP4OaJanOq9i5YvXa7YP+7cM4J2DSnR49Tn9eKXrtaYf870NGqrdeegJhEtTmt6nVbAxz4k+Z32CCY8PcQHRe49hh2pWL//v0UFxeza9cuUlNTiY+/+B/E6XQSHR0NQHR0NE6nc8A5b44dx6LZzw349wMdfyC0OeHoxz3/mRsroHiz+rybC9eyaPYKFs56li2FL4dMbH9oOAMn8qGjTXvVn9QOfFWj0rtgdBrg7FE487lWZ4Czx+DUXvV5rej1yc+g5phW6842OFME1UfV57Wi10c/gfpTPfvrE3ugsVJtTtXeBavXxR9q34cdbVq9j+7QDshUY0WvP98ILTU9++tDH0LHObU5rer1gT9px30dbdoN5Z+/B10BvGvAsCsV2dnZLF68GAC73U5ycvJFtxsxYgSNjY0ANDY24nA4+Pzzz9m2bRvHjx/nhRdewG5XfCo4hGmuAU9Hrze82n9u1dQ3VTJq+PV4vV7qmvX9VlQZ2x8aK8Hd3rPu9WgdDUF/6k/19bqrE5yn1Z/VtaLXzlPg6exZd3dotY69NXBtMisN5dp+oxt3u3bgGz1aXU7V3gWr1y01aJfezuPp1N4bNiJQLTIv7RdMwdrVBecaYPBQdTmt6LW3S7tCceF7Ha3aww0DgWFXKurr63G73bjdbtasWcP48eMvut20adPYunUrAFu2bGHq1Kl89atfZfjw4dTX12PrZ7yDzWbzvcrKynRrd1lZmZLYF8bV6zX1b76Ks7GnF9HV1cWugq1KcvWux8jho6lrqqC26Qyjogb2jdhfrf2NrarW//CPf0tLW8+VtE5PJ3/ctFZ5rfUg1Lx+9KmFtPWaLNzVcY5V//NL8VrBZ3/+xX/D1dlzWrGtvZmfPP5Q0Ht9sXoEu9fZH76Ku1cPrrnNybcz00LO6VDwevdnOXR19Qw8r2+o4e6U5KB2ur966BFfVZ1tNhuHjhzok6umpprE2+Is67WqWofZbZwqP9EnV1VVJcNHRSj7214Ow65UzJ8/n0WLFjFu3DgaGhp8VyoyMjIoKCjg2LFjLF26lLlz5+JwOEhJSSEpKYknn3wSgB/+8IeEhYX5rl5ciLfXnVfdj7Cvbazg5c1Pcab2GAlx47lnfMZVtzshIeGiscG/+BfG1ZMTe7ShITYbDIoIY+nD9/KL/6cmV3c90if9gLUfauMNF6Q/M6BY/dXa39gqa304B6qPaMNERo4OZ8XrP2Dl2z9QkssIr/2NrarWXi988T44y7V1R/xQXvnFL3nN/kvdc4G1ve7yaOOhW+o0rxO+GsWWp17BZntF91yg1r1g99rtgr1vg6tFc3zcnQ72P/2R7nlArdN6xldVa1cr7H1Lq3lHG0ycdS1lvyzWPQ/od5wA6rxW+b3Y5oR9f9TuGfIC96THUr+8SkmuUPBaZa0bq7QhT94uzeu0h0bT8av2y/6eKmxeVZ/0EsyYMYMdO3Zc8fYffvghX3zxBV9++SW//e1viYiIuOT2vf9D+0vEcJj+I/1jXxhXb9wd2s5zSKTam1ml1tDZDp+shpk/k1qrrnVHm3bwNXiY1Fplrb1erda5/wPffExNjm5U1iNkat2q3WQZfumvNr9Q6bSe8VXX2tUCu9ao9ToUaq16X93VBR0tED4U7OHq8kittRNBHa1aW1Xvry+H4U/U9ng8hIdfnWGzZs1i1qxZilpkTgYN1l6BZEvhK+w59D5hYXbunfgQk2+fHRKxr5buAwGVB7mCxuBhgc1vFadtNhhyTcDSWwqbTTv5E0is5HVEVMDSW4qwsMCN6+/GKl6H2QNf624Mf06F3W733TMhmJ8HUh/hse+uZe9R/f/mKmMLQn+I04IZEa8FMyJeG0tAH34nmJ/sXb/jkd+nMOvuhXyQ/xI1DeVs+Pg3fZb1iP3Wjudwtpxlc8HaPsuCoDfitGBGxGvBjIjXxmL48CfBWnxn+k9wRMXx0b71PJj2BL967QEenfsSkUMdvmU9Yt99+2xe3LSMR+e+yPGKA75lQdAbcVowI+K1YEbEa2MxZadiiI5jJi+MpVdsPdsY7NwQcwt1TRW0tDcQMfgabWpQm8237IiKvXyQy8QePWoMt954F4Ps4dx20yTfspkQr4MHcVo/VLonXl8d4rU+qNxX6xXfKk6DeG0kpuxUTPpeaMY2G/dNesi3vHTOGt75ZBU/f/BVsnOfxx42yLecOWOZ37GBvndKm/CuafE68IjT+iNeBx7xWl9UeydeXxnitfEEZEpZwTxYferNbravDPxUboJ+iNca4rV5CIWpN/uLrTfitXkIBa+NcBqCw2tTXqkQhECyc+dOcnJymDlzpu9namoq27ZtY+LEiX0e3pifn09hYSFLliwBYMOGDTidTjIzM8nNzcXr9RIfH095eTlpaWkMGxbgOVUFyyJeC2ZEvBbMSKC8ltmfBEFnJkyYQHx8vO9namoqAJWVlTgcDtatW8eSJUvIyspi8uTJREb2TFLf3t5OWloaJSUlJCUlMWbMGLKzs0lMTKSkpCRQH0kQxGvBlIjXghkJlNfSqRAEncnKyiImJoZ58+YRExNDaWkpAHFxcTidTubPn8/q1atZvnw5R44coaioiNbWVoqKioiIiCAnJ4exY8eSnJxMcnIyiYmJvvcEIVCI14IZEa8FMxIor+WeCsEvrma8YemZA9xywx39/rs/Y88vFVvG6ApXi3itIV6bh6sdG3617l1p/Kv9/6IC8do8hILXVrqnQq5UCIax+2A2VfVlIRdbEC6FeC2YEVXuidNCIBGv1WLKG7UL3wRXsz6xhkT1nb5Nr9gXxrUCcSMT8Xq7Qi52sCBeByfitX+odE+8Hjiq3BOnrw5VXlvRaRCvVWPKToWrWb8pxoyMbXZ6z+scSrGDBfE6OBGv/UO8Dk5UuSdOB398MyNeq0WGPwmCIAiCIAiC4BcB7VS4XC6mTJlCZGSk7850gGXLlpGSksKCBQvweDwBbKEgCIIgCIIgCJcjoJ2K8PBwNm7cyJw5c3zvFRUVUVNTQ25uLgkJCWzatGnA8c86T7Hize/z7BvzOOs8pUeTDYntL14vNFVDXRl0njMm58nqQzyzLpP1258Jqdj+4vVCY4W27O4wJqdVve7qAmc51J8Cj9uYnFb12uPW6gxa3Y3Aql67O6DupLYfMWouRqt63XlO+140CtXeBbPXrlaoOwEttcbltKrX7U1QeyLQrdAwtFOxatUqpk+fzsMPP0x6ejphYWHExsb22SYvL4/09HQA0tPTycvLG3C+zYVrWTR7BQtnPcuWwpf9aruRsf3B64WDf4H9f4TP/wx7XoXWOvV5b44dx6LZz4VcbH/wdsG+P8L+d7X1Pa9Au043510KK3rtcUPheijKhs83Qv5r0NmuPq8Vve5s1+pb9J62XrjemE6cFb1ub9b2G59v1PYj+98xpmNhRa9barXvw8//rK0f/Iv6Wqv2Lli9dpZD/qvw+fuw92049okxea3odfVRyF8HX5z3+tTewLbHsE7F/v37KS4uZteuXaSmphIfH3/R7ZxOJ9HR0QBER0fjdDoHnLO+qZJRw68nJvpG6porBxzH6Nj+0Fhx/gpFO3g6wNUCBz8IdKvMydljWr3d5w9u25vgyHb1ea3o9el90FIDbpf2anPC8d2BbpU5Ob5Lq6/n/JW3lhooP6A+rxW9PrxN2294OrT9SEMF1JRe/veEq6f4Q+37sNvr2hPQpFgF1d4Fq9eHNkNHm1brznNQcRDONQa6VebD64UjOdDZBp5O7b0Te4wbNXExDOtUZGdns3jxYgDsdjvJyckX3W7EiBE0Nmr2NTY24nA4ANiwYQM//OEP+41vs9l8r7KyMgBGDh9NXVMFtU1nGBU1ekDtLisrUxL7wrh6vb6V/h1amtr65DpcfExJrt710IP+aq13XL1eixf9lK4LzuDu+rhQea2t6PXKZ1+gz2x9Xnj79ffEawWf/Y9vvA+9zuB6u+C5f/tt0Ht9sXoEu9ef7ux7WrGrE3700JKQczoUvD5c3Le31tLYyqx7vx3UTvdXDz3iq6qzzWbj5Im+Q7Fqa2r4+oS7Leu1qloPstupquzbmayuruT6625S9re9HIZNKVtfX4/b7cbtdrNmzRoef/zxi243bdo0XnjhBTIzM9myZQtTp06loKAAh8Phu4JxMXo/GLz7CYjpk37A2g+fwuvtYkH6wMbBJSQkKIl9YVy9cLVoQxc6zvcrwgbB5G9+Be8KNdd5u+tR21jBy5uf4kztMRLixnPP+IyrjtVfrf2NrarWLbXapd3u+1bs4fB38ybx8PNqa21Fr+tPacMWuq8KDRoCP/5FBlmviNd6U3lIO/vldmnrgyLg31cv5fcbl+qeC9S6F+xen9gDZQU9Z8/Dh8L6P6/mmlGrdc/V+8nAKtwLdq9LtkHlQeg6P/fL8JHXsGPPRoZE6p5K6b5ar/iq6gxwIFu7n6L7RNB1o6/lYGkBgwbrnysUvFZZ64J10FTVs35D/Giq609jC9Ad04Z1KubPn8+iRYsYN24cDQ0NvisVGRkZFBQUcOzYMZYuXcrcuXNxOBykpKSQlJTEk08+yX/+538yZMgQ9u3bx+nTp7npppuuKOd1jniWPfiKks+jMrY/DImEr2ZAyRbtXoq4cXDrDPV5Y6Kv54l/XB9ysf0hMgaSZ8PRj7SbWeNug5snqc9rRa9HxsNtM+DLT+FcAyROhbjb1ee1otejx2knJcr3AzZImgaOK9vl+oUVvU6YrA1VqD4C7Y3a/uSaUerzWtHr29K0g9z6U2AfBOPSUdKh6I1q74LV6wnf0oabNVVpB+R3zkFJh+JCrOj11x/Q7g9qrdd8nnA/AetQgIGdiilTpnDw4EEAZsyYQVxcHADvvffeX227cuXKPuu/+MUvACgvL7/iDoWVGXE9TF0A21fCuHsD3RpzE5MIMQsD3QprMDpZe21fCTdPDHRrzM3NE6XGRmCzwVdStdf2ldr+RFBDmB3G3RfoVlgDezh89e+15e0rjekoW5XwofD1OZffzigMf6K2x+MhPDx8QL97YWdjIGwpfIU9h94nLMzOvRMfYvLts/2OaURsQegPcVowI+K1YEbEa8HMGH6RxG63s3XrVqPT9uGB1Ed47Ltr2XtU/3aojC0I/SFOC2ZEvBbMiHgtmJWAPvwuUGTv+h2P/D6FWXcv5IP8l6hpKGfDx7/ps6xH7Ld2PIez5SybC9b2WRYEvRGnBTMiXgtmRLwWzIrhw5+Cge9M/wmOqDg+2reeB9Oe4FevPcCjc18icqjDt6xH7Ltvn82Lm5bx6NwXOV5xwLcsCHojTgtmRLwWzIh4LZgVS3YqAG6IuYW6pgpa2huIGHwNba5msNl8y46o2MsHuUzs0aPGcOuNdzHIHs5tN03yLZuJIVHqYukVW882BjPitH6I18GDeK0PKp3WM754LV5fDaHgtVWcBgt2Ku6b9JBveemcNbzzySp+/uCrZOc+jz1skG85c8Yyv2MD2vQe3VzBg0NCjUnfC83YZkKc1h/xOvCI1/qi2jvx+soQr/VFvA4ubF5VT+QIIL0fhuIvEcNh+o/0j31hXBVsXwnffKxnfefOneTk5DBz5kzfz9TUVLZt28bEiRN9Ty8HyM/Pp7CwkCVLlgDaE82dTieZmZnk5ubi9XqJj4+nvLyctLQ0hg0bpvbDCOL1eXp7LU6HPirdE6/F60Cgcl+tV3wjnAbx2mpY8kZtqzJhwgTi4+N9P1NTUwGorKzE4XCwbt06lixZQlZWFpMnTyYysufJQO3t7aSlpVFSUkJSUhJjxowhOzubxMRESkpKAvWRBIsjTgtmRLwWzIh4bX6kU2EhsrKyiImJYd68ecTExFBaWgpAXFwcTqeT+fPns3r1apYvX86RI0coKiqitbWVoqIiIiIiyMnJYezYsSQnJ5OcnExiYqLvPUEIBOK0YEbEa8GMiNfmR4Y/XQazDBMRQh/xWkO8Nhcy/ElDvDYPMvypB/HaWlj+SkXpmQMhGVsQLoV4LZgR8VowI6rcE6cFo7F8p2L3wWyq6stCLrYgXArxWjAj4rVgRlS5J04LRmO5KWUvJG5kIl5vV8jFDhYK3wRXsz6xhkT1nb5Nr9gXxrUC4rV/iNfBiXg9cFQ6rWd88Tr44wYToeC1lZy2fKei97zOoRQ7WHA16zd21MjYZke89g/xOjgRrweOau/E64Gjyj2zOw3idbBh+eFPgiAIgiAIgiD4R0A7FS6XiylTphAZGembWgxg2bJlpKSksGDBAjweTwBbKAiCIAiCIAjC5QhopyI8PJyNGzcyZ84c33tFRUXU1NSQm5tLQkICmzZtGnD8k9WHeGZdJuu3P6NHcw2PP1DcLijN1ZbryozJedZ5ihVvfp9n35jHWeepkIntLx2tcHQHHNoMjZXG5FTpXbA6DXCuEQ7naMutdcbktKrXLbVQslWrt1GX/q3qdUOFtv8A6GhTn0+1d8HsdW0ZFH+ofT+6O4zJaVWvq49otQbocqvPZ1WvvV448wUc/ABO7YVA30JjaKdi1apVTJ8+nYcffpj09HTCwsKIjY3ts01eXh7p6ekApKenk5eXN+B8N8eOY9Hs5/xqcyDjDwRPJxSsh7ICbf2LTVB5SH3ezYVrWTR7BQtnPcuWwpdDJrY/dJ7Tan1qL1QchAPvQr0B+xqV3gWj06Ad2Ba+AeX7tfW9b0NLjfq8VvS6pQb2boAzn2v1LlxvTMfCil7Xn4SibG3/AVCwDjrb1eZU7V2wel15CA5ugspi7fuxcD14DDjYtaLXJ/K1kxKVxdr6Z2+rP9i1qtdHcrQTm1WHtM5y0XuBbY9hnYr9+/dTXFzMrl27SE1NJT4+/qLbOZ1OoqOjAYiOjsbpdBrVRFPgPH1+poLzjzR0t8OJT9XnrW+qZNTw64mJvpG6Zn1P2auM7Q/VR6G916wQnefg+O7AtcfMnN6vXRXqpqNN++JSjRW9/nIPdPY6Y+5qhfKiwLXHzBzfre03umlvhrPH1OZU7V2wen3iU+37EACv1lFuOB3QJpmW8gPaiIluzjVAi+Kry1b02uuFs0fBc/6qW5cbGquMueLZH4Z1KrKzs1m8eDEAdrud5OTki243YsQIGhsbAWhsbMThcPDb3/6Wf//3f+edd97pN77NZvO9ysrKdGt3WVmZktgXxtXr9Xd/N5vm5r7znx0+UqIkV+96jBw+mrqmCmqbzjAqarQuNdErtqpa//jHP8Jzwamu3bt2Ka+1HoSa1//xH399Nu6tN98UrxV89j9u2PBXuZ599tdB7/XF6hHsXl94Jd7jdrNo0cKQczoUvD5y5EifPM3NTaTPSg9qp/urhx7xVdXZZrNx6tTJPrlqamq442tfs6zXqmptt4dRVVXVJ1d1VRWx112n7G97OQybUra+vh63243b7WbNmjU8/vjjF91u2rRpvPDCC2RmZrJlyxamTp1KU1MTLpcLl8t10d8B8Hq9vuXuR9jXNlbw8uanOFN7jIS48dwzPuOq252QkHDR2OBf/Avj6oWnE/JfhzYn4IVBETDr/96O9z/0zwU99Uif9APWfvgUXm8XC9IHNr6zv1r7G1tVrTvOQcHrPT6ED4X/s2w6S/9bba1Veu1vbFW1PteoDX/qvloRPgye+O33+Pf1aib/trLXzWdh3zs9VysGXwP//daT/GH4k7rnArXuBbvXtWVQvKlnyNM1jkH8+eM/ED70D7rnUum0nvFV1briIBz9uOdqRcz1w9nzxWbs4bqn0u04AdR5rarOoF0VOvmZdrXCZof4W66ltLwIm4LT2KHgtcpal2yFqsM9Vyu+8rU4nC1nleS6EmxeVZ/0Avbs2cOiRYsYN24cJ06c4P333ycuLo6MjAwKCgpITExk6dKlzJ07l8cee4z8/HySkpL4wx/+wKBBWt/nZz/7Gf/xH/+B3W6/ZK7e/6H9JWI4TP+R/rEvjKsnbhec2AOuFogbBzGJavKA1NrVCmX5cHofTPxHGHG9mjwgtW5rgJOF4PVA/F0Qea2aPCC1bqmBk3uh8iDc80MYGq0mD6itRyjUuuGMdv/KoCGQOFnrxKlApdN6xldZ69ovoapEe/3Nv2g1V0Eo1FplnUE70K0phWEOSJgMdkWnsK1ea68XKj6H+tNQfRjSHoWwAE7BZNiViilTpnDwoHY32owZM4iLiwPgvffe+6ttV65c2Wf9/fff5/PPP2fw4MGX7VAI2o7yK98IdCuswZBr4LY0rVOhskMhwLARcPvfBroV1iDyWkhO1zoVKjsUAoy4QXsJ6olJ0l5VJeo6FIJG3FjtJajFZoMbvqa9qg8HtkMBAXiitsfjITz86q433n///dx///2KWiSoYkvhK+w59D5hYXbunfgQk2+fHRKxBaE/xGnBjIjXghkRr43H8D6N3W5n69atRqcVAsQDqY/w2HfXsveo/n9zlbEFoT/EacGMiNeCGRGvjSXAF0oEs5O963c88vsUZt29kA/yX6KmoZwNH/+mz7Iesd/a8RzOlrNsLljbZ1kQ9EacFsyIeC2YEfHaWAwf/mQEQ6LUxdIrtp5tDGa+M/0nOKLi+Gjfeh5Me4JfvfYAj859icihDt+yHrHvvn02L25axqNzX+R4xQHfspkQr4MDcVpfVLonXl854rV+qNxX6xXfCk6DeG00puxUTFIzy6Ty2GblhphbqGuqoKW9gYjB19DmagabzbfsiIq9fJDLxB49agy33ngXg+zh3HbTJN+ymRCvgwdxWj/E6+BBvNYH1d6J11eHeG0cpuxUCMHBfZMe8i0vnbOGdz5Zxc8ffJXs3Oexhw3yLWfOWOZ3bECbBqGbK3hIiyBcLeK0YEbEa8GMiNfGY9hzKgRzYvX5/LvZvhK++Zi2vHPnTnJycpg5c6bvZ2pqKtu2bWPixIk4HA7f7+Xn51NYWMiSJUsA2LBhA06nk8zMTHJzc/F6vcTHx1NeXk5aWhrDhg1T+0EEQLzuRrw2D6Ewn39/sfVGvDYPoeC1EU5DcHgtN2oLgs5MmDCB+Ph438/U1FQAKisrcTgcrFu3jiVLlpCVlcXkyZOJjIz0/W57eztpaWmUlJSQlJTEmDFjyM7OJjExkZKSkkB9JEEQrwVTIl4LZiRQXkunQhB0Jisri5iYGObNm0dMTAylpaUAxMXF4XQ6mT9/PqtXr2b58uUcOXKEoqIiWltbKSoqIiIigpycHMaOHUtycjLJyckkJib63hOEQCFeC2ZEvBbMSKC8luFPgl9czaXB0jMHuOWGO/r9d3+GiVwqttGX04XQR7zWEK/Nw9UO47ha9640/tX+f1GBeG0eQsHrQAx/ChRypUIwjN0Hs6mqLwu52IJwKcRrwYyock+cFgKJeK0WU87+VPgmuJr1iTUkqu/0bXrFvjCuFYgbmYjX2xVysYMF8To4Ea/9Q6V74vXAUeWeOH11qPLaik6DeK0aU3YqXM36zQZgZGyz03sKtlCKHSyI18GJeO0f4nVwoso9cTr445sZ8VotMvxJEARBEARBEAS/CGinwuVyMWXKFCIjI313pgMsW7aMlJQUFixYgMfjCWALBUEQBEEQBEG4HAHtVISHh7Nx40bmzJnje6+oqIiamhpyc3NJSEhg06ZNAWyhIAiCIAiCIAiXw9BOxapVq5g+fToPP/ww6enphIWFERsb22ebvLw80tPTAUhPTycvL2/A+c46T7Hize/z7BvzOOs85VfbjYztL41V8OkrsOtFOLwdugy4d+hk9SGeWZfJ+u3PhFRsf6ktg7y12vLxXWDEBM1W9bryEOz+A+x+CU7vMyanVb0+tQ92v6gtVx02JqcVvfZ6oXSXVuu8tVBXZkxeK3rd1QWHt2nfiwBN1epzqvYuWL32dMIXm7Ra578OrfXG5LWi153tsP/dHq9dLYFtj2Gdiv3791NcXMyuXbtITU0lPj7+ots5nU6io6MBiI6Oxul0Djjn5sK1LJq9goWznmVL4csDjmN0bH9wtUBRNrTWQnsjVByEozvU5705dhyLZj8XcrH9obUOiv8Cbed3mKf2wanP1Oe1otfO03DkIzjnhHMNcHy3MQe7VvS68hB8uRvONWrrR7aDs1x9Xit6fbIQTu/Vat1WDwf/YswBmBW9PvoRVBRr34sAB94FV6vanKq9C1avD/4Fzh7Vat1cDfv+CJ4O9Xmt6PWBd6HuRI/Xe9+GQE5CZdjsT9nZ2SxevBgAu91OcnLyRbcbMWIEjY1adRobG3E4HBw/fpx169YRFRXFo48+esU565sqGTX8erxeL3XNlf5/CINi+0NjJbjbe9a73Jpwgv7UnYDOcz3rng6oOgI3T1Kb14peVx/p67XbBdWHIU4eWqs71Ye1+nbT2a4dIDhuVJvXkl4f1s7qdtN5DurL4JqRAWuSaak7oX0fduN2QVMlXHuLupyqvQtWr5uq+x7YejqhpQ6iRweuTWbE26WdZKPXCAm3S+ssR0QFpk2GXamor6/H7XbjdrtZs2YN48ePv+h206ZNY+vWrQBs2bKFqVOn8oc//IGRI0cyaNAg+nsAuM1m873KysoAGDl8NHVNFdQ2nWFU1MBsLisrUxL7wrh6vdLuvYeG5ro+uQ58UagkV+966EF/tdY7rl6v+T+Yw7mOvqe6tuRsVF5rK3r99DM/p6PXka7H4+bFV14QrxV89rWv/3efCTI6Ott5avmjQe/1xeoR7F5v+7jvPYPnXC384//9h5BzOhS8Liruexm5obGOb3xzalA73V899Iivqs42m40vTxzrk6u29ixjkxMt67WqWofZbVRWVfTJVV1djSMmUtnf9nIYdqVi/vz5LFq0iHHjxtHQ0OC7UpGRkUFBQQHHjh1j6dKlzJ07F4fDQUpKCklJSTz55JPs2LGDb33rW+zYsYN9+/Zx1113/VX83p2N7seqp0/6AWs/fAqvt4sF6QMbB5eQkKAk9oVx9cLrhS/eh/pT2pndwdfA//3/JvHw82oG+3fXo7axgpc3P8WZ2mMkxI3nnvEZVx2rv1r7G1tZrbu0y7rNZ7W6h0fAsue/zdMvq621Fb32dMJnb2pnZdwdEBUziP96619YHfEvuucCa3vdeQ4K39DOdtmAqOsieDtnFfZBq3TPBWrdC3av25s0rztd2pXO678Syc6id7EpON3XXQtQ416we91SA/ve0epss8NXbhtF8dOfcgXHSVeNyn21XvFV1Rm044+Dm7T9tqcTvvqN66j8pZohE6HgtcpaVx2GIznaVbiwQTDpG7GcWx64GytsXlWf9BLMmDGDHTuufKD/3r17effdd2lpaeGZZ54hKurS13V6S+YvEcNh+o/0j31hXD3xeqGpCgrXQ+o/w+BhavKA1NrrhcYz2o4z+noYNERNHpBad3mg4Qzs2wAzfgr2cDV5QGrt6dRqbQuDETdAmF1NHlBbj1CotdsFjRWw/08w82coOcgFtU7rGV9lrTvatO/G8KEwPM7atVZZZ9Du72yuhgPZ8M3H1OWRWmv3ZLXWwlBH4IdOGv5EbY/HQ3j41R0N3HXXXRe9OiFcHJutZ+yiyg6FoNV6hOKx5oJGmB1Gnp/fQWWHQtDqOyoh0K2wBoOGwKhEbVnVQa6gMXgYxCQFuhXWYEik9hLUMzRaewUDhncq7Ha7756JQLCl8BX2HHqfsDA79058iMm3zw6J2ILQH+K0YEbEa8GMiNeCmQnow+8CxQOpj/DYd9ey96j+nRuVsQWhP8RpwYyI14IZEa8Fs2LJTkX2rt/xyO9TmHX3Qj7If4mahnI2fPybPst6xH5rx3M4W86yuWBtn2VB0BtxWjAj4rVgRsRrwawYPvwpGPjO9J/giIrjo33reTDtCX712gM8OvclIoc6fMt6xL779tm8uGkZj859keMVB3zLZmKIjnMhXxhLr9h6tjFYEaf1RbwODsRr/VDptJ7xxWvx+moIBa+t4HQ3luxUANwQcwt1TRW0tDcQMfga2lzNYLP5lh1RsX7HHj1qDLfeeBeD7OHcdtMk37KZmPS90IxtRsRp/RCvgwfxWh9UeydeXx3itT6I18GF5ToV9016yLe8dM4a3vlkFT9/8FWyc5/HHjbIt5w5Y5nfsYG+03nI1B6CAsRpwYyI14IZEa8FMxOQ51SoxupzzHezfWXf+aF37txJTk4OM2fO9P1MTU1l27ZtTJw4EYfD4ds2Pz+fwsJClixZAsCGDRtwOp1kZmaSm5uL1+slPj6e8vJy0tLSGDZM5q5VjXit0dtrcTr0sfpzKroRr82DPDuhB/HaWljyRm2rMmHCBOLj430/U1NTAaisrMThcLBu3TqWLFlCVlYWkydPJjKyZ5Lp9vZ20tLSKCkpISkpiTFjxpCdnU1iYiIlJSWB+kiCxRGnBTMiXgtmRLw2P9KpsBBZWVnExMQwb948YmJiKC0tBSAuLg6n08n8+fNZvXo1y5cv58iRIxQVFdHa2kpRURERERHk5OQwduxYkpOTSU5OJjEx0feeIAQCcVowI+K1YEbEa/Nj+eFPpWcOcMsNd/T77/4ME7lU7EAMfxJCG/FaQ7w2FyrdE6+FQHC1w5NUeR1op0G8thqWv1Kx+2A2VfVlIRdbEC6FeC2YEfFaMCOq3BOnBaOx3OxPFxI3MhGvtyvkYgcLhW+Cq1mfWEOi+k7fplfsC+NaAfHaP8Tr4ES8HjgqndYzvngd/HGDiVDw2kpOW75T0XsKtlCKHSy4mvWb5cLI2GZHvPYP8To4Ea8HjmrvxOuBo8o9szsN4nWwYfnhT4IgCIIgCIIg+EdAOxUul4spU6YQGRnpmwUAYNmyZaSkpLBgwQI8Hk8AWygIgiAIgiAIwuUIaKciPDycjRs3MmfOHN97RUVF1NTUkJubS0JCAps2bRpw/JPVh3hmXSbrtz+jR3MNj+8Png7tp1Fze511nmLFm9/n2TfmcdZ5KmRi64G7Azpajau1Su+C2WmAznZj81nVa68XOtqMrbdVvfZ6wdVqXD7V3gW7167Wnu9HI7Cs113gajEun5W97uqC9mboCoJz8IZ2KlatWsX06dN5+OGHSU9PJywsjNjY2D7b5OXlkZ6eDkB6ejp5eXkDzndz7DgWzX7OrzYHMv5AKSuAXS9qy3te0Q54VbO5cC2LZq9g4axn2VL4csjE9pcjH8HuF2HPq1C4XutgqEald8HqtNcLX7wPeWu19X1/NGYHakWvuzyw/4/w6SuQ9wf4YpMxHWYreu3ugMJ1kP+qtn50h/qcqr0LVq9drfDpy1qtd70IZYXG5LWi120N2r4j/zVtvbJYfU6ret1UBbv/HxS8rk01XHsisO0xrFOxf/9+iouL2bVrF6mpqcTHx190O6fTSXR0NADR0dE4nU6jmmgKWmrgZCF0ntPWW+vg4Afq89Y3VTJq+PXERN9IXXNlyMT2h/qT2s6y85x2Vrf5rNbJEPSn4iDUfAmdbdp6wxkoy1ef14pen/gUnGe0Wneeg9rjxhwUWJEjOdBUo+0/QPO8XvFJUNXeBavXxX+BtvrzV+DOwckCaKkNdKvMyecb4Vxjj9fHPlF/Nc6qXn/+Z+2KUEebdgL50GbocgeuPYZ1KrKzs1m8eDEAdrud5OTki243YsQIGhsbAWhsbMThcPDJJ5/w29/+lnvuuYeWlotfT7PZbL5XWVmZbu0uKytTEvvCuHq9Zs18gJbGc31yfbG3VEmu3vUYOXw0dU0V1DadYVTUaF1qoldsVbX+0fcfxe3qyePtgk82f6a81noQal4/l/V7ujp78nS5Yd2LfxavFXz2t17+C95eV4E8nfDv//q7oPf6YvUIdq9zt+6HXjN+ul3wg3/8l5BzOhS8PrivtE+e5sY27vubjKB2ur966BFfVZ1tNhtfHuvbM66pqeWO2ydb1mtVtbaH2ako79vBqaqsJO7aeGV/28th2JSy9fX1uN1u3G43a9as4fHHH7/odtOmTeOFF14gMzOTLVu2MHXqVL7xjW8wceJETp8+TWRk5EV/r/eDwbufNlnbWMHLm5/iTO0xEuLGc8/4jKtud0JCwkVjg3/xL4yrF6318NmbPVcqsMEdU25Rkgt66pE+6Qes/fApvN4uFqQPbHxnf7X2N7aqWjecgQPZ4D4/7txmh7T7J+L9rdpaq/Ta39iqal1VAiXbesZC28Ph//7z3/P0y+K13pTlw5ef9pztsg+Gp5/7Cf/93k90zwVq3Qt2rw9vgzMH8XXiBkXAKxteYMT1L+ieS6XTesZXVesD2VD7JXA+dFT0MLblvscwh+6pdDtOAHVeq6ozQMF6aOp1rHvttTEUHcln8FD9c4WC1yprnfcHaOs1oGf09aOpqj1FmF1JustiWKdi/vz5LFq0iHHjxtHQ0OC7UpGRkUFBQQHHjh1j6dKlzJ07F4fDQUpKCklJSTz55JMAvPXWWzz44INXlTMm+nqe+Mf1un8Wo+IPhGtGwi3fgOM7tfWhIyB5lvq81zniWfbgKyEX2x9G3AAJk+DkXm2oiOMmuPUb6vOq9C4YnQaIHQuNlVB1GGyAIx7iJ6rPa0Wvb54EzTXgPKVdUr9hAlx3q/q8VvT6KzO08ectNdqx7s0TYcT1anOq9i5YvU6eBfv/BO3nh+Xc+g2UdCguxIpef+3bsP+d88OfbDDuPpR0KHpjVa/v+AfY/y54XFq9v/ptAtahAAM7FVOmTOHgwYMAzJgxg7i4OADee++9v9p25cqVf/VeYWEhCxcuVNpGs3DDeLg+WRuOE0i5rEDCZLj5bsj5T7hzzuW3FwaGzQa3pcGtf6MdfIXJE3aUYQuDCd/SZhT5aBXcOiPQLTIv9kFw51zt5nhbmOa5oIbwCLh7nlbrj/4LRo8PdIvMy5BImPKQeG0Ewxxwz8Ier6MHNvJLNwx/orbH4yE8PPyqf+9///d/FbTGvNhs2nCcQLKl8BX2HHqfsDA79058iMm3zw6J2FeL7DCNwxamXakIFFZxGqTjZiSBPvljKa/lRJthBLrW4rXxGP61Ybfb2bp1q9FphQDxQOojPPbdtew9qv/fXGVsQegPcVowI+K1YEbEa2ORc1GCUrJ3/Y5Hfp/CrLsX8kH+S9Q0lLPh49/0WdYj9ls7nsPZcpbNBWv7LAuC3ojTghkRrwUzIl4bi+HDnwRr8Z3pP8ERFcdH+9bzYNoT/Oq1B3h07ktEDnX4lvWIfffts3lx0zIenfsixysO+JYFQW/EacGMiNeCGRGvjcWUnYohUepi6RVbzzYGOzfE3EJdUwUt7Q1EDL6GNlcz2Gy+ZUdU7OWDXCb26FFjuPXGuxhkD+e2myb5ls2EeB08iNP6odI98frqEK/1QeW+Wq/4VnEaxGsjMWWnYtL3QjO22bhv0kO+5aVz1vDOJ6v4+YOvkp37PPawQb7lzBnL/I4N9L1j2oR3T4vXgUec1h/xOvCI1/qi2jvx+soQr43H5lX1RA7BEvR+yI+/RAyH6T/SP/aFcVWwfSV88zFteefOneTk5DBz5kzfz9TUVLZt28bEiRNxOHomR8/Pz6ewsJAlS5YAsGHDBpxOJ5mZmeTm5uL1eomPj6e8vJy0tDSGDRum9oMIgHjdjXhtHlQ6rWd88Vq4GkLBayOchuDwWm7UFgSdmTBhAvHx8b6fqampAFRWVuJwOFi3bh1LliwhKyuLyZMn93lKfHt7O2lpaZSUlJCUlMSYMWPIzs4mMTGRkpKSQH0kQRCvBVMiXgtmJFBeS6dCEHQmKyuLmJgY5s2bR0xMDKWlpQDExcXhdDqZP38+q1evZvny5Rw5coSioiJaW1spKioiIiKCnJwcxo4dS3JyMsnJySQmJvreE4RAIV4LZkS8FsxIoLyW4U+CX8gwEY3elx2F0Ee81hCvzUMoDBPpL7beiNfmIRS8DsTwp0AhVyoEwyg9cyAkYwvCpRCvBTOiyj1xWggk4rVapFMhGMbug9lU1ZeFXGxBuBTitWBGVLknTguBRLxWiymnlC18E1zN+sQaEtV3+ja9Yl8Y1wrEjUzE6+0KudjBgngdnIjX/qHSPfF64KhyT5y+OlR5bUWnQbxWjSk7Fa5m/cbYGRnb7PSe1zmUYgcL4nVwIl77h3gdnKhyT5wO/vhmRrxWiwx/EgRBEARBEATBLwLaqXC5XEyZMoXIyEjfdFcAy5YtIyUlhQULFuDxeALYQkEQBEEQBEEQLkdAOxXh4eFs3LiROXPm+N4rKiqipqaG3NxcEhIS2LRp04Djn3WeYsWb3+fZN+Zx1nlKjyYbEttfvF6oPQ4VB+FcozE5T1Yf4pl1mazf/kxIxfaXLg+cPaYtu1qNyWlVrz0dUH0YKg9BZ7sxOa3qdec5rc6g1d0IrOq1qwUqirX9SJdB59Cs6vW5Ru17EbTvSdWo9i6YvW6tgzNfQP1JY2oN1vW6qVqrdTBgaKdi1apVTJ8+nYcffpj09HTCwsKIjY3ts01eXh7p6ekApKenk5eXN+B8mwvXsmj2ChbOepYthS/71XYjY/uD1wv7/ghf/AUObYHC9dBQoT7vzbHjWDT7uZCL7Q9dbq2+B/+iree/Dq316vNa0Wu3S6vvwQ/h0GbIf82YTpwVvXa1aLU+tFlbz1+n1V81VvS6ta6n1gf/AoVvGNOxsKLXDWegYL32vQiw/x31B7uqvQtWr88eg8/egpIt8PmfofgDY/Ja0evTB2D/H7VaAxzbGdDmGNep2L9/P8XFxezatYvU1FTi4+Mvup3T6SQ6OhqA6OhonE7ngHPWN1Uyavj1xETfSF1z5YDjGB3bH5ynobn6/NlFL3S0weFtgW6VOak+Ci11WucCoKMFjuSoz2tFr0/thbYG8HrA26XdpHh8V6BbZU5Kd2n17Z7IpM0Jp/erz2tFr4/kQEcr4NX2I6212n5F0J+SbdDZBpzvSDRVQUO52pyqvQtWr4/u0K52gnZCoq7MmBNuVsPrhRN5fa/cV3xhzEmg/jCsU5Gdnc3ixYsBsNvtJCcnX3S7ESNG0NiojdlpbGzE4XDw5z//meXLl7No0SLfv12IzWbzvcrKygAYOXw0dU0V1DadYVTU6AG1u6ysTEnsC+Pq9frW7G/T0tT3FO7hQ0eV5OpdDz3or9Z6x9XrtfiHS/B09p1CbnduvvJaW9Hrlc897zsY6GbDG++K1wo++ztvv9c3kRee+/f/DHqvL1aPYPf6092FffK4O7v48cLFIed0KHh99HBpnzzNTS3Mvu/+oHa6v3roEV9VnW02G6dO9h2KVVNTw51fm2hZr1XVepDdTmVV385kVXUlcdfdoOxvezkMm1K2vr4et9uN2+1mzZo1PP744xfdbtq0abzwwgtkZmayZcsWpk6dSkREBDU1NQBERUVd9Pe8va5jdj9WPX3SD1j74VN4vV0sSB/YOLiEhAQlsS+MqxcdbeeHhrRo6/ZwSLn/VrzPqbnO212P2sYKXt78FGdqj5EQN557xmdcdaz+au1vbFW1PtegDVfoaNPWBw2B7yyazL/8Tm2treh1YxUc+FPP2a9BEbAk6x/45avitd7UfKkNV3CfP/sVPhT+48Wf8b9xP9M9F6h1L9i9Li+C0k/Aff6+lYjIMN7+8H8YGv0/uufqrgWocS/YvS7NhdP7wNOprY8YFckne99n8FDdUyndV+sVX1WdAQ5+AGeP9lzFH33DtRw68Rl2BUecoeC1ylrv+6M2QsXbBdjg5jGjqWk4wxUc/yvB5lX1SS9gz549LFq0iHHjxnHixAnef/994uLiyMjIoKCggMTERJYuXcrcuXN57LHHyM/PJykpiT/84Q+sXr2af/qnf2L9+vVMnjyZ8ePHXzJXb8n8JWI4TP+R/rEvjKsnrfVQslW7tJt0DyROQZlgVq91UzUc3q59Ud14B9x0h5o8ILWuK9MODJqrYcL9EHubmjwgta46DGX5YAuDr6TCyJvV5AG19QiFWp/er3UuWmvh7u/D8NjL/85AUOm0nvFV1drrhROfQvURCB8G4+6FYQ7980Bo1Fql010eKN15fthTHaT8EwyJVJPL6rX2dMLhHGiqgGti4PZ7ITxCTa4rwbArFVOmTOHgQW3ahRkzZhAXFwfAe++991fbrly5ss96bGwsK1asoLa2lu9+97vK2xrqXDMSJj4I21dC0tRAt8bcDI+Fu+cFuhXWYFSC9tq+Um2HQoC4sdpLUM9NX9de21eq61AI2om1pGnaS1BLmB1unaEtb1+prkMhaKNRktMD3YoeDH+itsfjITw8/Kp+53vf0+9Z8lsKX2HPofcJC7Nz78SHmHz77JCILQj9IU4LZkS8FsyIeC2YGcOfU2G329m6davRafvwQOojPPbdtew9qn87VMYWhP4QpwUzIl4LZkS8FsxKQB9+Fyiyd/2OR36fwqy7F/JB/kvUNJSz4ePf9FnWI/ZbO57D2XKWzQVr+ywLgt6I04IZEa8FMyJeC2bF8OFPwcB3pv8ER1QcH+1bz4NpT/Cr1x7g0bkvETnU4VvWI/bdt8/mxU3LeHTuixyvOOBbFgS9EacFMyJeC2ZEvBbMiiU7FQA3xNxCXVMFLe0NRAy+hjZXM9hsvmVH1MDvmOuOPXrUGG698S4G2cO57aZJvmUzMeTiM/zqEkuv2Hq2MZgRp/VDvA4exGt9UOm0nvHFa/H6aggFr63iNFiwU3HfpId8y0vnrOGdT1bx8wdfJTv3eexhg3zLmTOW+R0b6DuXa6AmDlbIJP3uoTc0tpkQp/VHvA484rW+qPZOvL4yxGt9Ea+DC8OeU2EkVp9jvpvtK+Gbj/Ws79y5k5ycHGbOnOn7mZqayrZt25g4cSIOR8+k3fn5+RQWFrJkyRIANmzYgNPpJDMzk9zcXLxeL/Hx8ZSXl5OWlsawYcPUfhhBvD5Pb6/F6dDH6s+p6Ea8Ng9Wf3ZCb8Rra2HJG7WtyoQJE4iPj/f9TE1NBaCyshKHw8G6detYsmQJWVlZTJ48mcjInsml29vbSUtLo6SkhKSkJMaMGUN2djaJiYmUlJQE6iMJFkecFsyIeC2YEfHa/EinwkJkZWURExPDvHnziImJobS0FIC4uDicTifz589n9erVLF++nCNHjlBUVERraytFRUVERESQk5PD2LFjSU5OJjk5mcTERN97ghAIxGnBjIjXghkRr82P5Yc/lZ45wC033NHvv/szTORSsQMx/EkIbcRrDfHaXKh0T7wWAsHVDk9S5XWgnQbx2mpY/krF7oPZVNWXhVxsQbgU4rVgRsRrwYyock+cFozG8p2KuJGJeL1dIRdbEC6FeC2YEfFaMCOq3BOnBaOx3JSyF9J7CrZQih0sFL4JrmZ9Yg2J6jt9m16xL4xrBcRr/xCvgxPxeuCodFrP+OJ18McNJkLBays5bflOheAfrmb9ps4zMrYgXArxWjAbqr0Tr4VAIF4HFwEd/uRyuZgyZQqRkZG+WQAAli1bRkpKCgsWLMDj8QSwhYIgCIIgCIIgXI6AdirCw8PZuHEjc+bM8b1XVFRETU0Nubm5JCQksGnTpgC2UBAEQRAEQRCEy2Fop2LVqlVMnz6dhx9+mPT0dMLCwoiNje2zTV5eHunp6QCkp6eTl5c34Hwnqw/xzLpM1m9/xq92Byr+QHG1wMG/aMsVB43JedZ5ihVvfp9n35jHWeepkIntL20NULQR9v0Rakovu7kuqPQuWJ0GaD4LB7K1ZWe5MTmt6nX9adj/jlbv5hpjclrV67PHtP0HaPsT5fkUexfMXld8AXs3aN+PrlZjclrRa68XTn4Ge9/W1jvb1ee0qtddXXB8N3z2Nhz5CDydgW2PYZ2K/fv3U1xczK5du0hNTSU+Pv6i2zmdTqKjowGIjo7G6XQOOOfNseNYNPu5Af9+oOMPBLcLCt+AqvMPmDy6A07tVZ93c+FaFs1ewcJZz7Kl8OWQie0PrhbY+ybUHIP6k1C8Gc4eVZ9XpXfB6DRAax3sewdqj2vrn78HDWfU57Wi185y+GIj1JVp9d7/R2itV5/Xil5XHYFDW7T9B8Det9Qf7Kr2Lli9PvmZ9n3oPKV9Pxa+Ae4O9Xmt6PWxj+HLPHCe1tY/exO6FI9kt6rXBzfByUJoOA3lB7QTFIF8+pxhN2pnZ2ezePFiAOx2O8nJyRfdbsSIETQ2NgLQ2NiIw+HgL3/5C/v378fpdLJy5UpsNptRzQ45nOXQ0daz7nbB6QMQf5favPVNlYwafj1er5e65sqQie0PZ4/1PQBwt0NZIVx3a+DaZFbOfA6dvbzubNc6yyNuUJvXil6f+qzvmcWONq3+t/5NwJpkWk4VavuNblwt2kmKG+9Ql1O1d8HqdfmBvp2IzjbtQCxmTMCaZFqqj4KnV6072qClFobH9v87/mJFr71d0FAOXe6e9XMN0NEKQyID0ybDrlTU19fjdrtxu92sWbOG8ePHX3S7adOmsXXrVgC2bNnC1KlT2b59O8uWLWPYsGEUFRVd9PdsNpvvVVZWplu7y8rKlMS+MK5er1mz76W5ubFPrpKSYiW5etdj5PDR1DVVUNt0hlFRo3WpiV6xVdV60Y8W4Pb0PdW1M/cj5bXWg1Dz+tfP/RueC051rXvjFfFawWd/8+11ffJ0dXXxb7/OCnqvL1aPYPd61+5P+uTpcLtYsPD7Ied0KHh9+MihPnkamxq4N31mUDvdXz30iK+qzjabjVOnTvbJVVNzlglfHWdZr1XVOsxuo6q6qk+u6upqrr1upLK/7eUw7ErF/PnzWbRoEePGjaOhocF3pSIjI4OCggKOHTvG0qVLmTt3Lg6Hg5SUFJKSknjyyScZN24cL7zwAidOnCA8PPyi8b29rvd0P8K+trGClzc/xZnaYyTEjeee8RlX3e6EhISLxgb/4l8YVy+6PNpl3ZYardcaPhQyHk5m0Uo118O665E+6Qes/fApvN4uFqQPbHxnf7X2N7aqWrs7oOD18+OgvRA+DH60PI3H/ldtrVV67W9sVbXuaIWC9T3/9wZfA7/834f4j7ce0j0XWNvrtgZtuELH+atww0aE8Yf3lvP6sOW65wK17gW7142V2n0rnW1gs8GI64aw+dPXsQ9+XfdcKp3WM76qWtcch0ObofOctn594gg+O5JDmIJTq3odJ4A6r1XVGaD8cyjdqV2FCxsEScnXUVZ1iCs4Jr1qQsFrlbU+vhtO79NGpQCMmxJLU5sB41X7weZV9UkvwYwZM9ixY8cVb3/o0CE++OADPB4Pv/jFLy67fe//0P4SMRym/0j/2BfG1ZMut3aDtqsVrvsKRF2nJg9Ird0d2s1/R3fA1B/ANSPV5AGpdUeb5rW3C0YnQ0SUmjwgtW5vgopi+HI3pP4zDB6mJg+orUco1Lq1HqoPw6AhcP0EGDRYTR6VTusZX2Wtm6q1CTVOfAppS7UDXhWEQq1V1hm0odh1J2CYA0aPA5uicTFSa6g9oQ2DKsuHmT9DSeftSjH84Xcej6ffqw39MW7cOMaNG6eoReYjbJDaMblCD4MGa/erHN2htkMhaAe2CXcHuhXWIGI4JE3VOhUqOxSCtt9ImhboVliD4bHa68Sn6joUgobjRu0lqCcmUXuV5Qe2QwEB6FTY7XbfPROCudlS+Ap7Dr1PWJideyc+xOTbZ4dEbEHoD3FaMCPitWBGxGvjCejD7wTz80DqIzz23bXsPap/R1JlbEHoD3FaMCPitWBGxGtjkU6FoJTsXb/jkd+nMOvuhXyQ/xI1DeVs+Pg3fZb1iP3Wjudwtpxlc8HaPsuCoDfitGBGxGvBjIjXxmLKUYVDdLyB88JYesXWs43BzHem/wRHVBwf7VvPg2lP8KvXHuDRuS8ROdThW9Yj9t23z+bFTct4dO6LHK844Fs2E+J1cCBO64tK98TrK0e81g+V+2q94lvBaRCvjcaUnYpJ3wvN2GblhphbqGuqoKW9gYjB19DmagabzbfsiBr4E3G6Y48eNYZbb7yLQfZwbrtpkm/ZTIjXwYM4rR/idfAgXuuDau/E66tDvDYOU3YqhODgvkkP+ZaXzlnDO5+s4ucPvkp27vPYwwb5ljNnLPM7NtB32oNAT4EgmBJxWjAj4rVgRsRr4wnIcyoE82D1+fy72b4SvvmYtrxz505ycnKYOXOm72dqairbtm1j4sSJOBwO3+/l5+dTWFjIkiVLANiwYQNOp5PMzExyc3Pxer3Ex8dTXl5OWloaw4bJ/J5GIF5riNfmIRTm8+8vtt6I1+YhFLw2wmkIDq/lRm1B0JkJEyYQHx/v+5mamgpAZWUlDoeDdevWsWTJErKyspg8eTKRkZG+321vbyctLY2SkhKSkpIYM2YM2dnZJCYmUlJSEqiPJAjitWBKxGvBjATKa+lUCILOZGVlERMTw7x584iJiaG0tBSAuLg4nE4n8+fPZ/Xq1SxfvpwjR45QVFREa2srRUVFREREkJOTw9ixY0lOTiY5OZnExETfe4IQKMRrwYyI14IZCZTXMvxJ8IuruTRYeuYAt9xwR7//7s8wkUvFNvpyuhD6iNca4rV5uNphHFfr3pXGv9r/LyoQr81DKHgdiOFPgUKuVAiGsftgNlX1ZSEXWxAuhXgtmBFV7onTQiARr9ViytmfCt8EV7M+sYZE9Z2+Ta/YF8a1AnEjE/F6u0IudrAgXgcn4rV/qHRPvB44qtwTp68OVV5b0WkQr1Vjyk6Fq1m/2QCMjG12ek/BFkqxgwXxOjgRr/1DvA5OVLknTgd/fDMjXqtFhj8JgiAIgiAIguAXhnYqXC4XU6ZMITIy0ncnOsCyZctISUlhwYIFeDweI5skCIIgCIIgCIKfGNqpCA8PZ+PGjcyZM8f3XlFRETU1NeTm5pKQkMCmTZuMbJIgCIIgCIIgCH6i9J6KVatW8e677/K1r32N48ePs3nzZmJjY/tsk5eXR3p6OgDp6em8++67fPvb39Yl/1nnKdZufgqvt4uFs57lOke8LnFVx/aX2i/h8HbwdkFULEz4FtjD1eY8WX2I17ctJzFuAvO++a8hE9tfKouhdJe2XPwhjLsPbIq76lb1+mQhnNqrLcfdDrekgs2mOKcFvfZ64dgnUH1YWz/5Gdw8UX1eK3rd1QUlW6D+JGCDW1Jg9Dj1ea3otacTvtgEzdXaeu2XEJOkNqdq74LV6852+HwjtDm1Y4/k2RA9Wn1eK3rtaoGi97SfAK31cM3IwLVH2eHP/v37KS4uZteuXaSmphIff3HZnU4n0dHRAERHR+N0OnVrw+bCtSyavYKFs55lS+HLusVVHdsfzjVC8WbtJi5XC9SdgJJt6vPeHDuORbOfC7nY/tBUDUc/7pmFo/oIHN+tPq8Vva45Dif2aE67WqC8CM58rj6vFb3urm33l9SJT6H2hPq8VvT6y13afsPVou1Hjn4EzWfV57Wi1yVbte/Dbq8PbVZ/s7Nq74LV68//DM7TWq3bnNpBr9ulPq8Vvd7/J2iq6vF6/zvayYpAoaxTkZ2dzeLFiwGw2+0kJydfdLsRI0bQ2NgIQGNjIw6Hg3379pGRkcHBgwcBKCws5Omnn+YXv/gFXVdRrfqmSkYNv56Y6Bupa6708xMZF9sfmqvB0+s/r7cLGisC1x4z4zwNned61rvcUFemPq8Vva470fdLydOhnWkU9KfuuFbfbtwuY2ptRa9ry7T9Rjed7dp+RdCfxgrt+7Abd4d2Ykglqr0LVq/bLjg33OXRzqAL+uLtgo7Wvu91uaGjJTDtAYWdivr6etxuN263mzVr1jB+/PiLbjdt2jS2bt0KwJYtW5g6dSp33nknGRkZvm3+9Kc/8ctf/pI77riDoqKii8ax2Wy+V1lZGQAjh4+mrqmC2qYzjIoa2LW3srIyJbEvjKvXK2XmRJxNtX1yFezbqSRX73roQX+11juuXq/M//MtWtsbfXk8Hg9/3vKW8lpb0etfZC2hvaPNl6fD7eK/X3pOvFbw2f/nlZV0unt6Fe0drfz8XxcHvdcXq0ewe/2XbRvwdPVMTtJ6rpG582eHnNOh4HXhgV198jgba5n2N18Paqf7q4ce8VXV2WazcbT0UJ9cNTXV3HL7jZb1WlWtw+w2yiv6noWorq5mRMwwZX/by6Hsnor58+ezaNEixo0bR0NDg+9KRUZGBgUFBRw7doylS5cyd+5cHA4HKSkpJCUl8eSTTw4on9fr9S13P1Y9fdIPWPuhNt5wQfozA4qbkJCgJPaFcfXkyEdQVaKdRY8YDv/0bCqP/F5Nru561DZW8PLmpzhTe4yEuPHcMz7jqmP1V2t/Y6uqtderjdF1ntLWhw21k/Xig/z7ugd1zwXW9rqrS7us21KjeT3qhiH873u/4MXwX+ieC6zttacDPnsL2s8P63PEX8PG3f9DWNj/6J4L1LoX7F53tMFnb2pXKDrPQdLXo9nzrx9wBd/dV013LUCNe8Hu9bkG2LtBu7cCYMJdMZRm7dc9D6jdV+sVX+UxSPNZOPCudoWi8xxM+lYsNcvLleQKBa9V1rruJBR/cP4qnA2mz46lfXnbZX9PFTavqk/aixkzZrBjx44r3v7EiRM89dRTxMfH8/TTT1NcXMymTZtwuVz8+te/Jizs0hdYekvmLxHDYfqP9I99YVy9aW/S2jrjp2pv0pZaQ1uD9kV1zUgIs6vLY/Vae73QVg+fvgwzH1V7Q7zla90FrXVgs8Mwh9ob4lXWIxRq3T00JP9V+OZjanKAWqf1jK+y1p5ObWhOeISWRxWhUGvV34vuDq3WBa+L16pr3dmu3U8bEQWDh6nLcyUof6K2x+MhPPzqjmoTExN54403fOuTJk1i0qRJurRnS+Er7Dn0PmFhdu6d+BCTb5+tS1zVsa+W7h2m6lmfBBg2IrD5reK0zQbXjDq/LI/tVIotDCKvDWwbrOJ1mB2iAlxrq2APh6jrAtsGq3g9aDAMj738doL/hEdor2BA+Vez3W733TMRLDyQ+giPfXcte4/q3y6VsQWhP8RpwYyI14IZEa8Fs2LJ833Zu37HI79PYdbdC/kg/yVqGsrZ8PFv+izrEfutHc/hbDnL5oK1fZYFQW/EacGMiNeCGRGvBbOifPhTMPKd6T/BERXHR/vW82DaE/zqtQd4dO5LRA51+Jb1iH337bN5cdMyHp37IscrDviWBUFvxGnBjIjXghkRrwWzYslOBcANMbdQ11RBS3sDEYOvoc3VDDabb9kRNfDBgN2xR48aw6033sUgezi33TTJt2wmhkSpi6VXbD3bGMyI0/ohXgcP4rU+qHRaz/jitXh9NYSC11ZxGizYqbhv0kO+5aVz1vDOJ6v4+YOvkp37PPawQb7lzBnL/I4N9J02ReUUKgFi0vdCM7aZEKf1R7wOPOK1vqj2Try+MsRrfRGvgwtDppQ1GqtPB9nN9pVqp3ITjEW81hCvzYXVp5TtRrw2DzLNaQ/itbWw3JUKK7Nz505ycnKYOXOm72dqairbtm1j4sSJOBwO37b5+fkUFhayZMkSADZs2IDT6SQzM5Pc3Fy8Xi/x8fGUl5eTlpbGsGEBnhxZsCTitGBGxGvBjIjX5seSsz9ZlQkTJhAfH+/7mZqaCkBlZSUOh4N169axZMkSsrKymDx5MpGRkb7fbW9vJy0tjZKSEpKSkhgzZgzZ2dkkJiZSUlISqI8kWBxxWjAj4rVgRsRr8yOdCguRlZVFTEwM8+bNIyYmhtLSUgDi4uJwOp3Mnz+f1atXs3z5co4cOUJRURGtra0UFRURERFBTk4OY8eOJTk5meTkZBITE33vCUIgEKcFMyJeC2ZEvDY/lr+novTMAW654Y5+/92fseeXii1jdIWrRbzWEK/NhUr3xGshEFztPQ+qvA600yBeWw3LX6nYfTCbqvqykIstCJdCvBbMiHgtmBFV7onTgtFY/kbtuJGJeL1dIRc7WCh8E1zN+sQaEtV3+ja9Yl8Y1wqI1/4hXgcn4vXAUem0nvHF6+CPG0yEgtdWctrynYre8zqHUuxgwdWs39R5RsY2O+K1f4jXwYl4PXBUeydeDxxV7pndaRCvgw3LD38SBEEQBEEQBME/DO1UuFwupkyZQmRkpO+uf4Bly5aRkpLCggUL8Hg8RjZJEARBEARBEAQ/MbRTER4ezsaNG5kzZ47vvaKiImpqasjNzSUhIYFNmzbplu9k9SGeWZfJ+u3P6BbTyPj+cK5R++npNCbfWecpVrz5fZ59Yx5nnadCJrYetDmh+Sx0GdQfVuldMDvt9UJr3fllg4YJW9Vrbxe01Gj1Nmp+QKt63eXR9h9Godq7YPba0wlN1T3fj0ZgVa/dHdBUZVw+K3vd2a7VuqMt0C1R3KlYtWoV06dP5+GHHyY9PZ2wsDBiY2P7bJOXl0d6ejoA6enp5OXl6Zb/5thxLJr9nG7xjI4/UI58BAXrtOVPXzZmB7q5cC2LZq9g4axn2VL4csjE9gevFz7/MxS+Afv+CHteNeY/tUrvgtXpri7YtwE+e0tbL1hnTIfZil57OrT67j1f731/1OqvGit63dEGe17RagzwxfvqO3GqvQtWr881aN+H+9/R/D66w5i8VvS6+Sx8uhb2/0lbLytQn9OqXted7PH601egojiw7VHWqdi/fz/FxcXs2rWL1NRU4uPjL7qd0+kkOjoagOjoaJxOp6omWYKmKqg8BJ3ntPX2Jjj4gfq89U2VjBp+PTHRN1LXXBkysf2h9kuoO6HVuvMctNXDkZxAt8qclB+Axooer1tq4Uv9zj/0ixW9Pr5bq2+3140VcKYo0K0yJ4e3a1c6u72uPaHtU1Si2rtg9frgB9r3YbfXlcXaVQtBf77YBK6WHq9PFkK7TjM09YdVvT70IXS0alcrOtvg2CfGjVC5GMo6FdnZ2SxevBgAu91OcnLyRbcbMWIEjY3aqfTGxkYcDgf79u0jIyODgwcPAvzV+sWw2Wy+V1lZmW6fo6ysTEnsC+Pq9fq7v/0HWpvO9cl1qKhUSa7e9Rg5fDR1TRXUNp1hVNRoXWqiV2xVtf7xQ0v/6j9v7vbPlNdaD0LN69/82+o+w8u8XfDmKxvFawWffcPr7/cZXtblhhXLnw96ry9Wj2D3evdH+/rk8XTAou//S8g5HQpeH/q8tE+e5qY2Zs3MCGqn+6uHHvFV1dlms1F2vO/woNraWr6ePNmyXquqtT3MTmVF3w5OVVUlo6+LV/a3vRzKppStr6/H7XbjdrtZs2YNjz/++EW3mzZtGi+88AKZmZls2bKFqVOncuedd5KRkeHb5sL1i9H7weDdT5usbazg5c1Pcab2GAlx47ln/KVjXIyEhISLxgb/4l8YVy/ONULBeq3HCmALg4mpt+Bdoeaaenc90if9gLUfPoXX28WC9IGN7+yv1v7GVlXrpmrY/0ftDAFA2CC4d+5EvM+rrbVKr/2NrarWNV9C8V/A7dLW7YPhB0u/zdMvi9d6U150/mxXh7Y+aAgs/6+f8t/v/VT3XKDWvWD3ujQXTu3VOm4A4UPh9ewXiLruBd1zqXRaz/iqan3wL1B9pOd+rOEjhpGT9x4Rw3VPpdtxAqjzWlWdQRuqWt+rX3HtdTF8cSyfQUP0zxUKXqus9Z5XtfvfurnhxtFU1Z0iLEBzuyrrVMyfP59FixYxbtw4GhoafFcqMjIyKCgo4NixYyxdupS5c+ficDhISUkhKSmJJ598Urc2xERfzxP/uF63eEbHHwhDoyE5Xbus7vXC8FgYe6/6vNc54ln24CshF9sfhsfCrWlwPFe7tBs7FsZMU59XpXfB6DTAtUmQOBVOfaatx90ON3xVfV4ren3DV7Xx51Ul2hCGxKkQk6g+rxW9TrpHq3H3AdgtKRB1ndqcqr0LVq9vv1e7ebi5Wqv5uNko6VBciBW9nvD38PlGbWifPRySZ6OkQ9Ebq3r99Qeg6D3NaVcLfH0OAetQgMJOxZQpU3zDlWbMmEFcXBwA77333l9tu3Llyj7rJ06cYOvWrRw+fJinn36a6urqPuvDhg1T1WxTEJME038U6FZYg9HjtNf2lVpnTlDHzRO1l6AWmw2+8g3ttX2l1FwlYWGQPCvQrbAG9nC44zva8vaVEJMQ0OaYmvAIuCsz0K2wBkMi4e752vL2lXDNyMC2R/kTtT0eD+Hh4Vf1O4mJibzxxhv9rguhwZbCV9hz6H3CwuzcO/EhJt8+OyRiC0J/iNOCGRGvBTMiXhuP8oskdrudrVu3qk4jBCkPpD7CY99dy96j+jugMrYg9Ic4LZgR8VowI+K1sQRw5JVgBbJ3/Y5Hfp/CrLsX8kH+S9Q0lLPh49/0WdYj9ls7nsPZcpbNBWv7LAuC3ojTghkRrwUzIl4bi/LhT4K1+c70n+CIiuOjfet5MO0JfvXaAzw69yUihzp8y3rEvvv22by4aRmPzn2R4xUHfMuCoDfitGBGxGvBjIjXxmLKTsWQKHWx9IqtZxuDnRtibqGuqYKW9gYiBl9Dm6sZbDbfsiMq9vJBLhN79Kgx3HrjXQyyh3PbTZN8y2ZCvA4exGn9UOmeeH11iNf6oHJfrVd8qzgN4rWRmLJTMel7oRnbbNw36SHf8tI5a3jnk1X8/MFXyc59HnvYIN9y5oxlfscGtGlrurmCh7SEGuJ14BGn9Ue8Djzitb6o9k68vjLEa+OxeVU9kUOwBL0f8uMvEcP7ToWrV+wL46pg+0r45mPa8s6dO8nJyWHmzJm+n6mpqWzbto2JEyficDh8v5efn09hYSFLliwBYMOGDTidTjIzM8nNzcXr9RIfH095eTlpaWkynbJBiNca4rV5UOm0nvHFa+FqCAWvjXAagsNruVFbEHRmwoQJxMfH+36mpqYCUFlZicPhYN26dSxZsoSsrCwmT55MZGSk73fb29tJS0ujpKSEpKQkxowZQ3Z2NomJiZSUlATqIwmCeC2YEvFaMCOB8lo6FYKgM1lZWcTExDBv3jxiYmIoLS0FIC4uDqfTyfz581m9ejXLly/nyJEjFBUV0draSlFREREREeTk5DB27FiSk5NJTk4mMTHR954gBArxWjAj4rVgRgLltQx/EvxCholo9L7sKIQ+4rWGeG0eQmGYSH+x9Ua8Ng+h4HUghj8FCrlSIRhG6ZkDIRlbEC6FeC2YEVXuidNCIBGv1SKdCsEwdh/Mpqq+LORiC8KlEK8FM6LKPXFaCCTitVpMOaVs4ZvgatYn1pCovtO36RX7wrhWIG5kIl5vV8jFDhbE6+BEvPYPle6J1wNHlXvi9NWhymsrOg3itWpM2alwNes3xs7I2Gan97zOoRQ7WBCvgxPx2j/E6+BElXvidPDHNzPitVpk+JMgCIIgCIIgCH5haKfC5XIxZcoUIiMjfdNbASxbtoyUlBQWLFiAx+MxskmCIAiCIAiCIPiJoZ2K8PBwNm7cyJw5c3zvFRUVUVNTQ25uLgkJCWzatEm3fGedp1jx5vd59o15nHWe0i2u6tj+0uWG0wfg+C5oqjYm58nqQzyzLpP1258Jqdj+4u6AU59py631xuS0qtcdbVCWD19+atylf6t63d6k1Rm0uhuBVb1urYPju7X9iLvDmJxW9bqpWvteBO17UjWqvQtmr52noTQXKg6CUbcaWNXr2hNwbKe2HOiHRCjtVKxatYrp06fz8MMPk56eTlhYGLGxsX22ycvLIz09HYD09HTy8vJ0y7+5cC2LZq9g4axn2VL4sm5xVcf2hy4PFL4BRz+CE3tg/ztQ86X6vDfHjmPR7OdCLrY/uDug4HU4+om2vvctaKpSn9eKXne0arUuzYUvd0PBemhrUJ/Xil63ObX6frlbWy9YZ0zHwopeN1bCZ2/DiU/h2CdarT0GdCys6HXNce378MQebb3wTe37UiWqvQtWr8uLoGijdhLo8HbY/ydjDnat6PXx3XBwE5ws0NaLPwxse5R1Kvbv309xcTG7du0iNTWV+Pj4i27ndDqJjo4GIDo6GqfTqVsb6psqGTX8emKib6SuuVK3uKpj+4PztHaw1X1moPMclH4S0CaZluojcK4ROL+z7GjTDgxUY0WvT+2D9l6znXS0wpf6nX8QevFlnlbfbtqb4PR+9Xmt6PWxT6DzfIfN64VzDVB9LKBNMi3HPtG+D7tpc4KzXG1O1d4Fq9dle8Ddri13uaH5rHZFTtAXrxfOFIHb1fNeXVlfz41GWaciOzubxYsXA2C320lOTr7odiNGjKCxsRGAxsZGHA4H+/btIyMjg4MHDwLw/vvv8+yzz/LTn/6033w2m833KisrA2Dk8NHUNVVQ23SGUVGjB/Q5ysrKlMS+MK5er2/Nvp+W5pY+uQ4fPqIkV+966EF/tdY7rl6vxT9ejMfd97ru7l2fKq+1Fb1e+R//+Ve5Nrz1R/FawWd/Z8O7f5XruWd/E/ReX6wewe71p3n5ffJ43B5+tPDHIed0KHh99MjRPnlamluYnf53Qe10f/XQI76qOttsNk6d7jsUq6amhq/fcadlvVZV60F2O1VVfTuT1VVVxMWOVva3vRzKppStr6/H7XbjdrtZs2YNjz/++EW3mzZtGi+88AKZmZls2bKFqVOncuedd5KRkeHb5v777+f+++/nxz/+cb/5vL2urXU/Vj190g9Y++FTeL1dLEgf2Di4hIQEJbEvjKsXbhfseQ3atX4ag4bAzMzb8D6n5tpjdz1qGyt4efNTnKk9RkLceO4Zn3HVsfqrtb+xVdXa1aINV3Cd78MNioAH/2UqP3lBba2t6HVrPXz2Vs9Z3fCh8OiKufzqNfFabxrOQNF7PWe7Bg+D/3rt5/y/kT/XPReodS/Yva4+AiXbes7qDh1u5085axhyzRrdc3XXAtS4F+xen/xMG2bWfVZ35HWR7C76C4MG655K6b5ar/iq6gxwdAec+Rw8ndr6DTdfy5GT+wiz658rFLxWWevP/wy1X2pXhGx2SLw9jtrGSq7g+F8JyjoV8+fPZ9GiRYwbN46GhgbflYqMjAwKCgo4duwYS5cuZe7cuTgcDlJSUkhKSuLJJ5+8aLwVK1awcOHCq2rDdY54lj34ir8fxfDY/jBoCEz6R+1Sb9UhuDUNrr/4RSJdiYm+nif+cX3IxfaHIZFw14NQulO7v+Kmr8O1Y9TntaLX14yEO+dqN1nWHoevfhtGXK8+rxW9HnEDfPXvoawAbGFwy3St/qqxotext2kHAuUHoL4MJj4IQ65Rn9eKXt88EcIjoKoEBl8DX/kGSjoUvVHtXbB6/ZW/0R6uV/slOE9pxyQqOhQXYkWvJ3xLu0/IWQ5R18KYFALWoQCFnYopU6b4hi/NmDGDuLg4AN57772/2nblypV91k+cOMHWrVs5fPgwTz/9NL/97W85evQoERERTJo06YouwViZIdfA+Nlap8KIDoWVGTZCOwAT1BN1LdzxHdi+Ehw3Bro15sZxk/YS1HPdLdpr+0oYOiLQrTE314/XXoJabDatE3fzRM3rQUMC3SLzYguDpGmBbkUPyp+o7fF4CA8Pv6rfSUxM5I033vCt93f1YiBsKXyFPYfeJyzMzr0TH2Ly7bNDIrYg9Ic4LZgR8VowI+K1YGaUP6fCbrezdetW1WmuigdSH+Gx765l71H926UytiD0hzgtmBHxWjAj4rVgVgx9+F2wkL3rdzzy+xRm3b2QD/JfoqahnA0f/6bPsh6x39rxHM6Ws2wuWNtnWRD0RpwWzIh4LZgR8VowK8qHPwUj35n+ExxRcXy0bz0Ppj3Br157gEfnvkTkUIdvWY/Yd98+mxc3LePRuS9yvOKAb9lMDIlSF0uv2Hq2MVgRp/VFvA4OxGv9UOm0nvHFa/H6aggFr63gdDeW7FQA3BBzC3VNFbS0NxAx+BraXM1gs/mWHVGxlw9ymdijR43h1hvvYpA9nNtumuRbNhOTvheasc2IOK0f4nXwIF7rg2rvxOurQ7zWB/E6uLBcp+K+SQ/5lpfOWcM7n6zi5w++Snbu89jDBvmWM2cs8zs20HduL5m1SlCAOC2YEfFaMCPitWBmbF5VT+QIIL0fhuIvEcNh+o/0j31hXBVsXwnffKxnfefOneTk5DBz5kzfz9TUVLZt28bEiRNxOBy+bfPz8yksLGTJkiUAbNiwAafTSWZmJrm5uXi9XuLj4ykvLyctLY1hw4ap/TCCeH2e3l6L06GPSvfEa/E6EKjcV+sV3winQby2Gpa8UduqTJgwgfj4eN/P1NRUACorK3E4HKxbt44lS5aQlZXF5MmTiYyM9P1ue3s7aWlplJSUkJSUxJgxY8jOziYxMZGSkpJAfSTB4ojTghkRrwUzIl6bH+lUWIisrCxiYmKYN28eMTExlJaWAhAXF4fT6WT+/PmsXr2a5cuXc+TIEYqKimhtbaWoqIiIiAhycnIYO3YsycnJJCcnk5iY6HtPEAKBOC2YEfFaMCPitfmx/PCn0jMHuOWGO/r9d3+GiVwqdiCGPwmhjXitIV6bC5XuiddCILja4UmqvA600yBeWw3LX6nYfTCbqvqykIstCJdCvBbMiHgtmBFV7onTgtFYbvanC4kbmYjX2xVysYOFwjfB1axPrCFRfadv0yv2hXGtgHjtH+J1cCJeDxyVTusZX7wO/rjBRCh4bSWnLd+p6D0FWyjFDhZczfrNcmFkbLMjXvuHeB2ciNcDR7V34vXAUeWe2Z0G8TrYsPzwJ0EQBEEQBEEQ/MPQToXL5WLKlClERkb67voHWLZsGSkpKSxYsACPx2NkkwRBEARBEARB8BNDOxXh4eFs3LiROXPm+N4rKiqipqaG3NxcEhIS2LRpk5FNEgRBEARBEATBT5R2KlatWsX06dN5+OGHSU9PJywsjNjY2D7b5OXlkZ6eDkB6ejp5eXm65T9ZfYhn1mWyfvszusU0Mv5Aaa2Hz97Slr/MAyMmDT7rPMWKN7/Ps2/M46zzVMjE9pfGKihYB5++Aqf3G5NTpXfB6jRAbRnkv6YtVx02JqdVva46DHte1epdV2ZMTqt6fXq/tv8AaKpSn0+1d8HqtderfR9++rL2/dhab0xeK3rd5YEjH0HeWm29XacbqS+FVb32dELxh1qtP98InecC2x5lnYr9+/dTXFzMrl27SE1NJT4+/qLbOZ1OoqOjAYiOjsbpdOrWhptjx7Fo9nO6xTM6/kDoaIN9G6ChXFs/+Rkc360+7+bCtSyavYKFs55lS+HLIRPbH9oaoOhd7UCgtRaO74LyIvV5VXoXjE6D1nkr/gs0n9XWD2+Hmi/V57Wi1zXHtfq21Gj1PvgXYw52reh1+QE4nqvtPwAOvAvnGtTmVO1dsHp9fBecLITWOu37cd8G6DDgAMyKXh/aDGeKoO18x23vW9rBr0qs6vWBbKgq0Wp99hjsfduYE8n9oaxTkZ2dzeLFiwGw2+0kJydfdLsRI0bQ2NgIQGNjIw6Hg3379pGRkcHBgwcB+Pzzz/nP//xP/vmf/1nuubgMDRXQ2d6z7umAagPO6tY3VTJq+PXERN9IXXNlyMT2h9ovtU5cN24XVHwRuPaYmapDfc/AuNuh4nP1ea3o9ZnPtfp203lO+9IS9OfMF+Du6FnvaIPaE2pzqvYuWL2uPtL3wLazHRorAtceM+Ms165WdOPu0DpzKrGi194u7YRE71mDO9rA1RK4NinrVNTX1+N2u3G73axZs4bx48dfdLtp06axdetWALZs2cLUqVO58847ycjI8G3z1a9+leHDh1NfX4/NZrtoHJvN5nuVlZXp9jnKysqUxL4wrl6ve9Nn0NjU92rPwUMHlOTqXY+Rw0dT11RBbdMZRkWN1qUmesVWVesFi+bhuuBaY87HHyqvtR6Emtf/9uv/D7fH7cvT1dXFK+vWiNcKPvvrb/6Brq6ebym3p5Osf3si6L2+WD2C3euPc7f1yePqOMf3F2SGnNOh4HXxob6XkRub6pn5t6lB7XR/9dAjvqo6a+3rexn5bM1Zxk34imW9VlXrMLuNqqq+HZzq6mpGXRet7G97OZQ9p2L+/PksWrSIcePG0dDQ4LtSkZGRQUFBAceOHWPp0qXMnTsXh8NBSkoKSUlJPPnkkxeN98Mf/pCwsDDf1YwL8fa63tP9CPvaxgpe3vwUZ2qPkRA3nnvGZ1z150hISLhobPAv/oVx9cLrhf3vaGdgPG4YPBQyH7uDH69Scz2sux7pk37A2g+fwuvtYkH6wMZ39ldrf2OrqnWXBwrf0M7AdLlhSCT89DezeOIltbVW6bW/sVXV2u3S7l051wR4YdjwMFa8+mP+650f654LrO21q0Xz2tWinQEbfm04r29+ljcHP6t7LlDrXrB73VqvDVfobAObHa6NHcpHe98mzP627rlUOq1nfFW1bjgDRd1jzr1w8+0jKTq+kys4Trpq9DpOAHVeq6ozwNlSKNmi1XrQELh93HWU//KYklyh4LXKWpcf0Ib2dY9Q+fo3Y2ld3qgk15Vg86r6pL2YMWMGO3bsuOLtT5w4wVNPPUV8fDxPP/00n3zyCV988QVffvklv/3tb4mIiLjk7/f+D+0vEcNh+o/0j31hXD3xeqHuhDZe1HEjDI1Wkwek1l0ebRjU5xshZTEMuUZNHpBaezq0oSFeL4xKgPBL7wb8wuq17mzXvC7+AGb8FOzhavKA2nqEQq1drVB/EuyDISYRwuxq8qh0Ws/4Kmt9rlEbmnPoQ5j5M5R0KCA0aq2yzqB1mBsrtDyOm6TWKmvdfFZ7HdoM33xMXZ4rQfkTtT0eD+HhV/eNlJiYyBtvvOFbnzVrFrNmzdK7aabFZoOYpEC3whqE2eG6r2jLKjsUgnbQFXtboFthDcIjYPQ4rVOhskMhaPuN0eMC3QprMDRaex36UN1BrqBxzUjtJagn6jrtdWhzoFtiQKfCbrf77pkQrMWWwlfYc+h9wsLs3DvxISbfPjskYgtCf4jTghkRrwUzIl4bj6EPvxOsxwOpj/DYd9ey96j+HUuVsQWhP8RpwYyI14IZEa+NRToVglKyd/2OR36fwqy7F/JB/kvUNJSz4ePf9FnWI/ZbO57D2XKWzQVr+ywLgt6I04IZEa8FMyJeG4vy4U+BYEiUulh6xdazjcHMd6b/BEdUHB/tW8+DaU/wq9ce4NG5LxE51OFb1iP23bfP5sVNy3h07oscrzjgWzYT4nVwIE7ri0r3xOsrR7zWD5X7ar3iW8FpEK+NxpSdiknfC83YZuWGmFuoa6qgpb2BiMHX0OZqBpvNt+yIivU79uhRY7j1xrsYZA/ntpsm+ZbNhHgdPIjT+iFeBw/itT6o9k68vjrEa+MwZadCCA7um/SQb3npnDW888kqfv7gq2TnPo89bJBvOXPGMr9jA32n85CpPQQFiNOCGRGvBTMiXhuPIc+pEMyL1efz72b7yp75oXfu3ElOTg4zZ870/UxNTWXbtm1MnDixz8Mb8/PzKSwsZMmSJQBs2LABp9NJZmYmubm5eL1e4uPjKS8vJy0tjWHDhqn9IAIgXncjXpuHUJjPv7/YeiNem4dQ8NoIpyE4vJYbtQVBZyZMmEB8fLzvZ2pqKgCVlZU4HA7WrVvHkiVLyMrKYvLkyURGRvp+t729nbS0NEpKSkhKSmLMmDFkZ2eTmJhISUlJoD6SIIjXgikRrwUzEiivpVMhCDqTlZVFTEwM8+bNIyYmhtLSUgDi4uJwOp3Mnz+f1atXs3z5co4cOUJRURGtra0UFRURERFBTk4OY8eOJTk5meTkZBITE33vCUKgEK8FMyJeC2YkUF7L8CfBL67m0mDpmQPccsMd/f67P8NELhXb6MvpQugjXmuI1+bhaodxXK17Vxr/av+/qEC8Ng+h4HUghj8FCrlSIRjG7oPZVNWXhVxsQbgU4rVgRlS5J04LgUS8VospZ38qfBNczfrEGhLVd/o2vWJfGNcKxI1MxOvtCrnYwYJ4HZyI1/6h0j3xeuCock+cvjpUeW1Fp0G8Vo0pOxWuZv1mAzAyttnpPQVbKMUOFsTr4ES89g/xOjhR5Z44HfzxzYx4rRYZ/iQIgiAIgiAIgl8Y2qlwuVxMmTKFyMhI353oAMuWLSMlJYUFCxbg8XiMbJIgCIIgCIIgCH5iaKciPDycjRs3MmfOHN97RUVF1NTUkJubS0JCAps2bTKySabF64Uu6Z8ZgsyfZhzeLuiSYauGIHU2ji6P7EeMQr4XjaPLLV4bRZc70C3QUHpPxapVq3j33Xf52te+xvHjx9m8eTOxsbF9tsnLyyM9PR2A9PR03n33Xb797W/rkv+s8xRrNz+F19vFwlnPcp0jXpe4qmP7y5kv4HiuthwRDXfOgUFD1OY8WX2I17ctJzFuAvO++a8hE9tfTuyBU/u05X3vwB0ZEKb4TiUreu31wtEdUHUYbIAjHsb/HdhsavNa0WtvFxz8CzhPa+tHPoJbZ6ivtRW99rihKBtaasAL3HwXJExWn9eKXne2w/4/QXujtl5xEK4frzanau+C1WtXi/Z92NkG2OD2++DaJPV5reh1az0ceBc8Hdp6QwWMuD5w7VF2pWL//v0UFxeza9cuUlNTiY+/uOxOp5Po6GgAoqOjcTqdurVhc+FaFs1ewcJZz7Kl8GXd4qqO7Q+t9VC6EzratFdTFRR/qD7vzbHjWDT7uZCL7Q8NZ+Bk4fkdJ9pB2NFP1Oe1otfVh7WDgM7zXtceh5Ofqc9rRa9PFkLNca3OoNX97FH1ea3o9bEd2n6jo01zu6xQOyhQjRW9Lv5Q+z7s9vrYJ9Cm3+HGRVHtXbB6XbQRWmvPH4e0QsnmnrqrxIpeF2XDuYae+n7x58BejVPWqcjOzmbx4sUA2O12kpOTL7rdiBEjaGzUTh00NjbicDjYt28fGRkZHDx40Lfdhg0b+OEPf3hVbahvqmTU8OuJib6RuubKAX4S42P7Q0ttT48VAK92FkzQn8ZKcLt61r0eaDTggMCKXjvL+3rt6YSG8sC1x8w4y/teSvd0aO+pxopeN1RoV4a6cbdDU/A0z1S01qJdDjqPp0P7vlSJau+C1WtXS9/1ri441xiYtpgZb1ffY5Du9zpaA9MeUNipqK+vx+1243a7WbNmDePHX/w647Rp09i6dSsAW7ZsYerUqdx5551kZGT4tikoKMDhcPiuaFwMm83me5WVlQEwcvho6poqqG06w6io0QP6HGVlZUpiXxhXr9eU1PHUN/b0IjxdHnYWbFaSq3c99KC/WusdV6/Xd743k+Zep7o63R1s+PNLymttRa+XPrmAtvaeidnbO9pY+fv/T7xW8Nn/a80vcXWc8+Vpa2/iX37xf4Le64vVI9i9fueDtXR6On15mtuc3P/dvwk5p0PB612FW+nqdaNQfWMNk6aPC2qn+6uHHvFV1dlms3GwZF+fXDU1VSTcGmtZr1XVOsxu4+TpL/vkqqyqZPjIIcr+tpdD2ejv+fPns2jRIsaNG0dDQ4PvSkVGRgYFBQUcO3aMpUuXMnfuXBwOBykpKSQlJfHkk0/+VawdO3YwZMgQ9u3bx+nTp7npppv+ahtvr7uBuh+rnj7pB6z9UBtvuCD9mQF9joSEBCWxL4yrJ2UF54flnIPh19r52ZJ0nnhRTa7uetQ2VvDy5qc4U3uMhLjx3DM+46pj9Vdrf2OrrPXRHVB5SBtvPnz4YJ57dBH/+cdFSnJZ2WuvVxvnX39KGyZy/VeG8dov/o119n/TPRdY2+sujzZGt3ucf9Ltw9n61GvYbK/pngvUuhfsXrs7YN8GrY0dbZCc6qDo6Y91zwM9tQA17gW71x2tsPdt7d4KrxcmfuNaTv7ykO55QO2+Wq/4Kr8X2xpg/x+1K8odbTD9u3E4l1cryRUKXqusdVM1FL2njZTABjMfGE3Hr1yX+zVl2LyqPmkvZsyYwY4dO654+xMnTvDUU08RHx/P008/zbBhwwB47LHHWLly5WV/v7dk/hIxHKb/SP/YF8bVG08n7HgeZv5M7Q2WUmvtwKDLDeFDpdbKa+2Cj1+Abz6mLgdIrQE6zkFYmPpJHlTWIxRq7fVqJ4B2/l6t1yqd1jO+6lp3tMGgwWAPV5MDQqPWqvcfXq/Wkcv9X/Faea27NK/Dh0KYXV2eK0H5E7U9Hg/h4Vf3vzcxMZE33njjr96/kg7F5dhS+Ap7Dr1PWJideyc+xOTbZ/sd04jYV0v3DlPlQa6gMWgwMDhw+a3iNKg/wBV6GDw0sPmt4rXNBoOHBSy9pbDZYMg1gW2DlbweEhmw9JbCFhY8tVb+nAq73e67ZyJYeCD1ER777lr2HtW/XSpjC0J/iNOCGRGvBTMiXgtmxdCH3wUL2bt+xyO/T2HW3Qv5IP8lahrK2fDxb/os6xH7rR3P4Ww5y+aCtX2WBUFvxGnBjIjXghkRrwWzonz4UzDynek/wREVx0f71vNg2hP86rUHeHTuS0QOdfiW9Yh99+2zeXHTMh6d+yLHKw74lgVBb8RpwYyI14IZEa8Fs2LJTgXADTG3UNdUQUt7AxGDr6HN1Qw2m2/ZERV7+SCXiT161BhuvfEuBtnDue2mSb5lMzEkSl0svWLr2cZgRpzWD/E6eBCv9UGl03rGF6/F66shFLy2itNgwU7FfZMe8i0vnbOGdz5Zxc8ffJXs3Oexhw3yLWfOWOZ3bKDvndImvGt60vdCM7aZEKf1R7wOPOK1vqj2Try+MsRrfRGvgwtDppQ1GpkOUmP7yr5Tue3cuZOcnBxmzpzp+5mamsq2bduYOHEiDofDt21+fj6FhYUsWbIE0J5o7nQ6yczMJDc3F6/XS3x8POXl5aSlpfmm/RXUIV5r9PZanA59rD6lbDfitXmQaU57EK+thSVv1LYqEyZMID4+3vczNTUVgMrKShwOB+vWrWPJkiVkZWUxefJkIiN75ihrb28nLS2NkpISkpKSGDNmDNnZ2SQmJlJSUhKojyRYHHFaMCPitWBGxGvzI50KC5GVlUVMTAzz5s0jJiaG0tJSAOLi4nA6ncyfP5/Vq1ezfPlyjhw5QlFREa2trRQVFREREUFOTg5jx44lOTmZ5ORkEhMTfe8JQiAQpwUzIl4LZkS8Nj8y/OkymGWYiBD6iNca4rW5kOFPGuK1eZDhTz2I19bC8lcqSs8cCMnYgnApxGvBjIjXghlR5Z44LRiN5TsVuw9mU1VfFnKxBeFSiNeCGRGvBTOiyj1xWjAay00peyFxIxPxertCLnawUPgmuJr1iTUkqu/0bXrFvjCuFRCv/UO8Dk7E64Gj0mk944vXwR83mAgFr63ktOU7Fb3ndQ6l2MGCq1m/saNGxjY74rV/iNfBiXg9cFR7J14PHFXumd1pEK+DDcsPfxIEQRAEQRAEwT8M7VS4XC6mTJlCZGSkbyoxgGXLlpGSksKCBQvweDxGNkkQBEEQBEEQBD8xtFMRHh7Oxo0bmTNnju+9oqIiampqyM3NJSEhgU2bNumW72T1IZ5Zl8n67c/oFtPI+APF64XGSm25o82YnGedp1jx5vd59o15nHWeCpnY/uL1grMcak+A22VMTpXeBavTAF0eqD//5/d0GpPTql57OqGuTKt3l0HneazqtdsFtV9qy0ZM8K7au2D2uqNNq3VjpTG1But63d4MNceNy2dlr881aLVurQt0SxR3KlatWsX06dN5+OGHSU9PJywsjNjY2D7b5OXlkZ6eDkB6ejp5eXm65b85dhyLZj+nWzyj4w8Erxe+eB/2/0lb3/MqtNSoz7u5cC2LZq9g4axn2VL4csjE9gdvF+zbAEXZ8MWftVobMfZSpXfB6DRoB7kF6+Hz97T1/Negs119Xit63XlOc/nzjVq9C9eDx60+rxW9bm+CPa9o+2zQ9ieq76tV7V2wet1So3nd/f14cJMxHQsrel1/Cgpe7/H66A71Oa3qdVWJ9t34xfvw2VtQVhjY9ijrVOzfv5/i4mJ27dpFamoq8fHxF93O6XQSHR0NQHR0NE6nU1WTLEHjGag/Ce7zB1wdrVC8WX3e+qZKRg2/npjoG6lrrgyZ2P5QfVQ74+V2aQe97U1wOCfQrTInp/dDay24O7T1tgY4vkt9Xit6XbpLO/Pl6dTq3VIL5fsD3SpzUrJdO6PbfeWtsRJqSi/9O/6i2rtg9br4Q+370NOpfT/Wney5oi/oS8lW7apQ1/mTEZWHtH2KSqzotdcLRz/WTgR1ubWfJwt6vicDgbJORXZ2NosXLwbAbreTnJx80e1GjBhBY2MjAI2NjTgcDvbt20dGRgYHDx4E4Le//S3//u//zjvvvNNvPpvN5nuVlZXp9jnKysqUxL4wrl6vb836Di3Nfcc8HS4+piRX73qMHD6auqYKapvOMCpqtC410Su2qlr/8w9/6ttpdrP74wLltdaDUPN65a9f6HsG1wtvr8sWrxV89nfe+HOfPN4uWPFv/xX0Xl+sHsHu9ac79/bJ4+7o4ocPPRxyToeC14cP9e2ttTS2Mvtv/z6one6vHnrEV1Vnm83GyRN9hwfV1tRwx4RJlvVaVa0H2e1UVfbt4FRXVzL6uhuV/W0vh7IpZevr63G73bjdbtasWcPjjz9+0e2mTZvGCy+8QGZmJlu2bGHq1KnceeedZGRk+LYZOXIkLpcLl6v/QeveXtcxux9hX9tYwcubn+JM7TES4sZzz/iMfn+/PxISEi4aG/yLf2FcvXC1QP7r2hkZgLBBMOXer+BdoeY6b3c90if9gLX/f3t3HxbVeed//D0MKEEQR0nAxCBgahS0m/UhPkTIit2WuO2WNBptZbsxodn60+2aNPVq9FqpXX9N8qvrlTRutm4S81A1WZsWTUyiKLERJREaFKOATwENggoyIKA8zDC/P44MYMCIc+55OOf7uq5zeQYP3/vMzYfh3HPuOefDFbhcHSxMu7n5nX31tae1VfV180XtdGP7Fe2xdQB8N+NeFr+gtq9V5trT2qr62v4lFG/rOgMXPBD+5ekHyXpdcq23c6VQtrvrM0LBofCbl57gv999Qve2QG32/D3XFQVQ/knXmYqBg4LYvP2/GDT0v3RvS2Wm9ayvqq/LdkPVka53zwcPHcSegncZOEj3pnQ7TgB1uVbVzwDFW7XPrnS+EXTb8FspOVWIdYD+bQVCrlX2deHmq2fcrpYfMXI4F+oqsfjo2q7KBhUZGRlkZmaSmJhIfX29+0xFeno6BQUFnDhxgqVLlzJ37lxsNhvJyckkJCSwfPnyr9T68Y9/DMDPf/5z5s+fj9VqvaF9iIq8nad/tEm/J+Xl+jdjYDjc8yCU7ARnGwyLh2/8nfp2b7PFsmz+6wFX2xODhsG4f4Bje+DyRYidCLGT1LerMnf+mGkA250w5lvwxX7tlG/sRIi5W327Zsx1zFhtoHymSJuyMOZbYBuhvl0z5nrkZO11+lwpBFnh7lkwaKjaNlXnzl9zPToVcGkXILjSAPf8ACUDimuZMdfj/kE7BrlUDSG3aI9VDCi6M2uu7/kBHP0Ami5CSwNMnIfPBhSgcFAxdepU9/SlmTNnEhMTA8DWrVu/su2aNWt6PC4vLycnJ4eysjJWrlxJbm4uhw8fZsCAATc8oDCzwTEw9Z99vRfmMCwOpi+E3Wtg1H2+3htjixmjLUK9Oydoy+410ucqWSwwaoa2CLWCgmDM32vru9fA4Ojrby9unjUExn/X13thDiGh2sACtFwPDPft/ii/o7bT6SQkJKRf3xMfH8/mzZvdj7/3ve/xve99T+9dE4rtLHydT0veIyjIyrcnPcKUsbMDorYQfZFMCyOSXAsjklx7n/KTJFarlZycHNXNCD/1UMoTPPXwBj47rn8GVNYWoi+SaWFEkmthRJJr7/LhzCthBtn7fscTLyXzwL2P8cGBV6ipr2TLX37bY12P2m/veQ570wV2FGzosS6E3iTTwogk18KIJNfepXz6kzC3B2f8DFtEDB8VbWJ+6tP8+s2HeHLuK4TfYnOv61H73rGzeXn7Mp6c+zKnqg6514XQm2RaGJHkWhiR5Nq7DDmoGBihrpZetfXcR393R9RdXLxURVNLPaEDBnG5tREsFve6LeLmPzHXWXv4sFGMHjGRYGsId9852b1uJJJr/yGZ1o/K7Emu+0dyrQ+Vr9V61TdLpkFy7U2GHFRM/mFg1jaa70x+xL2+dM563vl4Lb+Y/wbZeS9gDQp2r8+buczj2oB2KZVON3CTlkAjufY9ybT+JNe+J7nWl+rcSa5vjOTa+ywuVXfkEKbQ/SY/ngodDDMe17/2tXVV2L0GvvWUtr53715yc3OZNWuW+9+UlBR27drFpEmTsNls7u87cOAAhYWFLFmyBIAtW7Zgt9uZN28eeXl5uFwuYmNjqaysJDU1lbCwMLVPRACS606Sa+NQmWk960uuRX8EQq69kWnwj1zLB7WF0Nn48eOJjY11/5uSkgJAdXU1NpuNjRs3smTJErKyspgyZQrh4V0Xlm5paSE1NZXS0lISEhIYNWoU2dnZxMfHU1pa6qunJITkWhiS5FoYka9yLYMKIXSWlZVFVFQUCxYsICoqipMnTwIQExOD3W4nIyODdevWsWrVKo4dO0ZxcTHNzc0UFxcTGhpKbm4uY8aMISkpiaSkJOLj491fE8JXJNfCiCTXwoh8lWuZ/iQ80p9TgyfPHuKuO+7p8/89mSZyvdrePp0uAp/kWiO5No7+TuPob/ZutH5/f19UkFwbRyDk2hfTn3xFzlQIr9l/JJtzdRUBV1uI65FcCyNSlT3JtPAlybVaMqgQXhMzNB6XqyPgagtxPZJrYUSqsieZFr4kuVbLkJeULXwLWhv1qTUwoufl2/SqfW1dM+h+CbZAqu0vJNf+SXLtGZXZk1zfPFXZk0z3j6pcmzHTILlWzZCDitZG/S4x5s3aQlyP5FoYkeRaGI3q3Emuhb/y6vSn1tZWpk6dSnh4uPuT6ADLli0jOTmZhQsX4nQ6vblLQgghhBBCCA95dVAREhLCtm3bmDNnjvtrxcXF1NTUkJeXR1xcHNu3b/fmLgkhhBBCCCE8pHRQsXbtWmbMmMHixYtJS0sjKCiI6OjoHtvk5+eTlpYGQFpaGvn5+bq1f8F+hmff+iee2byAC/YzutVVXdtT7S1w/C/w+Xao/cI7bZ4+X8LqjfPYtHt1QNX2VGszlO3W1uvPeqdNs+b6cj2U5sDRD6GpxjttmjXXjTVaPwNcqfdOm2bNtb0SjryvvY60NnunTbPmuuaU9ncRwNGqvj3VufPnXFeXan19aj84Hd5p04y5drngy0Nw+D3tcYePPyuubFBx8OBBjh49yr59+0hJSSE2NrbX7ex2O5GRkQBERkZit9t124cdhRvInP0sjz3wDDsLX9OtrurannC2Q+EmOPMZnC/T/lhVH1Xf7sjoRDJnPxdwtT3RdkXr68pD2uPirXCxQn27Zsz1lQb461tw9rCW58/+qB34qmbGXDdegKItXa8bhW9p/a+aGXNdWwGHt8K5Uu11pHATtF9R364Zc111RBsony/THhds0v5eqqQ6d/6a6y8+0QbJ58ug4gB89jZ448JIZsx16S44uRcuHNMeF//Zt/ujbFCRnZ3NokWLALBarSQlJfW63ZAhQ2ho0P5iNTQ0YLPZKCoqIj09nSNHjgBw6tQpVq1axdq1a/u1D3WXqhk2+HaiIkdwsbHag2fj3dqesH8JrU3A1VsaOlqh/FOf7pJhXTgOLd2uwNF+Bb7Q70Rbn8yY68pD0NbtXdz2y5JrVco/7Xlg29YMlcXq2zVjrsv3a2eWO7U0wvkTvtsfI6s4AI5r+tpeqbZN1bnz11yfPQzOq2eCXB3amxJNtb7dJyNyuaD2JDjbur7WeKHn30pvUzaoqKurw+Fw4HA4WL9+PePGjet1u+nTp5OTkwPAzp07mTZtGhMmTCA9Pd29zauvvsrQoUMJDg6mrxuAWywW91JRUQHA0MHDuXipitpLZxkWMfymnkdFRYWS2tfW1WuZPfsBGht7XmuurKxUSVvd+0MPffW13nX1Wh5//Cc4HT3P6+7bl6e8r82Y6+eee/Yrbb399mbJtYLnvmXL219p6zfP/F+/z3Vv/eHvud6fv79HOw5HO5mPPRpwmQ6EXJcdK+vRTmPjJR5I+45fZ7qv/tCjvqp+tlgsnDlzukdbNTU1/M093zRtrlX1tdUaxLnz53q0de78OW6LvlXZz/brKLukbEZGBpmZmSQmJlJfX+8+U5Genk5BQQEnTpxg6dKlzJ07F5vNRnJyMgkJCSxfvvwrtZqbm/nud7/Lnj17KCoqYuLEiV/Zpvtgo/O26mmTH2XDhytwuTpYmHZz8+Di4uKU1L62rl6cDih4E5rtgAuCQ2H2Y2Nx/Vb/tqCrP2obqnhtxwrO1p4gLmYc941L73etvvra09qq+rq9BQ682XVpv5Bb4J+fTuaJl9T2tRlz3XJJmxrSOed8QBgsf+FH/GbTj3RvC8yd66YabXpZ+2Xt8cBw+O8tK3gtYoXubYHa7Pl7rutOa/POO88MhdtCeC9vAyGhG3Rvq7MvQE32/D3X1SVw7CPtbIXFArfdMZhPj+7EquAoSOVrtV71VfUzQEXB1TNDV89WxH7jVk6dPcwNHJP2WyDkWmVfl+3Wsu1sg6BgGH1PDPXe+tBhLywuVc+0m5kzZ7Jnz54b3r68vJwVK1YQGxvLypUrKS0t5c9//jNNTU2sXr2aiIiI635/95B5KnQwzHhc/9rX1tWTow1OF2jTGCbMhaEj1bQD0tdtl+F0oTbAuOObEHlzb0bdELP39ZUG7bNCXxbBtIUwaJiadkD6uvkinCmCICuMnKS1pYrK/giEvm6o1qaLVH0OKf9HGzCroDLTetZX2dcXK7R5/gPDYeS9EDxATTuB0Ncq+xm06cE1p7TPZqUu1Q54VTB7X7tcWh/bv4SIaLjzHrB49bquPSm/+Z3T6SQkJKRf3xMfH8/mzZvdjydOnNjr2QnRu+ABMGqGNqhQOaAQ2gHAN+739V6Ywy2RcHeqNqhQOaAQWv+O/Xtf74U5RA7XlqrP1Q0ohGZYnLYI9W4brS3VR9UNKIR21u32cdriD5T/qK1Wq/szE/5gZ+HrfFryHkFBVr496RGmjJ0dELWF6ItkWhiR5FoYkeRaGJkPT5L4zkMpT/DUwxv47Lj+gx2VtYXoi2RaGJHkWhiR5FoYlSkHFdn7fscTLyXzwL2P8cGBV6ipr2TLX37bY12P2m/veQ570wV2FGzosS6E3iTTwogk18KIJNfCqEw50+3BGT/DFhHDR0WbmJ/6NL9+8yGenPsK4bfY3Ot61L537Gxe3r6MJ+e+zKmqQ+51Ixl4/c/Me1RLr9p67qO/kkzrS3LtHyTX+lGZaT3rS64l1/0RCLk2Q6Y7mXJQAXBH1F1cvFRFU0s9oQMGcbm1ESwW97otItrj2sOHjWL0iIkEW0O4+87J7nUjmfzDwKxtRJJp/Uiu/YfkWh+qcye57h/JtT4k1/7FdIOK70x+xL2+dM563vl4Lb+Y/wbZeS9gDQp2r8+buczj2gA9Lsys4iLNwvQk08KIJNfCiCTXwsi8cp8KbzP7NeY77V4D33qq6/HevXvJzc1l1qxZ7n9TUlLYtWsXkyZNwmazubc9cOAAhYWFLFmyBIAtW7Zgt9uZN28eeXl5uFwuYmNjqaysJDU1lbAwuRaiapJrTfdcS6YDn9nvU9FJcm0cZr93QneSa3Mx5Qe1zWr8+PHExsa6/01JSQGguroam83Gxo0bWbJkCVlZWUyZMoXw8HD397a0tJCamkppaSkJCQmMGjWK7Oxs4uPjKS0t9dVTEiYnmRZGJLkWRiS5Nj4ZVJhIVlYWUVFRLFiwgKioKE6ePAlATEwMdrudjIwM1q1bx6pVqzh27BjFxcU0NzdTXFxMaGgoubm5jBkzhqSkJJKSkoiPj3d/TQhfkEwLI5JcCyOSXBuf6ac/nTx7iLvuuKfP//dkmsj1avti+pMIbJJrjeTaWFRmT3ItfKG/05NU5drXmQbJtdmY/kzF/iPZnKurCLjaQlyP5FoYkeRaGJGq7EmmhbeZ7upP14oZGo/L1RFwtf1F4VvQ2qhPrYERPS/fplfta+uageTaM5Jr/yS5vnkqM61nfcm1/9f1J4GQazNl2vSDiu6XYAuk2v6itVG/q1x4s7bRSa49I7n2T5Lrm6c6d5Lrm6cqe0bPNEiu/Y3ppz8JIYQQQgghPOPVQUVraytTp04lPDzc/al/gGXLlpGcnMzChQtxOp3e3CUhhBBCCCGEh7w6qAgJCWHbtm3MmTPH/bXi4mJqamrIy8sjLi6O7du3e3OXhBBCCCGEEB5SOqhYu3YtM2bMYPHixaSlpREUFER0dHSPbfLz80lLSwMgLS2N/Px83do/fb6E1RvnsWn3at1qerP+zaqvgk9e09ZLdkKHF07+XLCf4dm3/olnNi/ggv1MwNT2VM0XkP+qdom/E3vBGxdoVpk7f800QNVR2P+Ktn76r95p06y5Pl0I+17W+rv6qJfaNGGuXS448bH2+gFQW66+TdW589dcdzi1v4f7/kf7+1hf5Z12zZhrZxsc3taV6+aL6ts0a67br0DRO1pfF272/ec/lA0qDh48yNGjR9m3bx8pKSnExsb2up3dbicyMhKAyMhI7Ha7bvswMjqRzNnP6VbP2/VvRmuT9svc+Ut8rhSO71Hf7o7CDWTOfpbHHniGnYWvBUxtTzTVQsmHcNmu/SJXHoTTBerbVZk7f8w0QN0ZLcdX6rXH5Z9AdYn6ds2Y6+oSrX9bGrT+PrYH7F+qb9eMua44AJWHug4Ejn6g/gBMde78NdfHPoJzJVpfN1/U/k62Nqlv14y5/vx9qDnVleuid8DRprZNs+b64J+grkLr64Yq+GwL+PKCX8oGFdnZ2SxatAgAq9VKUlJSr9sNGTKEhoYGABoaGrDZbBQVFZGens6RI0cA+Pjjj3n++ee57777aGrywqtAAGuoBkdL1+MOB1ysUN9u3aVqhg2+najIEVxsrA6Y2p6oq9DeJejkbIfzx322O4Z24XjPXDta4cIx9e2aMdfny3oeADha4MIJ3+2PkV04rr1udGq/AnWn1bapOnf+muu6ip5n7R2t0HDOZ7tjaI0Xeh7YOtvVD5bNmGtXx1fPTDjbvDNY7ouyQUVdXR0OhwOHw8H69esZN25cr9tNnz6dnJwcAHbu3Mm0adOYMGEC6enp7m3uv/9+fvKTn7g/5N0bi8XiXioqKnR7HhUVFUpqX1tXr2Xm30+n/lLP396Dhw8oaat7fwwdPJyLl6qovXSWYRHDdekTvWqr6usFjz7ElW6/vR0dHXy4O1t5X+sh0HL97//xFG3tXaMKh7Od9a8/L7lW8Nxf/cM6nE6Hu5229haW/2qp3+e6t/7w91zn7Hm3RzuXWxqZ/+P0gMt0IOS6+Ehhj3bqGy5yf+oUv850X/2hR31V/WyxWDj1Rc93IWprL3B3Upxpc62qr4OsFqqqe87jO3/+PLZbw5X9bL+OsvtUZGRkkJmZSWJiIvX19e4zFenp6RQUFHDixAmWLl3K3LlzsdlsJCcnk5CQwPLly3ut9/bbbzN//vw+23N1m8zeeQv72oYqXtuxgrO1J4iLGcd949L7/Tzi4uJ6rQ2e1b+2rl5cLu0U+sVy6OiA4AGwMGsKS36nZrJ/Z3+kTX6UDR+uwOXqYGHazc3v7KuvPa2trK87tFOPl85r7+aGDQnil+se5FdvqO1rlbn2tLaqvnY64K9vdU1/ChsUwu+2LOWlgUt1bwvMnev2Fm1ubluz9m5u1J2h/PGj5wkKfl73tkBt9vw91y2NWq7bW8ASBCNGRrDv863cwN/uflOZaT3rq+rrplo4eHUajrMNRk8aRsnKA0r7Gvw316r6GcBeCZ+/q71uB1nhb+69jXO/qlDSViDkWmVfnz8OZbu1WSnONpjy/WiurPLdqQqLS9Uz7WbmzJns2XPjE/vLy8tZsWIFsbGxrFy5krCwMH7605/y+9///oa+v/svtKdCB8OMx/WvfW1dvV06r/2hGhwNIaHq2jF7X7tccOkcFG6Cv/uZNohTxex93dEBl6q0Po8cDkEKb91p9r52OrT5uUVbIPVJCFJ4SQ+V/REIfe1o015DrCEwOAYlB7mgNtN61lfZ1+1X4NIFOPhH+NZTatqAwOhr1ccgrc3QVAMDwyE8Sl070tdXPydUpw2aVeb6Rii/o7bT6SQkJKRf3xMfH8/mzZt7fO1GBxRCMzj667cRnrNYtANcUDugENqB7ZARvt4Lc7AGw9Cr19ZQOaAQ2uvG0N6vYyJ0FnILDBvp670wh4GDtEWoFzpYW/yB8kGF1Wp1f2ZCmMvOwtf5tOQ9goKsfHvSI0wZOzsgagvRF8m0MCLJtTAiybX3yXtQQqmHUp7gqYc38Nlx/QeWKmsL0RfJtDAiybUwIsm1d8mgQiiVve93PPFSMg/c+xgfHHiFmvpKtvzltz3W9aj99p7nsDddYEfBhh7rQuhNMi2MSHItjEhy7V3Kpz/5wsAIdbX0qq3nPvqzB2f8DFtEDB8VbWJ+6tP8+s2HeHLuK4TfYnOv61H73rGzeXn7Mp6c+zKnqg65141Ecu0fJNP6Upk9yfWNk1zrR+VrtV71zZBpkFx7myEHFZN/GJi1jeqOqLu4eKmKppZ6QgcM4nJrI1gs7nVbxM1/qryz9vBhoxg9YiLB1hDuvnOye91IJNf+QzKtH8m1/5Bc60N17iTX/SO59h5DDiqEf/jO5Efc60vnrOedj9fyi/lvkJ33AtagYPf6vJnLPK4N9LwWo6rrMgpTk0wLI5JcCyOSXHufV+5TIYzL7Nfz77R7Tdf1offu3Utubi6zZs1y/5uSksKuXbuYNGkSNpvN/X0HDhygsLCQJUuWALBlyxbsdjvz5s0jLy8Pl8tFbGwslZWVpKamEhYWpvaJCEBy3UlybRyBcD3/vmrrTXJtHIGQa29kGvwj1/JBbSF0Nn78eGJjY93/pqSkAFBdXY3NZmPjxo0sWbKErKwspkyZQnh4uPt7W1paSE1NpbS0lISEBEaNGkV2djbx8fGUlpb66ikJIbkWhiS5Fkbkq1zLoEIInWVlZREVFcWCBQuIiori5MmTAMTExGC328nIyGDdunWsWrWKY8eOUVxcTHNzM8XFxYSGhpKbm8uYMWNISkoiKSmJ+Ph499eE8BXJtTAiybUwIl/lWqY/CY/059TgybOHuOuOe/r8f0+miVyvtrdPp4vAJ7nWSK6No7/TOPqbvRut39/fFxUk18YRCLn2xfQnX5EzFcJr9h/J5lxdRcDVFuJ6JNfCiFRlTzItfElyrZYhr/5U+Ba0NupTa2BEz8u36VX72rpmEDM0HperI+Bq+wvJtX+SXHtGZfYk1zdPVfYk0/2jKtdmzDRIrlUz5KCitVG/qwF4s7bRdb8EWyDV9heSa/8kufaM5No/qcqeZNr/6xuZ5Fotmf4khBBCCCGE8IhXBxWtra1MnTqV8PBw9yfRAZYtW0ZycjILFy7E6XR6c5eEEEIIIYQQHvLqoCIkJIRt27YxZ84c99eKi4upqakhLy+PuLg4tm/frlt7F+xnePatf+KZzQu4YD+jW13VtfXgaNVOj3prit/p8yWs3jiPTbtXB1RtPbRf0f711nXUzJzrtsvQ2uy9vjZrrl0uaG3ybptmzbXLBS2N0N7ivTZNm+sO704bUp07f851RwdcaQBnm/faNGuuO5xaX/sDpYOKtWvXMmPGDBYvXkxaWhpBQUFER0f32CY/P5+0tDQA0tLSyM/P1639HYUbyJz9LI898Aw7C1/Tra7q2p4q/wT2vwIFG+GT17WDMNVGRieSOfu5gKvtqbJdkL9BWy/4Azi88AJqxly7XHB4m5bnT9+Aoi3aC6lqZsx1h0Pr3wNvao8Pv+udQZwZc+1o1V43Cv4A+a9CWa532jVjrlub4JPXtL+LAOWfqm9Tde78NdeX7ZD/ChRugn2vwNnPvdOuGXPdUA37X9b6GqDmlG/3R9mg4uDBgxw9epR9+/aRkpJCbGxsr9vZ7XYiIyMBiIyMxG6367YPdZeqGTb4dqIiR3CxsVq3uqpre6KxBs4Uae+et12Gy3Vw9ANf75UxXayA6rKuMxWNtXDMCwcFZsx11edQWw7tl7WlvkobPAv9ffGp1r9tl7XHteVQdUR9u2bMdVmu9prddll7HTlXAnWnfb1XxnTkfe1gtzPXZz6Dphq1barOnb/m+vC72hmhtquv1yfzvPPmphl9/p42YO7MdelOcDp8tz/KBhXZ2dksWrQIAKvVSlJSUq/bDRkyhIYG7bxNQ0MDNpuNoqIi0tPTOXJE+0v27rvvsmrVKjIzM93bXstisbiXiooKAIYOHs7FS1XUXjrLsIjhN/U8KioqlNS+tq5ey+xZD9HUcKVHW59/dlJJW937Qw999bXedfVa/uXHT+Js7dZQB3y846/K+9qMuX7uVy/R0e2F0uWETa9uk1wreO7/+9r7uLqdBepoh9/8+wt+n+ve+sPfc71v10HodhbI0QqP/uhfAy7TgZDrowdP9minseEy35mZ7teZ7qs/9Kivqp8tFgtfnOg5Fau2ppZ7xk4xba5V9bU1yErV2XM92qo+V83wW2OV/Wy/jrJLytbV1eFwOHA4HKxfv55f/vKXvW43ffp0XnzxRebNm8fOnTuZNm0aEyZMID093b1NaGgoNTXaWwoRERG91ul+Y/DOOyCmTX6UDR+uwOXqYGHazc2Di4uLU1L72rp6uWyHws1d755jgb+ddpeStqCrP2obqnhtxwrO1p4gLmYc941L73etvvra09qq+rq+Cg79GRxX50JbrDDr+5NwvaC2r82Y6/PHtHdgOqeXBYXAPy/+Pitfk1zr7XQhfJEPznbtcfAAWPn//o3/2vpvurcFarPn77kuy4Wzh3EP4oJD4Y13XiRy+Iu6t9X9zsAqsufvuS7eenVqyNXSEZFh7Nq3lbAhujel9LVar/qq+hm0Y5CGqq7Ht94WRfGxAwy4Rf+2AiHXKvs6f4M2I6XT7bcP51ztGYKsSpr7WsoGFRkZGWRmZpKYmEh9fb37TEV6ejoFBQWcOHGCpUuXMnfuXGw2G8nJySQkJLB8+fKv1CopKWHNmjVs2rSJkpISxo0bd0P7cJstlmXzX9fzaXmltifCbDB6Jpz4GNqaYcjtkPiA+najIm/n6R9tCrjanhhyO8RP0Q7CsMDgaPjG/erbNWOuo++GhnNw7qh2mjd6NMROVN+uGXMdO0mbktN5c9jh47T+Vs2MuR59v/YBy8bz2ut1wjSIvLk3tPvFjLlOegAO/hmu2AELjP47lAwoulOdO3/N9Te/Dwf/BG1Xp+UkPYCSAcW1zJjre37Q9eZmUDCM/0d8NqAAhYOKqVOnuqcvzZw5k5iYGAC2bt36lW3XrFnT43F5eTk5OTmUlZWxcuVKoqOjefbZZ6mtreXhhx9WtcuGMTxRW3avgUkmvGOmN42crB2EAdzAmUHhgdH3wzdSIPc/tT9SQg2LBcbN7vpwtuRanaBg+NsfaH2d+5/eGSibVfBA7Q7Srg6wyB26lBo4CKb+WOvr3LUwLM7Xe2RcYUNg+qP+k2vld9R2Op2EhIT063vi4+PZvHmz+/EPf6jfkfHOwtf5tOQ9goKsfHvSI0wZOzsgagv/5euDLjNl2td9bSa+7mvJtVDB1wdepsq1HxzkmoW/9LXy3bBareTk5Khupl8eSnmCpx7ewGfH9d8vlbWF6ItkWhiR5FoYkeRaGJWfjG28K3vf73jipWQeuPcxPjjwCjX1lWz5y297rOtR++09z2FvusCOgg091oXQm2RaGJHkWhiR5FoYlfLpT/7owRk/wxYRw0dFm5if+jS/fvMhnpz7CuG32NzretS+d+xsXt6+jCfnvsypqkPudSH0JpkWRiS5FkYkuRZGZcpBBcAdUXdx8VIVTS31hA4YxOXWRrBY3Ou2iOivL/I1tYcPG8XoERMJtoZw952T3etGMrD3K/zqUkuv2nruoz+TTOtHcu0/JNf6UJlpPetLriXX/REIuTZLpsGEg4rvTH7Evb50znre+Xgtv5j/Btl5L2ANCnavz5u5zOPaQM9P4Bnw03iTFV5dSmVtI5FM609y7XuSa32pzp3k+sZIrvUlufYvFpeqO3L4UPeboXgqdDDMeFz/2tfWVWH3GvjWU12P9+7dS25uLrNmzXL/m5KSwq5du5g0aRI2m8297YEDBygsLGTJkiUAbNmyBbvdzrx588jLy8PlchEbG0tlZSWpqamEhYWpfTJCcn1V91xLpgOfyuxJriXXvqDytVqv+t7INEiuzcaUH9Q2q/HjxxMbG+v+NyUlBYDq6mpsNhsbN25kyZIlZGVlMWXKFMLDw93f29LSQmpqKqWlpSQkJDBq1Ciys7OJj4+ntLTUV09JmJxkWhiR5FoYkeTa+GRQYSJZWVlERUWxYMECoqKiOHnyJAAxMTHY7XYyMjJYt24dq1at4tixYxQXF9Pc3ExxcTGhoaHk5uYyZswYkpKSSEpKIj4+3v01IXxBMi2MSHItjEhybXwy/elrGGWaiAh8kmuN5NpYZPqTRnJtHDL9qYvk2lxMf6bi5NlDAVlbiOuRXAsjklwLI1KVPcm08DbTDyr2H8nmXF1FwNUW4nok18KIJNfCiFRlTzItvM30g4qYofG4XB0BV1uI65FcCyOSXAsjUpU9ybTwNtPdp+Ja3a/rHEi1hbgeybUwIsm1MCJV2ZNMC28z/ZkKIYQQQgghhGe8OqhobW1l6tSphIeHuy8lBrBs2TKSk5NZuHAhTqfTm7skhBBCCCGE8JBXBxUhISFs27aNOXPmuL9WXFxMTU0NeXl5xMXFsX37dt3aO32+hNUb57Fp92rdanqz/s1ydcCFE9r65Xqf7opQQGXu/DXTAI42qC7R1tuu+HZfhP7MmuuWRqg8rK13OHy7L0J/Zs11Uw18eUhbN96NC0RflA4q1q5dy4wZM1i8eDFpaWkEBQURHR3dY5v8/HzS0tIASEtLIz8/X7f2R0Ynkjn7Od3qebv+zXB1QNEf4cj72uPCzWCv9O0+CX2pzJ0/ZhqgvQUOvAklO7THBW9Ca5Nv90noy4y5bqqFgo1QlqM9LtwsAwujMWOuzx2Dz7bAsd3a4yP6vVcs/JyyQcXBgwc5evQo+/btIyUlhdjY2F63s9vtREZGAhAZGYndble1S6Zgr4RLF7r+MLVf7vrFFiJQnSmCKw3aoBm0d3dP7fftPgnhqWMfQVtz1+Omi3D+uO/2Rwg9nPwY2rudTa47A811vtsf4T3KBhXZ2dksWrQIAKvVSlJSUq/bDRkyhIaGBgAaGhqw2WwUFRWRnp7OkSNHAHj//fdZvXo1P//5z+nrBuAWi8W9VFRU6PY8KioqlNS+tq5ey3dnf5/mxuYebZWVHlfSlizeXcyc6/987nm45lf/fzf9yec/E1k8X1Rmz99z/en+wh7tONs7ePyxn/r8ZyKLZ4vK12q96qvKtMVi4czpMz3aqqmp4W+/OdHnPxdZPF++jrJBRV1dHQ6HA4fDwfr16xk3blyv202fPp2cHO3c786dO5k2bRoTJkwgPT3dvc3u3btZtmwZYWFhFBcX91rH5XK5l7i4OABqG6p4bccKPil5l/1Htt7U84iLi+u1tqf1r62r1/Jx4TYihw1yt2MdACnfH62kLVm8u3gj157WVpXrZ/9nKSG3dLUTHAr/+uuHfP4zkcXzRWX2/D3X6Y9NJnhgVzuh4UH8cefvff4zkcWzRa/jBJW5VpVpl8vF3yTHEtTthgXDR9xKacVnPv+5yOL58nWU3aciIyODzMxMEhMTqa+vd5+pSE9Pp6CggBMnTrB06VLmzp2LzWYjOTmZhIQEli9f/pVaixYt4sUXX6S8vJyQkJAb3oeoyNt5+kebdHtO3q5/M0JugYnzoGwXtF2GmLEwcrKv90roSWXu/DHTAIOjYfw/wsm92hSo+KkQFefrvRJ6MmOu7/imdgKu8hAED4C7Z0HoYF/vldCTGXM99tsw4BaoLYewSBjzbbCa/q5o5qDsxzx16lT39KWZM2cSExMDwNatW7+y7Zo1a3o8Li8vJycnh7KyMlauXInD4cDlcjF+/Pg+p1GJLmFDYMJcX++FEPoaeifcu8DXeyGEvkZ8U1uEMIqgIPjG/doizEX52NHpdPbr7AJAfHw8mzdvdj9OTEwkMTFR710TQgghhBBC6ED5fSqsVqv7MxNCCCGEEEII4/Hqze+EEEIIIYQQxiODCiGEEEIIIYRHDPl5/IER6mrpVVvPfRTmILkWRqQye5Jr4QsqX6v1qi+ZFipYXDdy4VkhhBBCCCGE6INMfxJCCCGEEEJ4RAYVQgghhBBCCI/IoEIIIYQQQgjhERlUCCGEEEIIITwigwohhBBCCCGER2RQIYQQQgghhPCIDCqEEEIIIYQQHpFBhRBCCCGEEMIjMqgQQgghhBBCeEQGFUIIIYQQQgiPyKBCCCGEEEII4ZH/D9DWODxfXggsAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + "# ## Create the time-evo op circuit\n", + "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "# Create instruction for rotation about XX+YY-ZZ:\n", + "Rxyz_circ = QuantumCircuit(2)\n", + "Rxyz_circ.rxx(t,0,1)\n", + "Rxyz_circ.ryy(t,0,1)\n", + "Rxyz_circ.rzz(-t,0,1)\n", + "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", + "\n", + "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "trotter_step_circ = QuantumCircuit(qr)\n", + "for i, color in enumerate(interaction_list):\n", + " for interaction in color:\n", + " trotter_step_circ.append(Rxyz_instr, interaction)\n", + "\n", + "\n", + "qc_evol = QuantumCircuit(qr)\n", + "for _ in range(num_trotter_steps):\n", + " qc_evol.compose(trotter_step_circ, inplace=True)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use an optimized circuit for state preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", + "for idx in range(n_qubits):\n", + " if idx % 2 == 0:\n", + " controlled_state_prep.swap(idx, idx+1)\n", + " else:\n", + " controlled_state_prep.cx(idx+1, idx)\n", + " controlled_state_prep.cx(idx, idx+1)\n", + "\n", + "\n", + "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(n_qubits)\n", + "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(0)\n", + "qc_real.h(0)\n", + "\n", + "S_real_circ = qc_real.decompose().copy()\n", + "\n", + "# # Create hadamard test circuit for imaginary part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag = QuantumCircuit(qr)\n", + "qc_imag.h(0)\n", + "qc_imag.sdg(0)\n", + "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(n_qubits)\n", + "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(0)\n", + "qc_imag.h(0)\n", + "\n", + "\n", + "S_imag_circ = qc_imag.decompose().copy()\n", + "\n", + "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 146\n" + ] + } + ], + "source": [ + "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", + "The derivation of the Hadamard test assumes that the operator $\\hat{O}$ which represents a collection of terms in $H$ preserves Hamming weight. For this reason, we decompose $H$ into ZZ:\n", + "\n", + "$$ \\text{ZZ} = \\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & -1 & 0 & 0\\\\\n", + "0 & 0 & -1 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "\n", + "$$ \\text{SWAP} = \\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "\n", + " $$ \\text{mSWAP} = \\begin{pmatrix}\n", + "-1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & -1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "instead of ZZ, XX, and YY.\n", + "Using the former decomposition yields terms that are all unitary AND number conserving." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", + "mswap = mswap_op.to_instruction()\n", + "mswap.label = 'mswap'\n", + "\n", + "# Hamiltonian terms\n", + "hamiltonian_circuits = []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " qr = QuantumRegister(n_qubits)\n", + " qc_ham = QuantumCircuit(qr)\n", + " active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", + " if 'X' in pauli.to_label():\n", + " qc_ham.swap(*active_qubits)\n", + " if 'Y' in pauli.to_label():\n", + " qc_ham.append(mswap,qargs=active_qubits)\n", + " for i in active_qubits:\n", + " qc_ham.z(i)\n", + " if 'Z' in pauli.to_label():\n", + " for i in active_qubits:\n", + " qc_ham.z(i)\n", + " hamiltonian_circuits.append(qc_ham)\n", + "\n", + "\n", + "\n", + "# Real part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_1 = QuantumCircuit(qr)\n", + "qc_real_1.h(0)\n", + "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real_1.x(n_qubits)\n", + "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_real_circ_1 = qc_real_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_2 = QuantumCircuit(qr)\n", + "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real_2.x(0)\n", + "qc_real_2.h(0)\n", + "H_real_circ_2 = qc_real_2.decompose().copy()\n", + "\n", + "# Imaginary part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_1 = QuantumCircuit(qr)\n", + "qc_imag_1.h(0)\n", + "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_1.x(n_qubits)\n", + "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_2 = QuantumCircuit(qr)\n", + "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_2.x(0)\n", + "qc_imag_2.sdg(0)\n", + "qc_imag_2.h(0)\n", + "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Execute using a quantum primitive" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate circuits to calculate all matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "S_real_circuits, S_imag_circuits = [], []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " \n", + "\n", + " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " S_real_circuits.append(circuit_real)\n", + " S_imag_circuits.append(circuit_imag)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "count = 0\n", + "H_real_circuits, H_imag_circuits = [], [] \n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " circuit_real = H_real_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " circuit_imag = H_imag_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " H_real_circuits.append(circuit_real)\n", + " H_imag_circuits.append(circuit_imag)\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Execute circuits for $\\tilde{S}$ with the Estimator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "210 circuits to run\n" + ] + } + ], + "source": [ + "\n", + "\n", + "estimator = Estimator()\n", + "\n", + "jobs = {'S': {'real':[], 'imag':[]},\n", + " 'H': {'real':[], 'imag':[]}\n", + " } # store executed jobs\n", + "\n", + "\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size_S = 20\n", + "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", + "\n", + "\n", + "\n", + "print(len(S_real_circuits), 'circuits to run')\n", + "\n", + "S_real_results_list, S_imag_results_list = [], []\n", + "for i in range(len(job_idxs_S)-1):\n", + "\n", + " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['real'].append(job.job_id())\n", + " S_real_results = job.result()\n", + "\n", + " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['imag'].append(job.job_id())\n", + " S_imag_results = job.result()\n", + "\n", + "\n", + " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", + " np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "11970 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs['H']['real'], jobs['H']['imag'] = [], []\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size = 50\n", + "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", + "\n", + "print(len(H_imag_circuits), 'circuits to run')\n", + "\n", + "H_real_results_list, H_imag_results_list = [], []\n", + "for i in range(len(job_idxs)-1):\n", + " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", + "\n", + "\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " # print(f\"job id: {job_real.job_id()}\")\n", + " jobs['H']['real'].append(job_real.job_id())\n", + " H_real_results = job_real.result()\n", + "\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " # print(f\"job id: {job_imag.job_id()}\")\n", + " jobs['H']['imag'].append(job_imag.job_id())\n", + " H_imag_results = job_imag.result()\n", + "\n", + "\n", + " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", + " np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process and analyze results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + "\n", + " eff_count = count % (job_size_S)\n", + " res_idx = count // (job_size_S)\n", + "\n", + " S_real_results = S_real_results_list[res_idx]\n", + " S_imag_results = S_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = S_real_results.values[eff_count]\n", + " expval_imag = S_imag_results.values[eff_count]\n", + "\n", + " # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + " # Fill-in matrix elements\n", + " S_circ[idx_bra, idx_ket] = expval\n", + " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", + "\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the matrix elements of $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " eff_count = count % (job_size)\n", + " res_idx = count // (job_size)\n", + "\n", + " H_real_results = H_real_results_list[res_idx]\n", + " H_imag_results = H_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = H_real_results.values[eff_count]\n", + " expval_imag = H_imag_results.values[eff_count]\n", + "\n", + " # # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + "\n", + " # Fill-in matrix elements\n", + " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", + " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", + " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", + "\n", + "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", + "\n", + "and get an estimate of the ground state energy $c_{min}$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The estimated ground state energy is: 19.001772561386353\n", + "The estimated ground state energy is: 8.886186757411066\n", + "The estimated ground state energy is: 1.7414658785731836\n", + "The estimated ground state energy is: 2.6407110576585704\n", + "The estimated ground state energy is: -2.1789120241090623\n", + "The estimated ground state energy is: -1.802298672047528\n", + "The estimated ground state energy is: -5.394027756861737\n", + "The estimated ground state energy is: -3.7933471412719424\n", + "The estimated ground state energy is: -6.680804698251523\n", + "The estimated ground state energy is: -5.256784025157172\n", + "The estimated ground state energy is: -7.286989741211739\n", + "The estimated ground state energy is: -6.081949425638568\n", + "The estimated ground state energy is: -7.753950647115604\n", + "The estimated ground state energy is: -6.611646116146415\n", + "The estimated ground state energy is: -6.618399572796952\n", + "The estimated ground state energy is: -7.40844667021687\n", + "The estimated ground state energy is: -8.136604965075088\n", + "The estimated ground state energy is: -8.59843083841513\n", + "The estimated ground state energy is: -8.372146644647229\n", + "The estimated ground state energy is: -9.600091507679045\n" + ] + } + ], + "source": [ + "gnd_en_circ_est_list = []\n", + "for d in range(1, krylov_dim+1):\n", + " # Solve generalized eigenvalue problem\n", + " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", + " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", + " print('The estimated ground state energy is: ', gnd_en_circ_est)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", + "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", + "plt.legend()\n", + "plt.xlabel('Krylov space dimension')\n", + "plt.ylabel('Energy')\n", + "plt.title('Estimating Ground state energy with Quantum Krylov')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Take home exercise:\n", + "Compute ground state energy with other methods" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.17" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From e85b5323cc516670f1b137fc09c752734eb63e7a Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 8 Feb 2024 11:30:57 -0700 Subject: [PATCH 02/22] switch to Hadamard test with pauli measurements --- docs/krylov-subspace-demo.ipynb | 180 ++++++++++++++++++-------------- 1 file changed, 103 insertions(+), 77 deletions(-) diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb index aa7e11a..a410ee1 100644 --- a/docs/krylov-subspace-demo.ipynb +++ b/docs/krylov-subspace-demo.ipynb @@ -97,15 +97,9 @@ { "data": { "text/plain": [ - "SparsePauliOp(['ZZIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIZZ', 'XXIIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIXX', 'YYIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j])" + "SparsePauliOp(['ZZIIII', 'IZZIII', 'IIZZII', 'IIIZZI', 'IIIIZZ', 'XXIIII', 'IXXIII', 'IIXXII', 'IIIXXI', 'IIIIXX', 'YYIIII', 'IYYIII', 'IIYYII', 'IIIYYI', 'IIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" ] }, "execution_count": 2, @@ -115,7 +109,7 @@ ], "source": [ "# Define problem Hamiltonian. Kicked Ising in this case\n", - "n_qubits = 20\n", + "n_qubits = 6\n", "J = 1 # coupling strength for ZZ interaction\n", "\n", "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", @@ -172,9 +166,9 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 4, @@ -206,9 +200,9 @@ "outputs": [ { "data": { - "image/png": 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", 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" + "
" ] }, "execution_count": 5, @@ -277,9 +271,9 @@ }, { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 6, @@ -334,7 +328,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 16644\n" + "The circuit has 2Q gates depth: 4447\n" ] } ], @@ -406,9 +400,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 8, @@ -459,9 +453,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" + "
" ] }, "execution_count": 9, @@ -496,9 +490,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, "execution_count": 10, @@ -547,7 +541,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 146\n" + "The circuit has 2Q gates depth: 76\n" ] } ], @@ -604,28 +598,38 @@ "metadata": {}, "outputs": [], "source": [ - "mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", - "mswap = mswap_op.to_instruction()\n", - "mswap.label = 'mswap'\n", - "\n", - "# Hamiltonian terms\n", - "hamiltonian_circuits = []\n", + "# mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", + "# mswap = mswap_op.to_instruction()\n", + "# mswap.label = 'mswap'\n", + "\n", + "# # Hamiltonian terms\n", + "# hamiltonian_circuits = []\n", + "# for idx_ket in range(krylov_dim):\n", + "# for idx_bra in range(idx_ket + 1):\n", + "# for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "# qr = QuantumRegister(n_qubits)\n", + "# qc_ham = QuantumCircuit(qr)\n", + "# active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", + "# if 'X' in pauli.to_label():\n", + "# qc_ham.swap(*active_qubits)\n", + "# if 'Y' in pauli.to_label():\n", + "# qc_ham.append(mswap,qargs=active_qubits)\n", + "# for i in active_qubits:\n", + "# qc_ham.z(i)\n", + "# if 'Z' in pauli.to_label():\n", + "# for i in active_qubits:\n", + "# qc_ham.z(i)\n", + "# hamiltonian_circuits.append(qc_ham)\n", + "\n", + "#TODO: can make a compact list of non-commuting observables to measure separately \n", + "# Hamiltonian terms to measure\n", + "observable_list = []\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " qr = QuantumRegister(n_qubits)\n", - " qc_ham = QuantumCircuit(qr)\n", - " active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", - " if 'X' in pauli.to_label():\n", - " qc_ham.swap(*active_qubits)\n", - " if 'Y' in pauli.to_label():\n", - " qc_ham.append(mswap,qargs=active_qubits)\n", - " for i in active_qubits:\n", - " qc_ham.z(i)\n", - " if 'Z' in pauli.to_label():\n", - " for i in active_qubits:\n", - " qc_ham.z(i)\n", - " hamiltonian_circuits.append(qc_ham)\n", + " # print(pauli)\n", + " observable = pauli[::-1].to_label() + 'Z'\n", + " observable_list.append(observable)\n", "\n", "\n", "\n", @@ -716,13 +720,14 @@ "H_real_circuits, H_imag_circuits = [], [] \n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", + " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", "\n", - " circuit_real = H_real_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", - " circuit_imag = H_imag_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", @@ -785,7 +790,7 @@ "\n", "\n", " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - " np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" ] }, { @@ -804,7 +809,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "11970 circuits to run\n" + "3150 circuits to run\n" ] } ], @@ -813,7 +818,10 @@ "\n", "jobs['H']['real'], jobs['H']['imag'] = [], []\n", "shots = 100000\n", - "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "\n", + "\n", + "\n", "\n", "job_size = 50\n", "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", @@ -825,19 +833,19 @@ " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", "\n", "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_real.job_id()}\")\n", " jobs['H']['real'].append(job_real.job_id())\n", " H_real_results = job_real.result()\n", "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_imag.job_id()}\")\n", " jobs['H']['imag'].append(job_imag.job_id())\n", " H_imag_results = job_imag.result()\n", "\n", "\n", " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" ] }, { @@ -951,26 +959,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "The estimated ground state energy is: 19.001772561386353\n", - "The estimated ground state energy is: 8.886186757411066\n", - "The estimated ground state energy is: 1.7414658785731836\n", - "The estimated ground state energy is: 2.6407110576585704\n", - "The estimated ground state energy is: -2.1789120241090623\n", - "The estimated ground state energy is: -1.802298672047528\n", - "The estimated ground state energy is: -5.394027756861737\n", - "The estimated ground state energy is: -3.7933471412719424\n", - "The estimated ground state energy is: -6.680804698251523\n", - "The estimated ground state energy is: -5.256784025157172\n", - "The estimated ground state energy is: -7.286989741211739\n", - "The estimated ground state energy is: -6.081949425638568\n", - "The estimated ground state energy is: -7.753950647115604\n", - "The estimated ground state energy is: -6.611646116146415\n", - "The estimated ground state energy is: -6.618399572796952\n", - "The estimated ground state energy is: -7.40844667021687\n", - "The estimated ground state energy is: -8.136604965075088\n", - "The estimated ground state energy is: -8.59843083841513\n", - "The estimated ground state energy is: -8.372146644647229\n", - "The estimated ground state energy is: -9.600091507679045\n" + "The estimated ground state energy is: 4.996846612987735\n", + "The estimated ground state energy is: -2.0169805323125676\n", + "The estimated ground state energy is: -1.2544170610566237\n", + "The estimated ground state energy is: -1.1598799405018336\n", + "The estimated ground state energy is: -0.9582267795672128\n", + "The estimated ground state energy is: -3.7140982342407463\n", + "The estimated ground state energy is: -4.007699282777389\n", + "The estimated ground state energy is: -3.838242692778295\n", + "The estimated ground state energy is: -4.096162385313948\n", + "The estimated ground state energy is: -4.363812874300807\n", + "The estimated ground state energy is: -4.52896248339562\n", + "The estimated ground state energy is: -4.630593705244608\n", + "The estimated ground state energy is: -4.708647040966806\n", + "The estimated ground state energy is: -4.550912411928362\n", + "The estimated ground state energy is: -4.6168766143968\n", + "The estimated ground state energy is: -4.677402157138201\n", + "The estimated ground state energy is: -4.813755791046398\n", + "The estimated ground state energy is: -4.997815001632314\n", + "The estimated ground state energy is: -5.056110423013211\n", + "The estimated ground state energy is: -4.957529560835039\n" ] } ], @@ -990,14 +998,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1011,6 +1017,26 @@ "plt.show()" ] }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-5.000000000000002" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1036,7 +1062,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.17" + "version": "3.10.13" } }, "nbformat": 4, From 25b35b7a44a408fff8179fbc3f3938107a2e6ebe Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 8 Feb 2024 16:20:52 -0700 Subject: [PATCH 03/22] attempting to measure commuting observables simultaneously --- docs/krylov-subspace-demo.ipynb | 301 +++++++++++++++++++++++++++++--- 1 file changed, 273 insertions(+), 28 deletions(-) diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb index a410ee1..b84b268 100644 --- a/docs/krylov-subspace-demo.ipynb +++ b/docs/krylov-subspace-demo.ipynb @@ -44,7 +44,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 108, "metadata": {}, "outputs": [], "source": [ @@ -57,11 +57,11 @@ "\n", "from qiskit.quantum_info import SparsePauliOp, Operator\n", "from qiskit.circuit import Parameter\n", - "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n", "from qiskit.circuit.library import PauliEvolutionGate\n", "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", "from qiskit.providers.fake_provider import FakePrague\n", - "from qiskit.primitives import Estimator\n", + "from qiskit.primitives import Estimator, Sampler\n", "\n", "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", " s_vals, s_vecs = sp.linalg.eigh(s)\n", @@ -594,7 +594,125 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['IZZIII', 'IIZZII', 'IIIZZI', 'ZZIIII', 'IIIIZZ']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IZZIII\n", + "['I', 'Z', 'Z', 'I', 'I', 'I']\n", + "IIZZII\n", + "['I', 'Z', 'Z', 'Z', 'I', 'I']\n", + "IIIZZI\n", + "['I', 'Z', 'Z', 'Z', 'Z', 'I']\n", + "ZZIIII\n", + "['Z', 'Z', 'Z', 'Z', 'Z', 'I']\n", + "IIIIZZ\n", + "['Z', 'Z', 'Z', 'Z', 'Z', 'Z']\n", + "['IXXIII', 'IIXXII', 'IIIXXI', 'XXIIII', 'IIIIXX']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IXXIII\n", + "['I', 'X', 'X', 'I', 'I', 'I']\n", + "IIXXII\n", + "['I', 'X', 'X', 'X', 'I', 'I']\n", + "IIIXXI\n", + "['I', 'X', 'X', 'X', 'X', 'I']\n", + "XXIIII\n", + "['X', 'X', 'X', 'X', 'X', 'I']\n", + "IIIIXX\n", + "['X', 'X', 'X', 'X', 'X', 'X']\n", + "['IYYIII', 'IIYYII', 'IIIYYI', 'YYIIII', 'IIIIYY']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IYYIII\n", + "['I', 'Y', 'Y', 'I', 'I', 'I']\n", + "IIYYII\n", + "['I', 'Y', 'Y', 'Y', 'I', 'I']\n", + "IIIYYI\n", + "['I', 'Y', 'Y', 'Y', 'Y', 'I']\n", + "YYIIII\n", + "['Y', 'Y', 'Y', 'Y', 'Y', 'I']\n", + "IIIIYY\n", + "['Y', 'Y', 'Y', 'Y', 'Y', 'Y']\n" + ] + }, + { + "data": { + "text/plain": [ + "['ZZZZZZ', 'XXXXXX', 'YYYYYY']" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "non_commuting_ops_list = []\n", + "paulis_to_non_commuting_ops_dict = {}\n", + "for grp_idx, paulis in enumerate(H_op.paulis.group_commuting(qubit_wise=True)):\n", + " print(paulis)\n", + "\n", + " total_op = ['I' for _ in range(len(paulis[0]))]\n", + " print(total_op)\n", + " for pauli in paulis:\n", + " pauli = pauli.to_label()\n", + " print(pauli)\n", + "\n", + " for idx, term in enumerate(pauli):\n", + " if total_op[idx] == 'I':\n", + " total_op[idx] = term\n", + " print(total_op)\n", + "\n", + " non_commuting_ops_list.append(\"\".join(total_op))\n", + "\n", + " for pauli in paulis:\n", + " pauli = pauli.to_label()\n", + " paulis_to_non_commuting_ops_dict[pauli] = \"\".join(total_op)\n", + "\n", + "non_commuting_ops_list\n" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'IZZIII': 'ZZZZZZ',\n", + " 'IIZZII': 'ZZZZZZ',\n", + " 'IIIZZI': 'ZZZZZZ',\n", + " 'ZZIIII': 'ZZZZZZ',\n", + " 'IIIIZZ': 'ZZZZZZ',\n", + " 'IXXIII': 'XXXXXX',\n", + " 'IIXXII': 'XXXXXX',\n", + " 'IIIXXI': 'XXXXXX',\n", + " 'XXIIII': 'XXXXXX',\n", + " 'IIIIXX': 'XXXXXX',\n", + " 'IYYIII': 'YYYYYY',\n", + " 'IIYYII': 'YYYYYY',\n", + " 'IIIYYI': 'YYYYYY',\n", + " 'YYIIII': 'YYYYYY',\n", + " 'IIIIYY': 'YYYYYY'}" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paulis_to_non_commuting_ops_dict" + ] + }, + { + "cell_type": "code", + "execution_count": 104, "metadata": {}, "outputs": [], "source": [ @@ -621,15 +739,35 @@ "# qc_ham.z(i)\n", "# hamiltonian_circuits.append(qc_ham)\n", "\n", - "#TODO: can make a compact list of non-commuting observables to measure separately \n", - "# Hamiltonian terms to measure\n", - "observable_list = []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " # print(pauli)\n", - " observable = pauli[::-1].to_label() + 'Z'\n", - " observable_list.append(observable)\n", + "# ## TODO: how does runtime estimator group commuting observables?\n", + "# # Hamiltonian terms to measure\n", + "# observable_list = []\n", + "# for idx_ket in range(krylov_dim):\n", + "# for idx_bra in range(idx_ket + 1):\n", + "# for pauli in non_commuting_ops_list:\n", + "# # print(pauli)\n", + "# observable = pauli + 'Z'\n", + "# observable_list.append(observable)\n", + "\n", + "# Measurement of Hamiltonian terms\n", + "hamiltonian_measurement_circs = {}\n", + "for obs in non_commuting_ops_list:\n", + " qr = QuantumRegister(n_qubits+1)\n", + " cr = ClassicalRegister(n_qubits+1)\n", + " qc_meas = QuantumCircuit(qr, cr)\n", + " qc_meas.measure(0, 0)\n", + " for idx, term in enumerate(obs):\n", + " if term == 'Z':\n", + " qc_meas.measure(idx+1, idx+1)\n", + " if term == 'X':\n", + " qc_meas.h(idx+1)\n", + " qc_meas.measure(idx+1, idx+1)\n", + " if term == 'Y':\n", + " qc_meas.sdg(idx+1)\n", + " qc_meas.h(idx+1)\n", + " qc_meas.measure(idx+1, idx+1)\n", + " hamiltonian_measurement_circs[obs] = qc_meas.copy()\n", + "\n", "\n", "\n", "\n", @@ -687,7 +825,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 105, "metadata": {}, "outputs": [], "source": [ @@ -712,7 +850,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 106, "metadata": {}, "outputs": [], "source": [ @@ -721,14 +859,14 @@ "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " for pauli in non_commuting_ops_list:\n", "\n", - " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = H_real_circ_1.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", - " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = H_imag_circ_1.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", " H_real_circuits.append(circuit_real)\n", @@ -746,7 +884,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 107, "metadata": {}, "outputs": [ { @@ -797,24 +935,24 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "And for $\\tilde{H}$" + "And use Sampler for $\\tilde{H}$" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 109, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "3150 circuits to run\n" + "630 circuits to run\n" ] } ], "source": [ - "estimator = Estimator()\n", + "sampler = Sampler()\n", "\n", "jobs['H']['real'], jobs['H']['imag'] = [], []\n", "shots = 100000\n", @@ -833,12 +971,12 @@ " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", "\n", "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " job_real = sampler.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_real.job_id()}\")\n", " jobs['H']['real'].append(job_real.job_id())\n", " H_real_results = job_real.result()\n", "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " job_imag = sampler.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_imag.job_id()}\")\n", " jobs['H']['imag'].append(job_imag.job_id())\n", " H_imag_results = job_imag.result()\n", @@ -864,7 +1002,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 110, "metadata": {}, "outputs": [], "source": [ @@ -903,6 +1041,112 @@ "And the matrix elements of $\\tilde{H}$" ] }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 0.01561,\n", + " 2: 0.01528,\n", + " 4: 0.01528,\n", + " 6: 0.01556,\n", + " 8: 0.01563,\n", + " 10: 0.01563,\n", + " 12: 0.01572,\n", + " 14: 0.01533,\n", + " 16: 0.01513,\n", + " 18: 0.01622,\n", + " 20: 0.01547,\n", + " 22: 0.01542,\n", + " 24: 0.01513,\n", + " 26: 0.01537,\n", + " 28: 0.01517,\n", + " 30: 0.01564,\n", + " 32: 0.01577,\n", + " 34: 0.01568,\n", + " 36: 0.0154,\n", + " 38: 0.01654,\n", + " 40: 0.01548,\n", + " 42: 0.01613,\n", + " 44: 0.01552,\n", + " 46: 0.01565,\n", + " 48: 0.01558,\n", + " 50: 0.01567,\n", + " 52: 0.01529,\n", + " 54: 0.01524,\n", + " 56: 0.01575,\n", + " 58: 0.01561,\n", + " 60: 0.01569,\n", + " 62: 0.01569,\n", + " 64: 0.01575,\n", + " 66: 0.01506,\n", + " 68: 0.01534,\n", + " 70: 0.01512,\n", + " 72: 0.01614,\n", + " 74: 0.01672,\n", + " 76: 0.01553,\n", + " 78: 0.01572,\n", + " 80: 0.01526,\n", + " 82: 0.01591,\n", + " 84: 0.01572,\n", + " 86: 0.01563,\n", + " 88: 0.016,\n", + " 90: 0.01579,\n", + " 92: 0.01547,\n", + " 94: 0.01604,\n", + " 96: 0.01549,\n", + " 98: 0.01629,\n", + " 100: 0.01544,\n", + " 102: 0.01589,\n", + " 104: 0.01479,\n", + " 106: 0.01599,\n", + " 108: 0.01586,\n", + " 110: 0.01574,\n", + " 112: 0.01576,\n", + " 114: 0.01567,\n", + " 116: 0.01526,\n", + " 118: 0.01532,\n", + " 120: 0.01529,\n", + " 122: 0.01624,\n", + " 124: 0.01545,\n", + " 126: 0.01604}" + ] + }, + "execution_count": 130, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H_real_results_list[0].quasi_dists[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'int' object has no attribute 'replace'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[131], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mqiskit\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mresult\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m marginal_distribution\n\u001b[0;32m----> 2\u001b[0m \u001b[43mmarginal_distribution\u001b[49m\u001b[43m(\u001b[49m\u001b[43mH_real_results_list\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mquasi_dists\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/opt/miniconda3/envs/krylov-sk/lib/python3.10/site-packages/qiskit/result/utils.py:224\u001b[0m, in \u001b[0;36mmarginal_distribution\u001b[0;34m(counts, indices, format_marginal)\u001b[0m\n\u001b[1;32m 199\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmarginal_distribution\u001b[39m(\n\u001b[1;32m 200\u001b[0m counts: \u001b[38;5;28mdict\u001b[39m,\n\u001b[1;32m 201\u001b[0m indices: Optional[Sequence[\u001b[38;5;28mint\u001b[39m]] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 202\u001b[0m format_marginal: \u001b[38;5;28mbool\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m,\n\u001b[1;32m 203\u001b[0m ) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m Dict[\u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28mint\u001b[39m]:\n\u001b[1;32m 204\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"Marginalize counts from an experiment over some indices of interest.\u001b[39;00m\n\u001b[1;32m 205\u001b[0m \n\u001b[1;32m 206\u001b[0m \u001b[38;5;124;03m Unlike :func:`~.marginal_counts` this function respects the order of\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[38;5;124;03m is invalid.\u001b[39;00m\n\u001b[1;32m 223\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m--> 224\u001b[0m num_clbits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcounts\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkeys\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreplace\u001b[49m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[1;32m 225\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m indices \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m (\u001b[38;5;28mlen\u001b[39m(indices) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mset\u001b[39m(indices)\u001b[38;5;241m.\u001b[39missubset(\u001b[38;5;28mrange\u001b[39m(num_clbits))):\n\u001b[1;32m 226\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m QiskitError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mindices must be in range [0, \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnum_clbits\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;250m \u001b[39m\u001b[38;5;241m1\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m].\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", + "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'replace'" + ] + } + ], + "source": [ + "from qiskit.result import marginal_distribution\n", + "marginal_distribution(H_real_results_list[0].quasi_dists[1], [0])" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -913,6 +1157,7 @@ "count = 0\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", + " ## TODO: process results according to the non-commuting op that was measured (remember to marginalize to get original ops)\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", "\n", " eff_count = count % (job_size)\n", From 72dadf3e615e3ec30f05ae073cf25c1adf28fae1 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:21:56 -0700 Subject: [PATCH 04/22] polish notebook with meas based approach --- ...h the quantum krylov subspace method.ipynb | 1067 +++++++++++++ docs/krylov-subspace-demo.ipynb | 1315 ----------------- 2 files changed, 1067 insertions(+), 1315 deletions(-) create mode 100644 docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb delete mode 100644 docs/krylov-subspace-demo.ipynb diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb new file mode 100644 index 0000000..b7636b7 --- /dev/null +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -0,0 +1,1067 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Calculating ground states on large scale systems: Quantum Krylov Subspaces" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map problem to quantum native format\n", + "\n", + "Given a matrix H that we are interested in, subspace methods use a set of states as a basis for the construction of a smaller representation of H, which captures its properties of interest (e.g. lowest eigenvalue).\n", + "\n", + "\n", + "What is the Krylov subspace? \n", + "\n", + "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "Is the krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", + "\n", + "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", + "\n", + "$$ \\vert \\psi \\rangle = c_1 \\vert \\lambda_1 \\rangle + c_2 \\vert \\lambda_2 \\rangle + ... + c_n \\vert \\lambda_n \\rangle $$\n", + "\n", + "Applying $j^{th}$ power of the matrix $H$ gives:\n", + "\n", + "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n", + "\n", + "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $A^{-1}$.\n", + "\n", + "Why is it useful for ground state energy problems?\n", + "\n", + "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", + "\n", + "\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "\n", + "\n", + "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", + "\n", + "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", + "\n", + "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", + "\n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "\n", + "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", + "\n", + "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Imports and definitions\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pylab as plt\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", + "from qiskit.quantum_info import SparsePauliOp, Operator\n", + "from qiskit.circuit import Parameter\n", + "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit.circuit.library import PauliEvolutionGate\n", + "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", + "from qiskit.providers.fake_provider import FakePrague\n", + "from qiskit.primitives import Estimator\n", + "\n", + "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", + " s_vals, s_vecs = sp.linalg.eigh(s)\n", + " s_vecs = s_vecs.T\n", + " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", + " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", + " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", + " if k==1:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", + " else:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define Hamiltonian\n", + "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['ZZIIIIIIII', 'IZZIIIIIII', 'IIZZIIIIII', 'IIIZZIIIII', 'IIIIZZIIII', 'IIIIIZZIII', 'IIIIIIZZII', 'IIIIIIIZZI', 'IIIIIIIIZZ', 'XXIIIIIIII', 'IXXIIIIIII', 'IIXXIIIIII', 'IIIXXIIIII', 'IIIIXXIIII', 'IIIIIXXIII', 'IIIIIIXXII', 'IIIIIIIXXI', 'IIIIIIIIXX', 'YYIIIIIIII', 'IYYIIIIIII', 'IIYYIIIIII', 'IIIYYIIIII', 'IIIIYYIIII', 'IIIIIYYIII', 'IIIIIIYYII', 'IIIIIIIYYI', 'IIIIIIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Define problem Hamiltonian. Kicked Ising in this case\n", + "n_qubits = 10\n", + "J = 1 # coupling strength for ZZ interaction\n", + "\n", + "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", + "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", + "for i in range(n_qubits-1):\n", + " H_int[i][i] = 'Z'\n", + " H_int[i][i+1] = 'Z'\n", + "for i in range(n_qubits-1):\n", + " H_int[n_qubits-1+i][i] = 'X'\n", + " H_int[n_qubits-1+i][i+1] = 'X'\n", + "for i in range(n_qubits-1):\n", + " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", + " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", + "H_int = [''.join(term) for term in H_int]\n", + "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", + "\n", + "# Get operator\n", + "H_op = SparsePauliOp.from_list(H_tot)\n", + "H_op" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set parameters for the algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set parameters for quantum Krylov algorithm\n", + "krylov_dim = 20 # size of krylov subspace\n", + "dt = 0.1 # time step\n", + "num_trotter_steps = 4\n", + "dt_circ = dt/num_trotter_steps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### State preparation\n", + "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_state_prep = QuantumCircuit(n_qubits)\n", + "for i in range(n_qubits):\n", + " if i%2 != 0:\n", + " qc_state_prep.x(i)\n", + "qc_state_prep.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time evolution\n", + "\n", + "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + " ## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "qc_evol = QuantumCircuit(qr)\n", + "qc_evol.append(evol_gate, qargs=qr)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" + ] + }, + { + "attachments": { + "H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hadamard test\n", + "\n", + "![H_test.PNG](attachment:H_test.PNG)\n", + "\n", + "\n", + "\\begin{equation}\n", + " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit for calculating the real part of the overlap in S via Hadamard test\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "## Create the time-evo op dagger circuit\n", + "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", + "evol_gate_d = evol_gate_d.inverse()\n", + "\n", + "# Put pieces together\n", + "qc_temp = QuantumCircuit(n_qubits)\n", + "qc_temp.compose(qc_state_prep, inplace=True)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", + "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", + "\n", + "# Create controlled version of the circuit\n", + "controlled_U = qc_temp.to_gate().control(1)\n", + "\n", + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", + "qc_real.h(0)\n", + "\n", + "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", + "qc_real.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 8047\n" + ] + } + ], + "source": [ + "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" + ] + }, + { + "attachments": { + "optimized_H_test.png": { + "image/png": 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AAAIIIIAAAgSQ3AMIIIAAAggggAACCCCAAAIIIIAAAgggkDIBAsiU0VIxAggggAACCCCAAAIIIIAAAggggAACCBBAcg8ggAACCCCAAAIIIIAAAggggAACCCCAQMoECCBTRkvFCCCAAAIIIIAAAggggAACCCCAAAIIIEAAyT2AAAIIIIAAAggggAACCCCAAAIIIIAAAikTIIBMGS0VI4AAAggggAACCCCAAAIIIIAAAggggAABJPcAAggggAACCCCAAAIIIIAAAggggAACCKRMgAAyZbRUjAACCCCAAAIIIIAAAggggAACCCCAAAIEkNwDCCCAAAIIIIAAAggggAACCCCAAAIIIJAyAQLIlNFSMQIIIIAAAggggAACCCCAAAIIIIAAAggQQHIPIIAAAggggAACCCCAAAIIIIAAAggggEDKBAggU0ZLxQgggAACCCCAAAIIIIAAAggggAACCCBAAMk9gAACCCCAAAIIIIAAAggggAACCCCAAAIpEyCATBktFSOAAAIIIIAAAggggAACCCCAAAIIIIAAAST3AAIIIIAAAggggAACCCCAAAIIIIAAAgikTIAAMmW0VIwAAggggAACCCCAAAIIIIAAAggggAACBJDcAwgggAACCCCAAAIIIIAAAggggAACCCCQMgECyJTRUjECCCCAAAIIIIAAAggggAACCCCAAAIIEEByDyCAAAIIIIAAAggggAACCCCAAAIIIIBAygQIIFNGS8UIIIAAAggggAACCCCAAAIIIIAAAgggQADJPYAAAggggAACCCCAAAIIIIAAAggggAACKRMggEwZLRUjgAACCCCAAAIIIIAAAggggAACCCCAAAEk9wACCCCAAAIIIIAAAggggAACCCCQhMDf//53uffee+Wggw6SsmXLSunSpaVcuXJRNe7Zs0e2bt0qO3bskC1btsiXX34pxxxzjKvcunXrzG1WXeXLl5dSpUrZZbZv3y67d++262jWrJm88cYb9vu8KF7gvffek0aNGpkFLWdtM/3ntNb2Umv998MPP8i0adOkRYsWxR/AKHHRRRfJ7Nmz7XvC2Y7WfaB11qtXT5YtWxZXnblciAAyl1uPc0cAAQQQQAABBBBAAAEEEEAAgYwLTJo0SVq1ahX4PIoKIOOtrEmTJjJ37tx4i1POEFizZo3UrFkzsMXAgQOlR48ece133nnnyfz584stW7duXfnggw+KLZfrBQggc70FOX8EEEAAAQQQQAABBBBAAAEEEMi4wM6dO81eiV9//bWMHTtWhg8f7ntOGjj99a9/lfr168sJJ5wgJUqUcJWLRCKyZMkSmT59umjPSu9So0YNadu2rWjAVbVqVfOf9q5jCSbw22+/mb1Rf/75Z5k3b5507tzZ7JXqraVdu3Zme6m19mp19pD0lnWub9u2TVasWCF//vOfZdWqVc635LrrrpObbrpJTj/9dDnkkEN8e8u6dsiDFQLIPGhELgEBBBBAAAEEEEAAAQQQQAABBLJL4LHHHpOOHTtGndSYMWNEQ614lp49e8rDDz9sFx00aJDcddddUrJkSXsbL8IRWLx4sZx11llRlfXr10/69u0btT3eDVOmTJGWLVvaxd9++21p3LixvV4oLwggC6WluU4EEEAAAQQQQAABBBBAAAEEEEirQJs2bWT8+PGuY1auXFk+++wzqVixomu734oGjtpbUpcJEyaYveb8yrEtHIFu3brJ0KFDoyr74osvEnpkWysaPHiw3HPPPWadOiZk06ZNo+ovhA0EkIXQylwjAggggAACCCCAAAIIIIAAAgikXWDTpk1Su3ZtcwIT58G1B6T2hCxqWb16tRx//PFmkQ4dOsioUaOKKs57IQhs3rzZNNfJYZzLxRdfLK+//rpzU1yv169fLyeeeKL5aPdDDz1kTlQU1455WIgAMg8blUtCAAEEEEAAAQQQQAABBBBAAIHsENCxHJs3bx51Mq+++qr88Y9/jNquG/bu3SsXXHCBOYmJjvmok5QwzqMvVegbp06dao7R6K148uTJvtu95ZzrOs7jc889Z471+eGHH8oBBxzgfLugXhNAFlRzc7EIIIAAAggggAACCCCAAAIIIJBuASuIch5XH8X+9NNPpVKlSs7N5uthw4ZJ165dzdcLFiyQRo0aRZVhQ+oELr30UnnttddcB9D2+vzzz6VChQqu7bFW5syZI82aNTPf1lnKdbbyQl4IIAu59bl2BBBAAAEEEEAAAQQQQAABBBBIucCPP/4o2pNxy5YtrmPddttt5ozZzo06PqQ+tqtLjx49ZODAgc63eZ0GAefj787D6QRAQ4YMcW7yfb1jxw45+eSTZe3atXLLLbfIM88841uukDYSQBZSa3OtCCCAAAIIIIAAAggggAACCCCQEYFp06bJNddcE3Vs56PYe/bskXPPPVcWLVokJ510kixdulTKli0btQ8bUi+gYzb27t076kDLly+X0047LWq7c8ODDz4offr0kYMOOsjsNXnEEUc43y7I1wSQBdnsXDQCCCCAAAIIIIAAAggggAACCKRb4PrrrxcdS9C5OB/FfuSRR6R79+7m28uWLZN69eo5i/I6jQI7d+6UOnXqmL0YnYetX7++LFy4UPbbbz/nZvu1zph9wgknmOuPP/64tG/f3n6vkF8QQBZy63PtCCCAAAIIIIAAAggggAACCCCQNgGdXblmzZpRj2K3adNG7rnnHvOxXT2Z+++/3+xBl7YTi/NAOquzTqqzePFi+eqrr+SXX36R4447zuytqWHdFVdcIWXKlCmyNg32dHbwn376yfyoj6fra/2nj6RXqVLF3F8fY16xYoXZG3T37t2mzSWXXCKlSpUqsv4w33SO4+isd/To0XLHHXc4N9mv9RxnzZolxQWV9g4F8oIAskAamstEAAEEEEAAAQQQQAABBBBAAIHMC0yZMkVatmwZ80S016M+gr3//vvHLJPuNzQM7NmzpwwfPtw+tPbc1EVDVWvRbX379pW2bdvGfHRcr10N/JaRI0dKx44dZd68eXL55ZdHBbVqo6Gg38Q9fvWFsc1vAiF9tFp7OlphqXWc559/Xm644QZzlR6slsp/PxJAuj1YQwABBBBAAAEEEEAAAQQQQAABBFIqcO2118oLL7zge4yPPvrIfPTX980MbFy1apW0atVKPvzwQ/PoN998s/z1r3+VunXrmuvr1q0zA0MdM1FnidZFg8KZM2eK39iHxQWQRx11lDRv3tysR2cCX7Jkibz77rvmuv4X70Qw9g5JvtiwYYPUqlUrKgxt3bq1PP3003bt2htUy2kgq+c9dOhQ+z1eiBBAchcggAACCCCAAAIIIIAAAggggAACaRT47rvvzHECvbNi6wQ02vsvW5YZM2bIVVddZZ/OuHHjRB8X91s0qDv//PPtEFKDxLffftt8RNtZft++faI9Kr/55hsZMGCAjB8/3n5bZ/1+7LHHzLDvzTfflAsuuEDOOeccVwDZoEEDcwxGe6c0vNBz0p6Z3kWvr3HjxubmLl26mD1EtReoBrEVKlTwFi/odQLIgm5+Lh4BBBBAAAEEEEAAAQQQQAABBDIhMHHiRLnxxhujDj137lxp0qRJ1PZ0b9i4caMZHlohqT5a3a9fvyJPQ3v/aWiovSZ10XEQtfdirMfJv//+e99eks8995zZ61LruOWWW2TChAn60ly0B6U+6pzORWcnP+uss0RnwHYuOtnMypUrzd6heq266CRD1113nbMYrw0BAkhuAwQQQAABBBBAAAEEEEAAAQQQQCADAjqBy9q1a11H1p6DGuDpOIOZXLSno9U7Uc9FA8kDDjig2FPyTtxS1IQ6e/fujZpURkO9zz77zD7O6tWrzaBWH8W+7LLLzEebjz/+ePv9dL1YunSpGah6j6ePnk+bNs0MJy+++GJ5/fXXvUVYNwQIILkNEEAAAQQQQAABBBBAAAEEEEAAgTQL6EQzDRs29D1qp06dZMSIEb7vpWOj9sJs2rSpfSgd8/Ef//iHvV7Ui0gkItWrVzcfsbbK/fzzz1KxYkVr1fWxRIkSrvXBgwdLt27dXNuyZaVz585FtotOTKOznLNECxBARpuwBQEEEEAAAQQQQAABBBBAAAEEEEiZwPbt2+WUU06J6v3oPKBzfEHn9nS8vvDCC0XHYLSWF1980Z4YxtpW1EedBds5Qcs///lPuf3223138QaQOjZktWrVfMtmeqMGqSeeeKJr5m/rnB544AHp3bu3tcpHjwABpAeEVQQQQAABBBBAAAEEEEAAAQQQQCCVAtrDz5olWScs0clXNORzLjVq1DDHFjzwwAOdm1P+WmdzrlSpkus4QWfmfuSRR6R79+52HTo5zVtvvWWvO194A0jtQZnNy6RJk+zxKa3z1Lb6+OOPpUyZMtYmPnoECCA9IKwigAACCCCAAAIIIIAAAggggAACqRLQno06UYsuI0eONGdX1hmka9WqZc7+7DzuXXfdJUOGDHFuSvnrd955x5zN2nmgdevWmY9VO7cV9Xr06NHSvn17u4iOIbl582Z73fnCGUB6x390lsuW19u2bZPy5cu7Tufuu++WQYMGubax4hYggHR7sIYAAggggAACCCCAAAIIIIAAAgikREBDuDp16pjjI2qvQB1rsWTJkuaxdKZnnfHZuyxYsEAaNWrk3Zyy9SlTpojONO1cdAKaww47zLmpyNd+17J161bx683pDCBzYRIXAsgimz7mmwSQMWl4AwEEEEAAAQQQQAABBBBAAAEEEAhP4M4775QnnnjCrFBnvz722GNdlV955ZXy8ssvu7bp470rV66UcuXKubanasXbe1GPo8FpkFm5/R5T3rRpU9Sj3Vq3M4C87rrrZPLkybo5axcCyMSahgAyMTf2QgABBBBAAAEEEEAAAQQQQAABBOIWeOONN0R7+Ony5JNPyp/+9Keofb/99lupXbt21KPYQWahjqo04IapU6eKBoHOJVZ46CzjfD1u3Di57bbbnJskVh0EkC6mvF0hgMzbpuXCEEAAAQQQQAABBBBAAAEEEEAgGwScsydrCPnaa6+5ev45z1Fnj9ZZpL3LwoULpUGDBt7Noa8vXrxYzjrrLFe9a9asEe2JGe8yatQo6dSpk6v4vn37fK+ZANLFlLcrBJB527RcGAIIIIAAAggggAACCCCAAAIIZINAmzZtZPz48eZjzKtWrZKjjjoq5mnpLNCXXXaZGVI6C+kELe+//76ULVvWuTn01z/++KMcfvjhrnp14pzGjRu7thW14nzUXMude+65Mm/ePN9dCCB9WfJuIwFk3jUpF4QAAggggAACCCCAAAIIIIAAAtkiMGPGDLnqqqvM09EQ8tZbby321L766is5+uijo8r17NlTBgwYELU97A2XX365zJw506720UcflS5dutjrxb2oUqWK/PDDD3YxnclbZ/T2Wwgg/VTybxsBZP61KVeEAAIIIIAAAggggAACCCCAAAJZIKCzRx933HHmmI4aQr700ktxn9WYMWN8x4nUR6Tr168fdz2JFNTzbNGihb2rzsKts3HHs3z66afmOJZW2cqVK4v2+jz00EOtTa6PBJAujrxdIYDM26blwhBAAAEEEEAAAQQQQAABBBBAIFMCv/32m9nzUcd71EUnmDnyyCPjPh19FFvHi5w9e7Zrn5NOOkmWLVsmZcqUcW0Pc2Xv3r3StGlT0UevrWXp0qVy+umnW6sxP/bq1cvVS1N7gF5xxRUxy+daALl169aoGcG7desmgwcPjnmNvGHMdm7c0BEgEEAAAQQQQAABBBBAAAEEEEAAAQTCEfjuu+/MR62t8PCggw6Sr7/+WipUqBDoAF988YXo2I/epXPnzjJs2DDv5lDX9Xzr1Kljz8it57FkyRI5+OCDYx5n0aJF0rBhQ/v91q1bi06qE2vZsmWLq75mzZqJzhaezcv69eulWrVqrlPUMT515m+W2AIEkLFteAcBBBBAAAEEEEAAAQQQQAABBBAoUkD7demj1trDUUO76dOny1NPPRW1jz7G3L9/fzn11FOLDSI3bNhghn0TJkyQKVOmRNWlGzTc08leNBjUiWlKlSpl/vMtnOBGDRQvuugiO4SsV6+eTJ482Xys3FuljhmpY0dai048oxaVKlWyNpkf9+zZI7t375ZffvlF9DHzvn37ut7XIE97X2poW65cOfOanL0kXYXTsKKzd+/atUu2bdsmGj4OGjRInn322agjT5w40Zxsp3z58nZ7lCxZMqpcoW4ggCzUlue6EUAAAQQQQAABBBBAAAEEEEAgaYFYE8bEqrhJkyYyd+7cWG+b272TuBRZ+Pc3U9V7cM2aNXL11VfLhx9+aJ+G9vjTmbq1N6SGrjq5zvz58+33ddKaTp06yX777Wdvs160bNkyZqhqlXF+nDVrlhmCOrel8/WZZ55phsFBjzl06FDp2rVr0N3ytjwBZN42LReGAAIIIIAAAggggAACCCCAAAKpFnAGkNprT3sjai847ZGoi9Xj79dffzV7EmowN2LEiCJPS8daXL58uegELqVLlzb/eevTXoQ7duyweyf+5S9/keHDhxdZb6Jvai/AV199VR544IEiwzgNJXUsxFq1asU8lPZ41HosK+f1qZUuOs6idW06gU3t2rVj1pfqN6xHzrVdnefqPa63nV955RUzpPWWK9R1AshCbXmuGwEEEEAAAQQQQAABBBBAAAEEEAgooD0eV69eLTo+5Y8//iiHH364ObnO2WefHfW4dcCqKZ7HAgSQedy4XBoCCCCAAAIIIIAAAggggAACCCCAAAKZFiCAzHQLcHwEEEAAAQQQQAABBBBAAAEEEEAAAQTyWIAAMo8bl0tDAAEEEEAAAQQQQAABBBBAAAEEEEAg0wIEkJluAY6PAAIIIIAAAggggAACCCCAAAIIIIBAHgsQQOZx43JpCCCAAAIIIIAAAggggAACCCCAAAIIZFqAADLTLcDxEUAAAQQQQAABBBBAAAEEEEAAAQQQyGMBAsg8blwuDQEEEEAAAQQQQAABBBBAAAEEEEAAgUwLEEBmugU4PgIIIIAAAggggAACCCCAAAIIIIAAAnksQACZx43LpSGAAAIIIIAAAggggAACCCCAAAIIIJBpAQLITLcAx0cAAQQQQAABBBBAAAEEEEAAAQQQQCCPBQgg87hxubTsERg5cmT2nEyenMnJJ58s559/fp5cDZeBAAIIIIAAAggggAACCEQL8LtktEmmtnTq1ClTh86L4xJA5kUzchHZLlCtWjVZv359tp9mTp3fW2+9RQCZUy3GySKAAAIIIIAAAggggEBQgdNPP12WL18edDfKp0AgEomkoNbCqZIAsnDamivNoAABZPj4BJDhm1IjAggggAACCCCAAAIIZJcAAWT2tAcBZHJtQQCZnB97IxCXAAFkXEyBChFABuKiMAIIIIAAAggggAACCOSgAAFk9jQaAWRybUEAmZwfeyMQl4AzgKxatar0798/rv0o9D+Bjz/+WAYPHmxvIIC0KXiBAAIIIIAAAggggAACeSrgDCBLlCghY8eOzdMrzb7LGjVqlCxbtsw+MQJImyKhFwSQCbGxEwLBBLwBJONBBvPT0vfccw8BZHA29kAAAQQQQAABBBBAAIEcFvAGkPv27cvhq8mtUz/jjDMIIENsMgLIEDGpCoFYAgSQsWTi304AGb8VJRFAAAEEEEAAAQQQQCA/BAggM9eOBJDh2hNAhutJbQj4ChBA+rIE2kgAGYiLwggggAACCCCAAAIIIJAHAgSQmWtEAshw7Qkgw/WkNgR8BQggfVkCbSSADMRFYQQQQAABBBBAAAEEEMgDAQLIzDUiAWS49gSQ4XpSGwK+AgSQviyBNhJABuKiMAIIIIAAAggggAACCOSBAAFk5hqRADJcewLIcD2pDQFfAQJIX5ZAGwkgA3FRGAEEEEAAAQQQQAABBPJAgAAyc41IABmuPQFkuJ7UhoCvAAGkL0ugjQSQgbgojAACCCCAAAIIIIAAAnkgQACZuUYkgAzXngAyXE9qQ8BXgADSlyXQRgLIQFwURgABBBBAAAEEEEAAgTwQIIDMXCMSQIZrX3AB5Lp166R69epSokSJcCUD1LZr1y7ZsGGDHHPMMQH2omguCxBAJt96BJDJG1IDAggggAACCCCAAAII5JYAAWTm2osAMlz7ggogx4wZI3/605+kffv28vjjj4crGaC28847T+bPny+jRo2SDh06BNiTorkqQACZfMsRQCZvSA0IIIAAAggggAACCCCQWwIEkJlrLwLIcO0LKoDs3LmzjBgxQurXry+LFy8OVzJAbbVq1ZLPP/9cjjrqKNEemSVLlgywN0VzUYAAMvlWI4BM3pAaEEAAAQQQQAABBBBAILcECCDT017r16+XI4880nUwAkgXR9IrBRVAam9D7flYr149WbZsWdJ4iVbQv39/ue+++8zd33zzTbngggsSrYr9ckSAADL5hiKATN6QGhBAAAEEEEAAAQQQQCC3BAggU99ew4YNk7/85S9RncMIIMO1J4BMwHPr1q3mGI779u0zx5MsW7ZsoFq016M1/mPr1q3l6aefDrQ/hXNPgAAy+TYjgEzekBoQQAABBBBAAAEEEEAgtwQIIFPXXp988onccccd0rFjR7nhhhuiDkQAGUWS1AYCyDj5vvjiCxk7dqyMGzdOfvjhB9dedevWlTvvvFNatWolFSpUcL0Xa+WSSy6RWbNmmW///PPPUrFixVhF2Z4HAgSQyTciAWTyhtSAAAIIIIAAAggggAACuSVAAJma9nrggQekb9++cvXVV8sLL7zgexACSF+WhDcSQMZB98gjj0j37t3tkldccYWcc845oj0hn3/+eXM8R32zcuXKMn36dGnQoIFdNtYL3c9K2HVynHbt2sUqyvY8ECCATL4RCSCTN6QGBBBAAAEEEEAAAQQQyC0BAshw20vnA9Eh8WbPnm1W/Pbbb0vjxo19D0IA6cuS8EYCyCLo9u7dK7fffrv9iLROGvPaa6/JySefbO+1Z88eGT9+vFnO2jhx4kQ7XLS2eT9u375djjjiCNmyZUvGJ8Xxnhvr4QsQQCZvSgCZvCE1IIAAAggggAACCCCAQG4JEECG014//fSTPPbYYzJo0CDZvHmzWanOEzJq1KiYByCAjEmT0BsEkEWwjR49Wtq3b2+WOOigg2TRokVy0kkn+e7xz3/+0xw7wHpTH9muWbOmter7UQc5HTlypPnexx9/HLNu353ZmFMCmQoghwwZInfffbdtpfexjllavnx5KVWqlGiAvnv3bvn111/NMNwq2Lt3b9Eu6daiX6A1gNfAXBerntKlS0u5cuXMbRqqa107duxwlfvqq69CGWKAANJk5j8EEEAAAQQQQAABBBAoIAECyOQaW39H1ZBR/61Zs8aurFKlSrJw4UKpVauWvc37ggDSK5LcOgFkDL8NGzaYN6IVuDzzzDNyyy23xCj9382XXnqp2UNS1xo1aiTvvPOO7LfffjH3Wbp0qdn7UQv07NlTBgwYELMsb+S2QKYCyF69epkht4aO3rFLixLVL8761yBr+fbbb80A8oQTTrCHHLDeK+pjjRo1RAf21aAy2YUAMllB9kcAAQQQQAABBBBAAIFcEyCATKzFVq9ebeYzOpfHBx98EFVJv379zDEgo95wbCCAdGCE8JIAMgaijsn41FNPme9qb6+NGzfKAQccEKP0fzdPmjTJnIjGKjR16lS55pprrFXfj3Xq1JFVq1aZ40d+8803sv/++/uWY2NuC2QqgFQ1HUpg586dZgD56KOPyvDhw12Y2qt32LBh5tAC2jPywAMPlBIlSrjK6IrO+q7/dNIk/ctRw4YNo8poiH7ttdfKoYceavayDPN+JoCM4mYDAggggAACCCCAAAII5LkAAWT8DWyFjjp0nv4ralm5cqVreD2/sgSQfiqJbyOA9LHTx1Gds1K3bNnSnGzGp6hr07Zt28zQxdp42WWXySuvvGKt+n4cMWKEdO7c2XxPy+o+LPknkMkA0qnZv39/c8Bd57b58+ebkyo5txX3Widg0mDeucRzvzvLB31NABlUjPIIIIAAAggggAACCCCQ6wLZHkD+5z//kc8++8wc1kuzlFj/KlSoIEX9q127tlSvXj1wcwUJHa3KmzdvLi+++KK1GvMjAWRMmoTeIID0YXv22Wfl1ltvtd/RXmNdunSx14t6obNjv/vuu3aR9evXS9WqVe117wt9LLZKlSrmZu0tqb0mWfJPIFsCyAsvvFDefPNNG1hDxE2bNpnjQdob43ihdWhdzkUH9L3zzjudm0J9TQAZKieVIYAAAggggAACCCCAQA4IZFsAqYGjzhytQ87NmzdP1q5dG5qiDvnVtGlTOf/8880n7nQeguIW7cjVokULc36D4spa72vmc/PNN1urMT8SQMakSegNAkgftptuukmee+45+53JkyfLddddZ68X9UJ7S06ZMsUuEs++zn2+//5783FsuwJe5IVANgSQOjmMNWGMhXrVVVfJSy+9ZK3G/VEnqOnbt6+r/IcffiinnHKKa1uYKwSQYWpSFwIIIIAAAgggkFsCn376qUQiEdGAoqhx9nPrqjhbBIoXyHQAqROXTps2TRYsWGD+W7FiRfEnHVKJs846S84++2wzjNRei7GG+NKn+jSE1Jmui1uOPfZY0UmAdZ6E4hYCyOKEgr1PAOnjddxxx7lS/Dlz5kT19vLZzdzknNlaN/To0UMGDhwYq7i5febMmXL55Zebr3V8Pq2DJb8EsiGA1C/K5513ngs20ftN69H6rEV7Uv7yyy9SsmRJa1PoHwkgQyelQgQQQAABBBBAIGsFdDx+fbJMx8t///33zTHN9WRLlSpl/tFbH9fUMNL7R/GsvSBODIEEBTIVQGqY9/TTT5v/PvroowTPPrzd9HNen1TVyYH192vvosGodhxzznTtLaPrHTt2NCdq9XvPu40A0iuS3DoBpMdPJ9g45JBDXFuXL18up512mmtbrBXvGHtNmjSRuXPnxipubte/KOgnkD6OrROCaBrPkl8C2RBAeu9NFQ5yb1stsn37dnOiGmtdP+oXeu3tm8qFADKVutSdqIBOzLRo0SL58ssvZdeuXeaQGtoTOJHxaxI9B/ZDAAEEEEAgnwR0XP0bb7xRZsyYEddl6e9pQ4YMMR/ZjGsHCiGQYwLpDiD151orePzqq6+K1dKffTX3+L//+z9zLo1KlSr5ftQOK0X90w4u+ki35iNFLYcddpgZQmoYeeqpp7qKLlu2zOx0o7+zxlqmT58uV155Zay3XdsJIF0cya8Y3dgLZjHGp4sYYpF69erFvOYvvvjCLKPlrH/r1q2LWd77xujRo+39dH/jr3LeIr7rf/vb3+z9lixZ4luGjbkrcOSRR9rta4wJmpELMb4p2Oeg96bRazHy22+/BT4XY6wPVz1alzH+Y+B6gu5w9913u4771ltvBa2C8giEJmD8hTXSunXrSJkyZVz3pfV9o379+pEnn3wytONREQIIIIAAAoUgYAyD5ft91fr+WtTHu+66qxCIuMYCFND8wrr3S5Qw+5ClREF/vjXmvogYE8XYx7OO6/yoP+d26tQpMmnSpIjRiSrUc9HfT43xJSN///vfI8Ykp+bvrM5je18b4zhGZs2aZZ+DMX5kkeeuv5cHWYzw11VfkH0pGy2g42gUzBJPAGn0CHPdYHqDb9iwIW4j41EB1/6VK1eOa99PPvnE3s94BDuufSiUOwKZDiCNvwDZ95f1RdsYIyMhwIceeiiqLmP8x4TqCrITAWQQLcqmUuDBBx+M+hywPq+8H40BtCP6hy0WBBBAAAEEEChawJjk0Pf76+GHHx7R76cdOnQwQ49mzZpFjJ5WvmW7du1a9EF4F4EcFEh1AKmhX58+fXw/p6yfbY3JdiNjxoyJGD0i0yq4efPmyMsvvxy59tprizy/tm3bRi699NIiy+i13HHHHYHOnwAyEFexhQkgPUR+vbuMiWE8pWKvjh8/Puqmj13a/U6jRo3MfbVnmgZGLPkjkOkA0ujKHnVfjhgxIiFgv56Ue/fuTaiuIDsRQAbRomyqBPQPRNYPYvF+NGbvi6QjpE/VNVMvAggggAACqRbYuXOn7/fXzp07xzy0MZa57z48TRaTjDdyVCCVAaT2HrRyCL+fbY25KiJTp07NCjnjEe3I7bffHjHGgfX93Pee/3333Rcxxot0ldXelUEWAsggWsWXJYD0GBlTuLtuUL2Jf/zxR0+p2KsTJkyI2n/37t2xd3C84+w9aYyn53iHl7kukOkA0hj/Meq+1N6+QRe/Hw6N8R+DVpNQeQLIhNjYKUQBY0KxqM8j7w86sdaNsXEi8X4vCPGUqQoBBBBAAIGcENCei97vofEEBcb4/ZE//OEPrn2NMSEjxhhyOXHdnCQC8QikIoDcunVrpHv37q7PHefnoD7aPHv27HhOL+1lVq5cGTHmB4gYY0HGPH9nT8c///nPdrmgj4wTQIbbvASQHs+JEyfaN6f1Cbhp0yZPqdirfvsbs0fF3sHxjjEgq33siy++2PEOL3NdINMBpF+vxUR+MDNmIrTvUevzIx3jP2r7E0Dm+mdBbp+/MQNn1L1vfQ7E+7Fbt265jcDZI4AAAgggkAKBZ555Jup77KeffhroSPoEmfP7sYYTLAjki0DYAaQxCUvEG6xZnz/NmzeP5Eov4q+//jrSsGFD1+e+dR116tSJvPDCC/YtoD+H63tBF69T0P0p7xYI3gLu/XNqLZ4xIMeOHRt1A+tf1uJd/AJIDRbjXW677Tb7+EEmv4m3fsplRiCTAWSY4z8+/PDD9v1pfXFP16OlBJCZuXc56n8FrO8f1n2f6MeNGzdCigACCCCAAAIOAZ3Uzfl99R//+Ifj3fhevvHGG646jj/++Ph2pBQCOSAQZgB5//33uz5XrM+9ihUrRh599NEc0PjfKcYahsG6Jv3Yt29fe4fevXvbr+N9QQAZr1R85cwplIyGKYjFGLhYHn/8cTE+gUWnZ/dbjJmcpFWrVq63jB6QolPJx7MYj2CbU8I7yxqPcMuhhx7q3BTztU4737hxY/N9Y+YnMWbHjlmWN3JHoFq1arJ+/XrzhI1ZsO3X6biCBQsWyLnnnus6lDFLoBhd0V3b4llp3769GI/D2EWNvzaLEbBLyZIl7W2pemH8JVsGDx5sV2/Mgi3GgOT2Oi8QSKWAMQC+6NfyZBdj8G5p165dstWwPwIIIIAAAnkjcMYZZ9i/mxmPVIrxx7qEru2qq66SGTNm2Psaj1qKfv9mQSDXBYwQTIzhs8zLMGbBln379iV0SUZnEunZs2fUvkavRzGCOjn11FOj3svWDUbPaTH+eOE6PWPcdfnmm29c23RFr61fv35R2+PZ4Pz6pOWNmC2e3SgTQ4AA0gMzc+ZMMQZadW0NEiD6fSLs2rVLSpcu7aoz1op+MTH+Yidr166VGjVqiDF7alrCnVjnk+z2QYMGiTGeZbLV5Pz+77//vhizi5nXke4AUoPse++9NyWGxviPaWtfbwB54oknigagLAikWqBWrVqif1wKY9Ffjqw/RoRRH3UggEDiAjVr1pTVq1cnXgF7IoBAKAJLly61f6k3JsMQ/eN5IkuPHj3E6D1p78rPijYFL3Jc4OOPPxbjqTbzKhINII3ejaKdUJyL0evRDOa6dOni3Jz1r/UPDfoztXMxxn6VOXPmiHboMnp5iv7+7VwSDSEJIJ2KIbyOr6NkfpSyHqHTLsyxFp1ZyWB1/TN+WYxVPGq7cyIZq56oQsVs6NOnj338dD3eWswpJfx2IjPGWm75+tEIIBP2TGRH7/iP6nrSSScF/ufXHuka/1Gv2/sItt/5sM39tQuPcDzq169vf01O1vTMM88Mra5kz4X9w7k/cMxdx7PPPpvPR8/PvNzPuXs/50vbOSeOCPpz73PPPcfnNJ/TeX8PGAFk0E+NiP7O5v0aoWMkrlixInBdmd7hnXfeiey///6u6zn22GMja9assU9Nh9DTiVK91+x8HNsuXMwLHsEuBijg24wB6QH74IMPom7UIGMxPvnkk679K1eu7DlC8avGY652Hf/5z3+K3yGLSxBARv8gm84AcseOHfa9ZH0BTnTWaqMnZVRd6QzICSCj7yWrTfmYWhvjL59R936i5t4fYhKth/1S2+b4FoYvAWRhtDOfz7nVzp06dUr4N5upU6eG9v2a+ya37ptCaq+gAaTfHBcaPhq9KhP+XMvUjkavxqiZrw855JCIMbye7ymFEUJ6f3b3PRAb4xYggPRQffnll1HfuIJ8cg4cONC1/wknnOA5QtGrW7dutfc3xrcrunAOvEsAGf3NO50BpF+P3kR7LTZr1sy+N/WbvM42uHfv3rTdhQSQ0fdSIf2wlclrDTOkaNq0qevzKJPXxbH5nCr0eyDMz+1Ct+T6+XoS1j2gP28mujz00EN8j6UHZN7fA0ECyH/9619RHrkaPmrHLGPoFNf1GPMQRN58880iv2QkG0ISQBbJG/hNxoA0vls6l19//VV0LATnsnDhQmnQoIFzU8zXOq6Cjq9gLTr5h45DEO9ifJGQm2++2Sz+7LPP2q/j3T/byhl3ZLadUkbORwfEtcZ9S+cYkAMGDJBevXq5rtno5St169Z1bStuZefOnVK2bFlXMeOLedrGf9QDe8eA1ElorAmbXCfGCgIhC+jYvOXKlZPdu3cnXfOQIUOka9euSddDBQggkLyA/oyiY2mxIIBAZgWMX/DFeBTUPInq1auL8fRZQid00003ifEYtr3vt99+K/pzNwsCuS6g4xAmMgnN66+/Li1btpQtW7aYBEb4aP7+ZgzHlVMkOump8ccJ0fFincu0adOkRYsWzk2+r9VgypQp9nv6O7LfZDx2AccLxoB0YITxMnBkmcM7xDMGpF6e9lo0bO1/r776atxX7U3YtddWkEV7PVrH1t6QySzGL8sR4xfnZKpg35AEjjzySLtd09kDMqxei2H2pEyU1NsD0gggE62K/RAILOD92m59nQ768bPPPgt8bHZAAAEEEEAgnwVuvPFG++dk/b46fPjwwJerPxeWKVPGrufoo48OXAc7IJCtAjqHhfUzZ5AekHo9+nucMcltJFd7Puo1XHjhhfb1Ww7jxo3Tt+JerJ/lR44cGfc+WpAekIG4ii3MI9g+RO3atXPd4E888YRPKf9Nxsxtrn11MOR4F2PGa3tfHQcykWXlypWRDh06RIwed2ZdOgalXo/WvW3btojxV4LIkiVLEqmafZIQyEQA6Tf+4zXXXJPQVfTv39++N60v+ukc/1FPmgAyoaZjp5AE5s6dG/U5YH0uxPvxhhtuCOlsqAYBBBBAAIH8EejXr1/U91idRCLIcsopp7jqMGbIDbI7ZRHIaoFkAki9MJ1sJsiwctmEob+/en/WHjp0aEKnqI+kB10IIIOKFV2eANLHx3j02XWTd+/e3aeU/yYN/JyfIEFm0NZZmax9jce+/Q9QxNbHH3/c3l+/6U6ePDny8MMPR/Sc9J/xGLn5vo7dZzxqXkRNvBW2QCYCyAULFtj3g3VfBf2Lj+XgnUk73eM/6nkQQFqtwcdMCTgnCLM+p+L9WL58+cjq1aszdeocFwEEEEAAgawWOO2001w/t5566qlxn2+fPn1c+2oPMf05mAWBfBFINoDMVYfbbrvN9bmtP3cnMpN1MtdPAJmMXvS+BJDRJhF99FkDFusXy3gnktHeh9Y++vGPf/yjT+3+m3777TczJNT94j2eVZP2bLzlllvsY3t7bGrvR+f16DGSfbzbOjYf4xPIRADpN2u1zhwWdPHrSald2NO9EECmW5zj+QlcdNFF9tda59f74l5r73MWBBBAAAEEEPAX0Eeovd9LDz744Mgbb7zhv4Ox9ZNPPon4fV8O0nkkZuW8gUAWCRRiANmtW7eorwnGOOppbxUCyHDJCSBjeBqTybhueGPijhgl/7fZOwN2kF84Z82aZR9v8ODB/6s0jledOnWy9/3b3/7mu0ePHj3sMvXr1/ctw8bUCWQigPQb/3HPnj2BL9KvJ2WiM2kHPrhjBwJIBwYvMyagM7+3atXK/nrq/WXJu37YYYdFpk+fnrHz5cAIIIAAAgjkioD39y/re6o+2aWhog5tNWnSpMi9994buf7666M6WGj5WrVq5crlcp4IxC1QaAHk/fffH/Wzdps2beL2CrMgAWSYmsbsf+FWl921xTsJjV6FTvPu7DVYXNq+fft21+Q1l112WSAMY2Ym+5MsyGPbznBIe07u2rXL97jORxOMGZ98y7AxdQLpDiD9ei0aM4QldIF+PSnTPf6jnjgBZELNx04pEtCBr43Z5O2v29YvSdbHkiVLmuPxbtiwIUVnQLUIIIAAAgjkn4D+zmV9Lw36USfzZEEgHwUKKYAcNmxY1NeARH+PDeNeIIAMQ/F/dRBA/s8i6tXEiRNdN/9LL70UVcba4B0b7Ouvv7beKvbjxo0b7eMEGTBZQybnjN1PPvlkzGM5J8fR3pYs6RVIdwDpDKatH95GjBiR0EX79aTUXmDpXggg0y3O8eIR+Pe//20GjTo7X+PGjSNXXHFFZMKECZHNmzfHsztlEEAAAQQQQMAjsHjx4oiOAWn9DBvPx+eff95TC6sI5I9AoQSQ48ePj/q8v+CCCyKZ+N3TunsIIC2JcD4SQBbjqN39nd/0xo4dG9HxGq1l06ZNEecj0Fr21Vdftd6O66NODGIdY8aMGXHto4WmTp1q76f7a5Dpt2zZssVVTtdZ0iuQ7gBywIABrjbX+2P58uWBL3rnzp1R9WRi/Ec9cQLIwM3HDmkSuPrqq12fJ+vWrUvTkTkMAggggAAC+Smgwwbpz341a9Z0fY+1fmfSj0cddVREe0Z9/vnn+YnAVSHwu0AhBJDa2cv5+a2vdXKqn376KaP3AQFkuPwltDqjcQti6dChgxgzRYvxCSzLli2L+5qNv6jJDTfcYJevUaOGGOOLSKlSpeTtt98WI9Az3zN6I4oRIJrv2YXjePGHP/xBjEdaxXjkW4xPMNl///3j2EvEGAdBjL8SmGWNHo5i9Hrz3W/OnDli9GIrtpzvzmwMRaBatWpiPFpv1lW1alX7dSiV+1RiDMgts2fPtt/Re8sIy8171t4Yx4v33ntP9N5yLsb4j2IMZ+DclJbX99xzjxjjo9rHMgYrF+NRG3udFwhkSuCaa64RY8xf+/BGACnVq1e313mBAAIIIIAAAokLGJ0szJ9HjYk1zUqMWa7FeNpM9OdrFgQKQcAIwcToTGJeqt7/+/bty6vLfuedd6Rp06Zi/OHBvi7NXPT3Wf2YyeWMM85wZUcFFJ+lhj3cPDO7awsyBqT3Sn7++eeITryhY4s4x4bUv7xpj7BXXnklsnv3bu9uxa4bQaid9OtEMUEWnUzGuCvMf7169Yq5a+/eve1y+pol/QLp7AGp96p1X1gfgzza79S57777ourKxPiPek70gHS2DK+zSYAekNnUGpwLAggggEA+CmhPKOvnWh1nmQWBQhLI5x6QK1asiOikjdbnt3485JBDEnp6LxX3BD0gw1WlB6RxhyeyGOMvSunSpWW//fZLZHd7ny5dusjw4cPN9Y8++kjq1Kljv1fciypVqsgPP/xgFnvhhRfE+CXYd5eGDRvKokWLzPeM8R9Fe8fpX02Mx3TNfWrXru27HxvDE0hlD0jjS4Lo/WhMhCRr164VY9IYMWbddZ18kyZNZMyYMVKxYkU58MADzXvXVeD3FWN4AdF/Rohp9u69+eabo4oZYbsY4beUL19eypQpI8YPgVFlUrGBHpCpUKXOMAToARmGInUggAACCCAQW0CfYDOCCrOA/uxpjAkXuzDvIJBnAvnaA9KY+Nfs+bhmzRq7xTRf0Z6PxtiP9rZMvqAHZLj6BJDhegaqTUMjDRH1Ee4GDRrIwoULA+3v/EJkTIQgZ555ZtT+33//vRxxxBH29l9//VUOPvhg0fJ6zMmTJ4vRg9N+nxepEUhVAOn3iHQ8V3DuuefKvHnzXEW9j2273ixiZf78+XLOOecUUSKctwggw3GklvAFCCDDN6VGBBBAAAEEnAIEkE4NXheagPP3/nx5BPuXX34xw0fv0HgvvviiNG/ePGuamAAy3KYggAzXM1BtU6ZMkZYtW5r7aO+0du3aBdr/1ltvlWeffdbcJ1YIpGP1PfHEE2aZunXrygcffGC+Nh5nlSFDhsh3331nhqCBDkzhwAKpCiBffvllufLKK+3z0bEey5Yta/ZOtDYaQwOI/tPA2xqvVO87HdvUuWjv21WrVpmbtB5dKlSoYPeW9KtHy+j4paeccoq+TOlCAJlSXipPQoAAMgk8dkUAAQQQQCAOAQLIOJAokrcC+RZA6hN8OkfF3LlzXW02btw4c54L18YMrxBAhtsABJDhegaq7ZJLLhF9JFoXfeRVH48NsugkHPporS4DBw4UYwxJe3d9LKFfv37y0EMP2duMcQDFmF3KfMTWGLtSGjdubPaAtAvwImUCqQogU3bCWVgxAWQWNgqnZAoQQHIjIIAAAgggkFoBAsjU+lJ7dgvkWwDp/dlZ9YcOHSpdu3bNuoYggAy3SQggw/WMuzadJfWYY44xy7du3VqefvrpuPd1Frz99ttl7Nix5gza2qNNvznrbNjDhg0T7RWpoaT2ktOebRo6zpw5U0aPHi06k7GW885w7Kyb1+EJEEAmb0kAmbwhNaRGwPtDFLNgp8aZWhFAAAEECleAALJw254rF8mnAFKf+nzqqadczaodp/r27evali0rBJDhtgQBZLiecdfWv39/MWYYNstrT0Zjdu2493UW1Mditfej9xNWg8U+ffqYE87o5DbXX3+9/Xit7j9y5Ejp2LGjsypep1CAADJ5XALI5A2pITUCBJCpcaVWBBBAAAEELAECSEuCj4UokC8BZLdu3cyejs421F6P2vsxWxcCyHBbhgAyXM+4atPHo7X34zfffGP2StTeMsnOJKwzF3/yySfmrNj6SeJ9nFuPqWP1bdy40Zysxvt+XCdOoYQFCCATprN3JIC0KXiRZQIEkFnWIJwOAggggEDeCRBA5l2TckEBBPIhgHzggQeiOk21bds2qjdkAJa0FCWADJeZADJcz7hqc47dqD0he/XqFdd+FMpdAQLI5NuOADJ5Q2pIjQABZGpcqRUBBBBAAAFLgADSkuBjIQrkegA5fPhw6dKli6vpWrRoIdOmTXNty8YVAshwW4UAMlzPuGpzzl7NWGFxkeV8IQLI5JuQADJ5Q2pIjQABZGpcqRUBBBBAAAFLgADSkuBjIQrkegD52muvif68vGPHDrP5dCLd2bNnJ/0UaDruBQLIcJULKoC8++67ZciQIebEKzoBS6aWKlWqmI9KX3zxxfL6669n6jQ4bhoFCCCTxyaATN6QGlIjQACZGldqRQABBBBAwBIggLQk+FiIArkeQGqbvffee3LttddK1apVZc6cOVKpUqWcaEoCyHCbqaACyHfffVc6dOggd911l7Rp0yZcyQC1PfjggzJ16lRzNuoGDRoE2JOiuSpAAJl8yxFAJm9IDakRIIBMjSu1IoAAAgggYAkQQFoSfCxEgXwIILXdVq1aJWXLlpVjjz02Z5qRADLcpiqoADJcOmpDIH4BAsj4rWKVJICMJcP2TAsQQGa6BTg+AggggEC+CxBA5nsLc31FCeRLAFnUNWbrewSQ4bYMAWS4ntSGgK8AAaQvS6CNBJCBuCicRgECyDRicygEEEAAgYIUIIAsyGbnon8XIIDM3K1AABmuPQFkuJ7UhoCvAAGkL0ugjQSQgbgonEYBAsg0YnMoBBBAAIGCFCCALMhm56J/FyCAzNytQAAZrj0BZLie1IaArwABpC9LoI0EkIG4KJxGAQLINGJzKAQQQACBghQggCzIZueifxcggMzcrUAAGa49AWS4ntSGgK8AAaQvS6CNBJCBuCicRgECyDRicygEEEAAgYIUIIAsyGbnon8XIIDM3K1AABmuPQFkuJ7UhoCvAAGkL0ugjQSQgbgonEYBAsg0YnMoBBBAAIGCFCCALMhm56J/FyCAzNytQAAZrj0BZLie1IaArwABpC9LoI0EkIG4KJxGAQLINGJzKAQQQACBghQggCzIZueifxcggMzcrUAAGa49AWS4ntSGgK8AAaQvS6CNBJCBuCicRgECyDRicygEEEAAgYIUIIAsyGbnon8XIIDM3K1AABmuPQFkuJ7UhoCvAAGkL0ugjQSQgbgonEYBAsg0YnMoBBBAAIGCFCCALMhm56J/FyCAzNytQAAZrj0BZLie1IaAr4A3gJw9e7ZvOTbGFhg3bpwMHjzYLvDWW2/J+eefb6/zAoFMCRBAZkqe4yKAAAIIFIoAAWShtDTX6SfgDSBXrlzpV4xtKRBo3bq1LFu2zK45EonYr3kRXIAAMrgZeyAQWMAZQAbemR18BQggfVnYmAEBAsgMoHNIBBBAAIGCEiCALKjm5mI9As4A0vMWq2kWIIBMDpwAMjk/9kYgLgECyLiYAhUigAzEReEUChBAphCXqhFAAAEEEDAECCC5DQpZgAAye1qfADK5tiCATM6PvRGIS4AAMi6mQIUIIANxUTiFAgSQKcSlagQQQAABBAwBAkhug0IWIIDMntYngEyuLQggk/NjbwTiEtCxI1jCFWjbti1jQIZLSm0JChBAJgjHbggggAACCMQpQAAZJxTF8lKA3yWzp1nHjx+fPSeTg2dCAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAM6tXVUAAAIASURBVAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOShAAJmDjcYpI4AAAghkjwABZPa0BWeCAAIIIJCfAgSQ+dmuXBUCCBSWAAFkYbU3V4sAAgggELIAAWTIoFSHAAIIIICAR4AA0gPCKgIIIJCDAgSQOdhonDICCCCAQPYIEEBmT1twJggggAAC+SlAAJmf7cpVIYBAYQkQQBZWe3O1CCCAAAIhCxBAhgxKdQgggAACCHgECCA9IKwigAACOSjw/wAAAP//LxpKDAAAQABJREFU7Z0J9CRFfceL3XUDPEUgJCi3QtAQF0RXgvo4gkmEGCBGAkROJSjwAAVFDgMElkNAlAcuVzgeh4rcLIYj4C6X4VxYUfBAkUMBkVMQBMFJfUerp6r/3TPdM9093T2feu//76ru6jo+1dPV/e2qXy3Wsc7gIAABCEAAAhAYisDHPvYxc+mll0bnPvzww2aVVVaJwnggAAEIQAACEBiNwHve8x5zzz33dBOZNm2aef3110dLkLMhAAEIQKByAoshQFbOnAwhAAEIQKBFBBAgW9SYVAUCEIAABGpJAAGyls1CoSAAAQjkIoAAmQsXkSEAAQhAAAIhAQTIkAchCEAAAhCAQNEEECCLJkp6EIAABKongABZPXNyhAAEIACBFhFAgGxRY1IVCEAAAhCoJQEEyFo2C4WCAAQgkIsAAmQuXESGAAQgAAEIhAQQIEMehCAAAQhAAAJFE0CALJoo6UEAAhCongACZPXMyRECEIAABFpEAAGyRY1JVSAAAQhAoJYEECBr2SwUCgIQgEAuAgiQuXARGQIQgAAEIBASQIAMeRCCAAQgAAEIFE0AAbJooqQHAQhAoHoCCJDVMydHCEAAAhBoEQEEyBY1JlWBAAQgAIFaEkCArGWzUCgIQAACuQggQObCRWQIQAACEIBASAABMuRBCAIQgAAEIFA0AQTIoomSHgQgAIHqCSBAVs+cHCEAAQhAoEUEECBb1JhUBQIQgAAEakkAAbKWzUKhIAABCOQigACZCxeRIQABCEAAAiEBBMiQByEIQAACEIBA0QQQIIsmSnoQgAAEqieAAFk9c3KEAAQgAIEWEUCAbFFjUhUIQAACEKglAQTIWjYLhYIABCCQiwACZC5cRIYABCAAAQiEBBAgQx6EIAABCEAAAkUTQIAsmijpQQACEKieAAJk9czJEQIQgAAEWkQAAbJFjUlVIAABCECglgQQIGvZLBQKAhCAQC4CCJC5cBEZAhCAAAQgEBJAgAx5EIIABCAAAQgUTQABsmiipAcBCECgegIIkNUzJ0cIQAACEGgRAQTIFjUmVYEABCAAgVoSQICsZbNQKAhAAAK5CCBA5sJFZAhAAAIQgEBIAAEy5EEIAhCAAAQgUDQBBMiiiZIeBCAAgeoJIEBWz5wcIQABCECgRQQQIFvUmFQFAhCAAARqSQABspbNQqEgAAEI5CKAAJkLF5EhAAEIQAACIQEEyJAHIQhAAAIQgEDRBBAgiyZKehCAAASqJ4AAWT1zcoQABCAAgRYRQIBsUWNSFQhAAAIQqCUBBMhaNguFggAEIJCLAAJkLlxEhgAEIAABCIQEECBDHoQgAAEIQAACRRNAgCyaKOlBAAIQqJ4AAmT1zMkRAhCAAARaRAABskWNSVUgAAEIQKCWBBAga9ksFAoCEIBALgIIkLlwERkCEIAABCAQEkCADHkQggAEIAABCBRNAAGyaKKkBwEIQKB6AgiQ1TMnRwhAAAIQaBEBBMgWNSZVgQAEIACBWhJAgKxls1AoCEAAArkIIEDmwkVkCEAAAhCAQEgAATLkQQgCEIAABCBQNAEEyKKJkh4EIACB6gkgQFbPnBwhAAEIQKBFBBAgW9SYVAUCEIAABGpJAAGyls1CoSAAAQjkIoAAmQsXkSEAAQhAAAIhAQTIkAchCEAAAhCAQNEEECCLJkp6EIAABKongABZPXNyhAAEIACBFhFAgGxRY1IVCEAAAhCoJQEEyFo2C4WCAAQgkIsAAmQuXESGAAQgAAEIhAQQIEMehCAAAQhAAAJFE0CALJoo6UEAAhCongACZPXMyRECEIAABFpEAAGyRY1JVSAAAQhAoJYEECBr2SwUCgIQgEAuAgiQuXARGQIQgAAEIBASQIAMeRCCAAQgAAEIFE0AAbJooqQHAQhAoHoCCJDVMydHCEAAAhBoEQEEyBY1JlWBAAQgAIFaEkCArGWzUCgIQAACuQggQObCRWQIQAACEIBASAABMuRBCAIQgAAEIFA0AQTIoomSHgQgAIHqCSBAVs+cHCEAAQhAoEUEECBb1JhUBQIQgAAEakkAAbKWzUKhIAABCOQigACZCxeRIQABCEAAAiEBBMiQByEIQAACEIBA0QQQIIsmSnoQgAAEqieAAFk9c3KEAAQgAIEWEUCAbFFjUhUIQAACEKglAQTIWjYLhYIABCCQiwACZC5cRIYABCAAAQiEBBAgQx6EIAABCEAAAkUTQIAsmijpQQACEKieAAJk9czJEQIQgAAEWkQAAbJFjUlVIAABCECglgQQIGvZLBQKAhCAQC4CCJC5cBEZAhCAAAQgEBJAgAx5EIIABCAAAQgUTQABsmiipAcBCECgegIIkNUzJ0cIQAACEGgRAQTIFjUmVYEABCAAgVoSQICsZbNQqAkj8Pjjj5sVVlhh5Fq/6U1vMu9+97vNrFmzzFprrdX922ijjcy0adNGTpsE6k0AAbLe7UPpIAABCECg5gQQIGveQBQPAhCAAAQaTwABsvFNSAVaQKAoATIJhX7jxx9/vNl4442TDrOvJQQQIFvSkFQDAhCAAATGQwABcjzcyRUCEIAABCaHAALk5LQ1Na03gVdffdX8/ve/Ny+++KL52c9+Zr74xS+aG264ISj0ZpttZk499VSz3HLLmRkzZkTHXnvtNfPMM8+YX//61+aOO+4wF154oZk/f350XJ4tt9zSnHDCCWa11VYL9hNoBwEEyHa0I7WAAAQgAIExEUCAHBN4soUABCAAgYkhgAA5MU1NRRtGYMGCBWaTTTYJSi3x8dOf/nSwLy3w7W9/23z84x83L7zwQhRlzTXXNLfddptZZpllon142kEAAbId7UgtIAABCEBgTAQQIMcEnmwhAAEIQGBiCCBATkxTU9GGEVi4cKGZPXt2UOqzzjrLfOITnwj29QvcfPPNZsMNNwyiaBTlvHnzghGUQQQCjSSAANnIZqPQEIAABCBQFwIIkHVpCcoBAQhAAAJtJYAA2daWpV5NJ3D33Xeb9773vUE18gqQOnnTTTc11157bZDO4Ycfbg4++OBgH4FmE0CAbHb7UXoIQAACEBgzAQTIMTcA2UMAAhCAQOsJIEC2vompYEMJFCVAnnvuuWannXYKKGi17KeeesrMnDkz2E+guQQQIJvbdpQcAhCAAARqQAABsgaNQBEgAAEIQKDVBBAgW928VK7BBIoSIB966CHztre9bQqJW2+91ay//vpT9rOjmQQQIJvZbpQaAhCAAARqQgABsiYNQTEgAAEIQKC1BBAgW9u0VKzhBIoSIJ999lmz7LLLTqFxwQUXmG222WbKfnY0kwACZDPbjVJDAAIQgEBNCCBA1qQhKAYEIAABCLSWAAJka5uWijWcQFEC5PPPP2+WXnrpKTTOO+88s/3220/Zz45mEkCAbGa7UWoIQAACEKgJAQTImjQExYAABCAAgdYSQIBsbdNSsYYTKEqA/OUvf2lWWmmlKTRuuukms8EGG0zZz45mEkCAbGa7UWoIQAACEKgJAQTImjQExYAABCAAgdYSQIBsbdNSsYYTKEqAnDdvntlyyy2n0NDIyKWWWmrKfnY0kwACZDPbjVJDAAIQgEBNCCBA1qQhKAYEIAABCLSWAAJka5uWijWcQFEC5HbbbWe+8Y1vBDT22msvc+KJJwb7CDSbAAJks9uP0kMAAhCAwJgJIECOuQHIHgIQgAAEWk8AAbL1TUwFG0qgCAHywQcfNKuvvnpA4H3ve5+54YYbzJJLLhnsJ9BsAgiQzW4/Sg8BCEAAAmMmgAA55gYgewhAAAIQaD0BBMjWNzEVbCiBUQVIiY+bb765uf/++yMCsgV51113meWXXz7ah6cdBBAg29GO1AICEIAABMZEAAFyTODJFgIQgAAEJoYAAuTENDUVbRiBYQTITqdjFi1aZC677DIzZ86coMYa+fj1r3/d/NVf/VWwn0A7CCBAtqMdqQUEIAABCIyJAALkmMCTLQQgAAEITAwBBMiJaWoq2jACSQLk29/+dvPWt751Sk1effVV8/jjj5tf/OIXU46tueaa5phjjukuRLPYYotNOc6OdhBAgGxHO1ILCEAAAhAYEwEEyDGBJ1sIQAACEJgYAgiQE9PUVLRhBJIEyCxVWHvttY3+1lprre72wx/+sJkxY0aWU4nTYAIIkA1uPIoOAQhAAALjJ4AAOf42oAQQgAAEINBuAgiQ7W5fatdcAkkC5EEHHWSOPPLI5laKkpdGAAGyNLQkDAEIQAACk0AAAXISWpk6QgACEIDAOAkgQI6TPnlDIJ0AAmQ6G45MJYAAOZUJeyAAAQhAAAKZCSBAZkZFRAhAAAIQgMBQBBAgh8LGSRAonQACZOmIW5UBAmSrmpPKQAACEIBA1QQQIKsmTn4QgAAEIDBpBBAgJ63FqW9TCCBANqWl6lFOBMh6tAOlgAAEIACBhhJAgGxow1FsCEAAAhBoDAEEyMY0FQWdMAIIkBPW4CNWFwFyRICcDgEIQAACk00AAXKy25/aQwACEIBA+QQQIMtnTA4QGIYAAuQw1Cb3HATIyW17ag4BCEAAAgUQQIAsACJJQAACEIAABPoQQIDsA4dDEBgjAQTIMcJvYNYIkA1sNIoMAQhAAAL1IYAAWZ+2oCQQgAAEINBOAgiQ7WxXatV8AgiQzW/DKmuAAFklbfKCAAQgAIHWEUCAbF2TUiEIQAACEKgZAQTImjUIxYHAnwggQHIp5CGAAJmHFnEhAAEIQAACMQIIkDEgBCEAAQhAAAIFE0CALBgoyUGgIAIIkAWBnJBkECAnpKGpJgQgAAEIlEMAAbIcrqQKAQhAAAIQcAQQIB0JthCoF4GFCxea2bNnB4U68MADzVFHHRXsIwABEUCA5DqAAAQgAAEIjEAAAXIEeJwKAQhAAAIQyEAAATIDJKJAYAwEFixYYDbZZJMg5z322MPMnTs32EcAAiKAAMl1AAEIQAACEBiBAALkCPA4FQIQgAAEIJCBAAJkBkhEgUAFBF5//XXzyiuvmBdffNE8+OCDRqMdb7jhhiDnN73pTebss88273//+80b3/hGs8QSS5jp06ebadOmBfEITB4BBMjJa3NqDAEIQAACBRJAgCwQJklBAAIQgAAEEgggQCZAYRcEKibwwgsvmDXWWMM8+eSTuXPWiEiNjMRNNgEEyMluf2oPAQhAAAIjEkCAHBEgp0MAAhCAAAQGEECAHACIwxCogMDjjz9uVlhhBaMRjhrVOHPmzO7fjBkzgtxfe+21blijJF9++WUj4RIBMkA0sQEEyIlteioOAQhAAAJFEECALIIiaUAAAhCAAATSCSBAprPhCAQgAIGmEECAbEpLUU4IQAACEKglAQTIWjYLhYIABCAAgRYRQIBsUWNSFQhAYGIJIEBObNNTcQhAAAIQKIIAAmQRFEkDAhCAAAQgkE4AATKdDUcgAAEINIUAAmRTWopyQgACEIBALQkgQNayWSgUBCAAAQi0iAACZIsak6pAAAITSwABcmKbnopDAAIQgEARBBAgi6BIGmUQePTRR8tIljQnjMDKK688YTWmunUkgABZx1ahTBCAAATyEUCAzMeL2BCAAAQgAIGAAAJkgINAjQisu+66ZtGiRTUqEUVpGoGHHnrIrLrqqk0rNuVtIQEEyBY2KlWCAAQmjgAC5MQ1ORWGAATaQOCuu+5qQzVaUYcvfOELZsGCBVFdrrzySvOWt7wlCuMZL4HZs2ePtwBjzB0BcozwW5L1JAuQjz32mNEfrh4Ett9+e/PjH/+4W5hp06aZ22+/vR4FoxRdApPc13IJQAAC2QkgQGZnRUwIQAACtSGw+OKLm1deeaU25aEgEKgjgZNPPtnsvvvudSxaJWVCgKwEc6szmXQBcsUVV2x1+1I5CBRB4KqrrjKbbbZZEUmRBgQg0HICCJAtb2CqBwEItJMAAmQ725VaFUsAAbI3BXv69Olmiy22KBYwqbWSwGWXXRbVCwESATK6GPBAIIUAAmQKGHZDAAJTCCBATkHCDghAAAL1J4AAWf82ooTjJ4AAGQqQr7322vgbhRLUmkDcpi0CJAJkrS9YClcLAgiQtWgGCgGBRhBAgGxEM1FICEAAAiEBX4CcNWuW+cAHPhBGIASBCSVw2mmnRTVHgESAjC4GPJkIIED2MMn+oz8Fe/PNNzcrrLBCLwI+CEwwAb+vRYCc4AuBqkMgJwEEyJzAiA4BCECgDgTiAuS9995bh2JRBgiMlcAZZ5xhdt1116gMCJAIkNHFgCcTAQTIHqYkAXLevHm9CPggMKEEDj74YHPEEUdEtUeAjFCU5sHGZmlocyd89dVX5z6HE3oEECB7LPBBAAIQaAwBBMjGNBUFrZAAAmQI21+ERjYgmYId8iE0lQACZI8JAmSPBT4I+AQQIH0a1fjf+973mrvvvruazMilL4FOp9P3OAf7E0CA7M+HoxCAAARqSQABspbNQqHGTAABMmwABMiQB6HBBBAge4wQIHss8EHAJ4AA6dOoxo8AWQ3nLLkgQGahlB4HATKdDUcgAAEI1JYAAmRtm4aCjZEAAmQIHwEy5EFoMAEEyB4jBMgeC3wQ8AkgQPo0qvEjQFbDOUsuCJBZKKXHQYBMZ8MRCEAAArUlgABZ26ahYGMkgAAZwkeADHkQGkwAAbLHCAGyxwIfBHwCCJA+jWr8vgC52GKLmV/96lfVZEwuRvY3Fy5cGJFAgIxQDOVBgBwKGydBAAIQGC8BBMjx8if3ehJAgAzbBQEy5EFoMAEEyB4jBMgeC3wQ8AkgQPo0qvHHBcg//OEP1WRMLmb27NkIkAVeBwiQBcIkKQhAAAJVEUCArIo0+TSJAAJk2FoIkCEPQoMJIED2GCFA9ljgg4BPAAHSp1GNHwGyGs5JuSBAJlEZfh8C5PDsOBMCEIDA2AggQI4NPRnXmAACZNg4CJAhD0KDCSBA9hghQPZY4IOATwAB0qdRjR8BshrOSbkgQCZRGX4fAuTw7DgTAhCAwNgIIECODT0Z15gAAmTYOAiQIQ9CgwkgQPYYIUD2WOCDgE8AAdKnUY0fAbIazkm5IEAmURl+HwLk8Ow4EwIQgMDYCCBAjg09GdeYAAJk2DgIkCEPQoMJIED2GCFA9ljgg4BPAAHSp1GNHwGyGs5JuSBAJlEZfh8C5PDsOBMCEIDA2AggQI4NPRnXmAACZNg4CJAhD0KDCSBA9hghQPZY4IOATwAB0qdRjR8BshrOSbkgQCZRGX4fAuTw7Co588UXXzQvv/xykNdiiy1m3vzmN5s3vOENwf6kwPPPP2+0StYSSyxhJFjIvfbaa+Z3v/udeeWVV8yf//mfJ53GPghAoOYEECBr3kAUbywEECBD7AiQIQ9CgwkgQPYYIUD2WOCDgE8AAdKnUY0fAbIazkm5IEAmURl+HwLk8OxKP/PHP/6xeec735mYz1prrWW+973vmRkzZiQe185f//rX5i//8i9Tj+vAVVddZTbbbLO+cTgIAQjUjwACZP3ahBKNnwACZNgGCJAhD0KDCSBA9hghQPZY4IOATwAB0qdRjR8BshrOSbkgQCZRGX4fAuTw7Eo/86WXXjJnnXWWeeqpp8z9999vLrrooiDPb37zm2bbbbcN9vmB3//+9+akk04y//d//2cuueSS6NCb3vQmowfMNddc0+yxxx7d0ZTRQTwQgEAjCCBANqKZKGTFBBAgQ+AIkCEPQoMJIED2GCFA9ljgg4BPAAHSp1GNHwGyGs5JuSBAJlEZfh8C5PDsKj3z8ssvNx/96EeDPCUgSpicPn16sD8pcPTRR5uDDjrIrL322uaGG24wyyyzTFI09kEAAg0hgADZkIaimJUSQIAMcZctQN52223m/e9/f5SpPnDK5Msb3/jGaIaGPqa++uqrXXMyL7zwQjfu+uuvb2699dboPN/jp+nSmzlzptGf0omndf3115sPfehDfhL4RyCAANmDhwDZY4EPAj4BBEifRjV+BMhqOCflggCZRGWEfZ0Gu4ceeqhj7RuOtQbWlmLn5z//eell+OxnP9uxzdyxIx67W/n1Z0c2ZsrbCpDd+HbKdab4RIIABOpN4M/+7M+ie8GsWbPqXVhKB4GKCPz3f/939LtQH3nyySdXlHM9s3n3u98d8bAfKwsv5NVXXx2l755Lsmy33nrr1LJcdtlludJctGhRalocyE/gX//1XwP+etaeVPfLX/4yYLH55ptPKgrqDYGAwH/+538Gvw3eLwM8pQTe8573RMztehCl5EGinY6dcToFgxV/I/Z6xsGNRqCxBN1Lxm677TYagRHP3mCDDboX5Ny5c0dMqf/p1uZjx9pz7DzzzDMdOyIg+hHYEY2ZRNgPf/jD3XN++9vf9s+IoxCAQCMINEWAfOSRRzr6APLcc881giuFbDYB92zgRDAEyHIFSF0t1txLR88WEmvOOeec6PnEtYG21mRM59FHH+3eBxR/kFN6DzzwQOe0004LnnmU1kc+8pHOFVdc0bnvvvs6dnTloKQ4npMAAmQPWJMEyO9+97sT/8Gl13L4yiaAAFk24anpI0BOZVLkHj1z/Nu//VtikgiQiViG3tlYAXKvvfbqPuS+733vG7ryRZxop0F3y7HSSit1Xn/99SKSnJLGr371q24e22+/fffYYYcdFjzgX3nllVPO8XdolKYe2jfeeGN/N34IQKDBBJoiQLr71XXXXddg2hS9KQQQIMOWKnsEZJhbpyMRxBce5T/yyCPj0XKFjz322CjNr33ta7nOJXJ+AgiQPWZNEiDdgAgGGvTaD195BBAgy2ObljICZBqZ0fcfddRR3eeMm2++OTExBMhELEPvbKwAufvuu3cvFP0Yx+mOOOKI6MF4/vz5pRTl0ksv7eZhbVt103/66aejPPVwLxG231R090IwZ86cUspHohCAQPUEmiJAfvCDH+zer6wtreohkePEEUCADJu8agHSPcT7IuRdd90VFipn6LjjjuveQ8b9wTlnsRsbHQGy13RNESCtbdXub0SDInAQqIIAAmQVlMM8ECBDHkWErrnmmo61Y929f+69996pSSJApqIZ6sDEC5DqtH/yk590fvSjHw01lUe2cdyD9k477TRUIww6ydl/VBmdswvKRPkq/2uvvdYdmrL90pe+1I174403TjnGDghAoJkEmiBA8lLUzGuryaVGgAxbr2oBcpNNNgmeTWQyJsuU67DUYUh29/Scc9JJJ4UHCJVCAAGyh7UpAqRdiKn7G9HsMBwEqiCAAFkF5TAPBMiQxyihJ598srPPPvtEzysyc6cp2GkOATKNzHD7J1KAlOC4//77d20qOvHQbWVT8ZRTTsllr8zZV1Qazz777HAt0ecsZ//RH+XopmW7cmuUUZpz5cNWUhoh9kOgeQSaIEDyUtS866rpJUaADFuwSgFSzxjumcRtt9xyy7BAOUMSL11a9957b86ziT4MAQTIHrWmCJCHHnpo93dy8cUX9wqPDwIlEkCALBFuStIIkClgcu4+/fTTO86Ennu+GGQqBgEyJ+QB0SdOgPRtCemi05f1Y445pnPwwQcHF6OU8FtvvXUAvj8evuCCC6IHZDdNOtOJGSI98cQT3bSd/Uf/lP322y/KV3VJmgLu7D9qVAIOAhBoD4EmCJCHHHIIL0XtueQaURMEyLCZqhQgb7rppuCZRM8lX/3qV8MC5Qzdcccd3TQ1krIsO9s5i9T66AiQvSZuigDpTJ08/vjjvcLjg0CJBBAgS4SbkjQCZAqYjLs1KGLTTTed8pwya9aszosvvtg3FQTIvnhyH5wYAfK1117r7LzzztFFp0Vjvv/97wfA9KVdAqJTw7XVyo2DnAw+u5Wpi7ZRFLf/6Jcl/mCUtMiMs/8oW5U4CECgPQSaIEDyUtSe660pNUGADFuqSgHSt4ntnqNGtf94/PHHd5/J0lamDGtLqAgCCJA9ivHnbA1aqJv7zW9+0/2NYP+xbi3T7vIgQFbfvgiQ+Zlr3Yzzzz+/s9122wX6jntG0Xbu3LkDE0aAHIgoV4SJESBPPfXU6MKTWHjfffelgtLQXP/C7GcTwCWy5557Ruf0S9vFz7pNsv/onyuDqX5Zb7nlFv9wx9l/1MgEHAQg0B4CdRcgeSlqz7XWpJogQIatVaUAGbf/qGeTUe0/fuQjH+k+45x88slhxQiVRgABsoe2CQLkdddd1/2N9FtAoVcjfBAohgACZDEc86TSZAHyqaee6tx///2dBQsWdLcKl+V80XHZZZcNdBJfM5FfxzXbdJBDgBxEKN/xiRAgtfqqG6Goi+3cc88dSGmzzTaLLliN4tEIyn7uzjvvjOIfcMAB/aLmOpZk/9FP4JFHHonyVd1k79F32H/0aeCHQHsI1F2A5KWoPddak2qCABm2VlUC5Msvvxw8i+h5ZNTRYq+++mqUZnzGSlhLQkUSQIDs0WyCAOlMnVxyySW9guODQMkEECBLBpyQfJ0FyJ///Oeds88+u/P5z3++s+OOO3b1iHXXXbezwgordGbMmBH15Xo2cH/ar+OKJ71C5+l86TSPPvpoAoH0XXlER5e/trvuumt6ot4RBEgPRgHeiRAgP/nJT0YXu4RI2UUc5DT12r9Asxh2llioc2Q/Ug/Oo7p+9h/9tHfbbbegrLfffnv3MPYffUr4IdAuAnUXIGVXV/dDXoradd3VvTYIkGELVSVAOnMv/nPTqPYfb7vttu49RM9t2H8M27XMEAJkj24TBMj111+/+zvJMoqnVzN8EBiNAALkaPyGObtOAqQTHKWxxBd08Z8DRvH/zd/8Teczn/lM58ILL8wkSMoG7t/+7d8Gmsig/K+55ppMTYEAmQlT5kitFyCfe+654ELceuutM8GRMVL/otU0oEHuxBNPjM759re/PSj6wOP97D/6J//sZz+L8lWZ3agD90IwaGUnPy38EIBAMwjUXYDkpagZ11HbSokAGbZoVQKkM/fiPzdpZsgo7rjjjus+22R9bhslL87tEUCA7LGouwCJqZNeW+GrlgACZLW8ldu4Bcibb765s88++3S03oXf11flf//739/N/8Ybb0yFr3U5/vmf/zlT+dZbb73UdOIHECDjREYLt16A1DBe/4dxwgknZCbmFlBw52sqdz/3q1/9KsrrYx/7WL+omY4Nsv/oJ+KP8lR577777sj+Y9wupH8efghAoJkE6ixAPv/88917oUaF4yBQJQEEyJB2VQKkM/finpe0HdX+ozOFc8opp4SVIlQqAQTIHt66C5DO1IneF3AQqJIAAmSVtP+Y17gEyK9//esdZ4/Z7+Oz+pdaaqnOqquu2llnnXU6WjBXzyWrrbZaZ+mll450k6xpuXj/8A//0DnzzDNTV6+O6yLuPH+rmVpZHQJkVlLZ4i2maLYxGuf22GMPYx9Kjf0xmoULF6aW3656ZL7xjW9Ex+0wXmNXU4zC/Tz2q7u56KKLoihZzvXPsYKksdOxo/PzeuzQY2ONtBo7rcIstthifU//8Y9/bN75zndGcVRH+2XUXHvttcbaZjKLL754dAwPBCDQfAL6Tb/yyivdisyaNcvce++9pVRK9zFrNNr85Cc/MSuvvLL5wAc+YN7xjnf0zev666839uHA2JciY6dhTomre9q3vvWtbvl32GEH89a3vnVKnLrssKPhzTPPPGOeffZZY23MdP3a6s8uumHsSM9uUdUWdsVf8+CDD5qHHnrILLnkksZOS+n+DeKlBKyd4W7aykt/Sl/3f/3ZBzZjvzh387FTUY015G3s9FRjp5uY1Vdf3divvebNb35z93i/f7/4xS/M5ZdfbqyZDvPwww8b+6XY2AdAs9FGGxn1XX4fEk+nKg7xfPOGzzjjDGNt+kSn2cVLzO677x6FJ81jbSuZRYsWdas9ffr07nVWNANd+/FnDDsTw8ybN2/orKwZG2M/snTPt/Yfzbve9a6h0+LEfATsB3RjZ+BEJ+l+Zl8eo/AkeezAA7PiiitGVR71uo4SSvD88Ic/NHbmklGeev63gyDMW97yloSYvV3W/qOZM2dOt70++tGP9g78yafngv/5n/8xyyyzjPnEJz4R/aamRKzBjqr6GGueKupj1deqj3V9uhUtzPLLL9+loXene+65p9vX6n6ke9Cmm25qrN26gbQmoa+14o054ogjIhZXXXWVsR+NojCe4glYEczYAUbdhKUL/OEPfyg+kz+laNeY6Oon0lDUBw9yVlw0G264Yfe5WO8KerbUn+4906ZN63u6na1q/D+7cK6xoy2Ntvrt9XNve9vbzDbbbGO23XZbozI4N3/+fPOhD33IBRO3t956a/QMnxjB2zl79uxAb2qofObVaMzebDpl/WLZF4quaq6vAf3c29/+9kBdty/G/aIHx/yVrW0zdfbff//geFJAU68VV3+akj2sy2r/0U9/++23j/J2ZdAXAhwEINA+AlWMgIyPIHf3lUEr0rov4zIjEXcaUSI7uS4t2Y4ZdaRUPI8iw/4CZq7MbisOWnxD00/9Ornjbqvp6Oob+tmxU1oufnxrXyy7VbKiYeLUF5XRfohLrbb4ujZxaeuclVZaKchT/alMdyS5qjgk5Z1nHyMgQ1pVjIC0D/HBdaRr7Ctf+UpYkJwhl6auu36/m5zJEj0DAUZA9iBVMQJS17eb8eTuz9rq2tfvoJ9zpk40Ayvu7ACE4HeZdbGFeDpVhavqY+wAjYCLz/xrX/tat7qa4plUHvWRVrRMRTJJfW38mcIKkKlcOFAMAV1/7nq1AmQxicZS0XOmNBb7UTvKy+Xpb2Vrce+99+5odGRZ9mftx82OFRI7VujuaEbEoDJttdVWHU0Tt4MBOlb47Ft++0EhVvP+QUZA9ueT92irp2Crk/B/LPJranJWpwveP9+Odhl4qjof9yI6yvTDrPYf/QL94Ac/CMqrsh911FF+FPwQgEBLCJQtQLqpXbqPnHXWWR07kqLjFtrSPr3cpLl+L0W6J/n3VfntV860pMa+P+klxJV/v/32C2zyfOpTn+oay7Yjv7p2auICn+zzvvDCC4l1GiRAytavK4v90tuxswACjmn9jf2K3fHNiahMV155Zcd+Oe+WQ/3kXnvtFaSlB764c3m7uvvbIjnE880bRoAMiVUhQB5zzDHB9aNrY1T7jy7NrPYf9exlR2l3BfQrrriie8/Sb0r2oHD5CCBA9nhVIUD+13/9V/f3o49x6lf1Au3fX+0IvV6BPN8gUycagOCnI79e6OvqqupjBgmQdpZAxE3CsN9/iqFs4CW5SetrESCTroJy95UtQGoB3jXWWCO6/uP3D02Z1m/Czqoot6IpqWuRmaOPPrpjZ+ukllHvRssuu2xwPGkVbl2/eRwCZB5ag+O2WoB84IEHggtQPyQp+1ndaaedFpyvh4Ms7sADD4zOG/YhfJdddummYafaZckyihPvWNNGs0Qn4IEABBpJoEwB0he79GHDOYkB7oEk7SF80EtRkgCpkZZ1dRI2JBrqgUu2a1z9/a3260U17iR+xF8C11577U7SaBUJgi+99FI3nS9/+ctBPltuuWVngw026O5zi4odeuihQRyVJy62/OhHP4pESx3Xi1SaAOq3reJqBWLfVcXBz3MYPwJkSK0KAbIM+48uzaz2H/fdd98pvwddx/79KyTTzNCvf/3rznnnndexph5KqwACZA9t2QLkZZdd1r1u9QFJfadzvhinOEnOjXBM64vjfY9+D+rb6+qq6mM04lQLjap/3GmnnYL7hma6OfbuQ1xcgNQH1ribxL4WATJ+FZQfLkuA1IK98Q/Rul+4P9lr1IcSrXxdB6eZR3o2cIMdXDnTthoUcP7553dmzpwZ1Sn+jDuoXgiQgwjlO95qAVKjHeMXo9TzrE6jfvzzNbIxi7N2XKLz9IPO69xDhfLO+/Csl2S/zNbWSd7siQ8BCDSAQJkCpPuQ4aYjORwSz9z9JekhXPHc/SvtpcjaWgpGUio9GZJugtMUI1d/t9WCY9ZGTWrxk0RITSVxIxDTTvRHm7q8NMLSOWvrMCiLXpr8NOXXqH13rrb9FlJ78sknoxcvxZUAlOaq5JBWhrT9CJAhmbIFSI2o8q8x+WWsfhSn5xaXZtZnIL1MaNSkRhm7c/WbsLZVRylKrc61thijuuleXJZDgOyRLVOA1HXuZkz5JjTis7fSRuo4AShNoNQ0RPdbcFsJZU1wVfUxztyV4+O21u5dhClu3io+KntS+1p3/TlmTMGOLpnSPGUIkGq3uLjm2lTPD1q819pAL61OoyasUZvWNuuUe52rg6aJOych0tr07cbVB488Ls4oz7nEnUqg1QKkbHi4C9Btk0aeTMXyxz3nnHPOlPPT4sb3uy9megDWqJZBTiMVtWKTf3NRmXW+Or88L+gaLaNzsf84iDrHIdBcAmUJkBpZo/uHpur6L+/xF7E0keGggw7qnp/2UiTiP/3pT4N7q6YEN8E5u3SuPxGjLA9m1iB9UF+dP3fu3L5VThq94o+y1EhGTcVWWuo34g//eihz5dQ2y2p/xx9/fHDO9773vcQyVskhsQB9diJAhnDKFiDj14KuNV1Hozg9DykdPf/ktf+o0YHuune2U0cpS53OPe6446K6yb55WQ4Bskc23u9J4C7KaUSOrtWdd945SNIufhm1c7/fk12YrBtPH4/SXLwf6Ge/MC2NceyP31fK6mv1jOPuF24bn+2m2XSOtZ57ZOrBd3HGk9LXIkD6V0E1fl8jKMIGZLwN3W9AW414bJKzC+5N+S27+hxwwAFRVW644YbOX//1X0fhrB4EyKykssVrtQDpLwjjLsI0WypJuNzDgTtX234jXfw0/NGTdvVs/1CiXz8Opa8Hbn0RVWfrvoxqfx4x0Y2ClP0jHAQg0E4CZQmQTkA8/PDDA3AnnXRS0LkfdthhwXEXcA/q/V6KFFcjJN29tZ89GY0SsSvwdSRo6p6m+7peAPIKE658o2w1ysqVWVtN+8zq9IHJP1f39379iUZJ+vHTBN+k/DWVz+8/lI4YDnLxWQOf+9znEk+pkkNiAfrsRIAM4ZQtQB577LHBdapr7Y477ggLkTMkG09KJz7SKEsyGiXsfjfxEdxZzq9zHAkhekbU86Hug2U5BMge2TIFSDd9UC/EvpNw7q5hbRcsWOAf7vo1ZVLH0mz/uhM0Os+fueCPkndx3Fb9hn67Gv0nE1Tf+c53Ek2LuPhlbqvsY3zW8uf5gDLJfW1cvIp/BC3z+pjUtIsUIO3K0cF9xv0OZFIo6Z5TZ+ZxUwquLv5WM7ucs6vbO2/mLQJkZlSZInaXULIN1DhnDfAbO//f2B9jsCy6X5ELLrjA/Pu//7u/y9ivf90l4YOdKYGk8+30QWONm6ac0dttO6Xu8vPaY6eymWuuuaZ3cIJ8dpSOsbYaJqjGVBUC1RBYeeWVjRWwupnNmjXL2EViCsl4nXXW6aZlbUUZO8omStN2vsYKVFHYClrGriIXheVx9z37UmTuu+++4Fg8YBfaMnb6cne37hGLL754EMUKjMa+CJnPf/7zxoqZ3WP25dvoniKne78VKsw//uM/dsNV/Lv99tuNfWmMsrICpLEvK1G4n0e87ItgEMUulmG22GKLYJ8L/NM//ZO5+uqrXdCoP7IPjFG4n+db3/qWsaMjoyhWjDR2qpmxX8yjfUkeOxqk2785xna0j7FTVqZErZLDlMwH7LBT041d7TWKZaflGjvCKApPmudDH/qQsdOYu9WePn26URsX6XT92hHMQZJ2apOxRt+DfXkCG264obELcZhTTz3VfPrTn85zqtF90Y447p6j+5UdFZHr/LpH1n1Rv+Np06aVVlTdl3V/ds5ODzZW9HTBidrqvqk+0bm0e6I7nnWrd4nllluuy9Xapo/a0w6SMH/xF38RJaN7txVBp/ye/vd//7f7bmE/5Bm74nwUP8nzmc98xpx44onGCgvGCgtTovzmN7/ppmE/KkbH/L7WvrgbHbOjhqLjZXuq7GPi/aLuH3aaZqYqTnJfa0d6GrtYa8TJjgQ11uxLFMZTPAE7GCl61td1az8oDJWJFeyMtb0+5Vw76tFY++JT9td5h7u/+WW0U7KNNTdhrNkSf7fRvcwOCgv2ZQ3Mnj070Jusypb1VOIlEcgkU9YwkpaIt/XpTj1LK56mLSuO/5dlupxLLz6sXunoq2NW5494ybP4Tdb0mxCvn1Fbv13wh9fpuHi4L/Ljyp98h7sOrABZ2O3Aijcd32aKEtboOb9tNMoxyQ2y/+ifo5Wvlaa+6MadRmloWprLU6MvNeVYTlPINPrSHUsbiRlPs4jwKKMylH98VKLMa6S5+AhIjU7M6vy+R5xkCzKrc+ZDdF58KppLo0oOLs+s2/gISHedsDUdK0BmxZg5XvyazjNSNykT++Ei+m3ntVen5yzXzhop6JuQSMqLfckE4iMgHVO2pmtjNJlavr0aOaeRRjL15DstrOBz9qcO+vHcTAWt2DzIWZGom+YXvvCFKVH1TuTsDeu3LHMo7nejEbf+4mTXXXfdlPPL2lFlH+Pzlj+Pm+S+Nj4CMs6R8HDP81m5WQEyz6UaxdUzfjwP3YuaNupRFTrkkEOm1OU//uM/unXVgjn+e4Srsz8SMoKSwcMIyAyQckTJd6fNkXDZUbMIkEkCYh77J74tIXfh5pnC7dug1Mqvk+gQIMvtgNx1WdQWAbJZ7eXavUgBMuk+FX/QTFuZ9sADD+w+DGR5KXI2dpOmMfsrZadN6zn77LOjBw/5k5ymaUvQ0EIWWf98O4vxNEd9KdJDnmszbdOEXOUbFyDzLKDmpsG7vCTGzJkzJ9Of4rrztE1yVXJIyr/fPgTI9HtY0QKkPgr414r8eiEYxe25557dNIdZZEVTR115ZAsbNxwBBMj031CRNiCTWid+704zneHiaVX0Qc69hNsR90FUfehzq83rvq9FjuJOfagvsqUtCqV7QdY+1sXrNyCkyj7G3TO0TfvoFufiwq4dXBqT1NfGnwsdA7bp948i2QwjQCa9kw8ryLnfwLi2cZvlYptUFzuiM3oucPyT4g2qBwLkIEL5jie/XeRLYyyxswiQo9qAdC/I7oLVVis+ZnXquGUoXOdpq/CkuaSbnc8TfzUdVVbOCJD1ao+s7VamAKmXFNkc88uStpiXexjP8lLkhAatSuc7pe3y6jdyT+Vy+Wnkhlabjjs7hTNKy6U5aOuvNB1Pb9SXoviXZ72spLm4AOlGpaTF9/fHR6UNqnPa8TT7YlVy8OuVxY8AmX4PK1qA1O88fu1ksXmd1o76QOzS04Ired1uu+0WnW+nnKaeLturun80xem3n3fFzlHqhgCZ/hsqU4C0Zk+i61e/gzQRXsKdjqfdn+NtL1FN8eP9sj7uud/bkUceGT8tCvt9cpqw7xZEc+ll2forTUeZ/clTZR/jl1WCbB43yX0tAmT6fcK/psry5xUg99tvv+j37so0jBCX5/dRVtykGa791sooQoREgCy2NVttA/KWW24xG2ywgf2d9dxjjz1m3vrWt/Z29PHZUTXGfvkLYlj8QXhQQLYU7GIO3Wiy0SZbbZPkZMMpbh9qkurftLrKzpOzn9W0sk9aeWVX1r5Ed6ut+0pRNiDjHO1KyMYuZBHtTrNpa81TdO3rys6hzunnZGNwqaWW6kaR/SkrxEXRZdfRTi/rhnUPtqM3omNxj+6tzl6NbP/tsssuQRTZ/7NT2IJ9gwJWgDTWAH9itFHsUinBL37xi8aO7gzSTrOX59uAFB9xyurEVoyds1PvjB0B6YKZtrIv9IY3vCExbpUcEgvQZ2fcBqTslK6yyip9zmj3IT0HuWunaBuQskFrF8MKAMpeoOyzDuNky84ufNS9HzzyyCORHe2saa2++urmwQcf7EaPl+Oll14yp59+etd2uF3EqpuH7OfJ5pWu9To6+xHdfOlLXzJ2VfBu8ezLorHTy0q3exu3Afl3f/d3ZokllqgjotLLZBdBM/Pnz4/yKcoGZJSg55k7d66xH+aiPeq/dO+OO/X99gOVyWKD2L0H6V3Imj0JkpL9ZDuturvPTrc2a6yxRnDcDzi7rNon22rveMc7/MNGNtesCZZg36CAbDzH7fS7c6rsY/zfv35jeWzETXJfG7cBaT8IB/ZLXVuyLY6A35/runXvAINy8LUIFzfvte7OG/f2kksuMVtttVVQjPXWW697L3PvFcHBPwVkx1b9ve/yMMAGpE+uAH+xemZ1qWUZAWlfgqeo/XlsMdqH1eB8fenK6/wv8knTG/KmR3wIQAACIlDWKthxum5FWtvddO+HGlWY5OyCKd3jSVOq4/HdyESNgow7NyVM+dmFKOKHg7BvZiNpZIp9eQ/u4a4O/bZljoCMr9SXdQRkv3gBkD8FZFfTr2MS56Tzsu4bdXRKHg5Zy+TixUdAauX0SXZlr4IdHx0dX9E3K/u77rorumbzrELr0reCZXS+rn1/xKBGlmk0mfbrt+CbeIhPS3XpjXurEWkqr2Yl6Br2bfEtSFgVucjyxkdATvKza5mrYMfbTCN4/Pt22nRnZ+oky7XrrpuLLrooyE6jgP28FO7n/HcZ+6FgSlS/3/bT7ecvcwRknj7GL6MVJKbUrd+OSe5r4yMg08zl9OPHsXwE/OvNCpCZT5b2YT9CRL/5vNd55oxKjnj99ddHdXC/W43wzqrtWAEyOn/ppZfuaKZsVscIyKykssVr9RTsn1sDpO4CdVvZA8vq4i+veW2DvPjii1H+sv2FgwAEIFAUgaoEyPhLUdrLqIzl6z476KVIC3m5aUsSBnynqYbuXq3to48+6h+e4vdFC8WPOzvyq6MXyDx//ewEjyq8uSnjro79ptD5U7DzCpB6uHR5aFv0w2aVHOJtOiiMABkSKluA9K9TXWtpHyjCUoUhPau5e4IWsfHFwzBmeijtY4QWxtLvR781LaohJ7/7ffSbepqeW7lHZK9V5dNiYI6FHeEelVniSpkOAbJHtyoBMi4ISthPc64fiU+pjsd392mZgHLXkYujRc3cb0DHB7mvfvWrUfyPfvSjU6LLPn6eflZxk8ymuIRd2V0Zs3zYdOdq6xi58/v1tS6Otnn7yknuaxEg/SuuGv+wAqRK9/TTT3dkQiHvNV5NzQbnoud9iYb+71XPDeob8ziJkNJztE5HHocAmYfW4LhT39gGn1OLGFlGQOpF179Q5b/11lszl/+zn/1scL6+HuRx559/fnS+FrTBQQACECiKQFUCpBMGdP+UP825B/5BC3W5+2rSqDyN+PDv2YPsHvqr3uo8ffQp0436UiQhxK+fRpWkOV/YyStA+l95lV+WF8y0ciTtr5JDUv799iFAhnTKFiBl89G/prXgRR4nwd/ZqJNIoNWBh3H+CC2JJXLOTpRGZ+l5UO7ll18OyquXmjo5JwzpRdMfleb2i7VWqi/TIUD26FYlQFqzAMF1mSYyO/uPafYhXcklOLpRv0l2Wd0sBF1P/Wwtu/T8BZ40KrdsV2Uf49+/8oozk9zXIkCW/SuYmv4oAqRSy7OOxdTcx7dHHw9XW2214B6pdyBrVmKoQt1zzz25z0OAzI2s7wmtFiBVc/dg6zqYPEPE41+2rG2ivjDjB/0VT8t+MY7nTRgCEGg3gaoESF80S/sI4xaPGPRS5Ize676cNPpB08TcvVrbQS7+cpg2OnNQOlmPj/JSdOeddwZ1U/36Tf8YRYC0Nrqm5JW2cFBa3TUDIE1MqpJDWvnS9iNAhmTKFiD1QuN/pNB1be23hYVICSmeE0l0nxnl9yuR3d07rM3EjrX31A1LmIyP/jrrrLM6GtktMzt1c+53H1/92NoHjOqX9rssqi4IkD2S8T4mydRHL/bwPn+Eq65jXb9JzvWhg95HrB3l7vWiFayTnD4Aut+LrrlBzv/Q0G905qB0sh6vso9xHLTNK0BOcl+LAJn1ai4u3qgCZHElqS4ljfReZ511ovuV+73a9SWqK4TNCQGyWNyD3/CKza+w1LKMgFRmdlGC4KLNMz1IX5ndha5tP3sl8YpJrXfn9hvlEj+PMAQgAIEsBKoSIP3pimkvHlleivRC7cRM2edNcnHxKCmOvy++Cq9deMI/XLg//lK0ww47ZM5DU19cn6CtRozGhRE/MSdEKG7eEZBKx/8ApjSS7Hb5+fl+t+ppWr5VcvDLlcUfv4awAfnu6LorehVs1x6ySehf2/rAEDev4OJqqw8We+yxR3SOBMw77rjDj5LLL1MN8fwVdiMhcyX2p8gXX3xxxy5y1RWCJAYV8afp3vfff3/f4mi05gknnDAljl0YJqqjXWhpyvEidyBA9mhWJUC6e667jnfddddeITyfM3Uyb948b2/o1YwrpSNR3i5GFh78U+jjH/94dD1lEVUvv/zyKL7SLttV2cc45trmFSDFYVL7WgTIsn8FU9OfNAFSswA22mij4N6j3+k4ZpUiQE69HkfZU34vMkrp+pybVYB0HbHrYOyKcn1SDQ/Fv+rbFbTDCH1CdsWp6AeTZ9p3nyQ5BAEIQCAiUJUAue2220b3Mt1Hk+xO7b///t04aS9FdqXNSHzU6KM097WvfS3IKy2e2++mo7n7u+y9leniL0XqI5JGcsbLIGHUldFtf/jDH8ajBeFRBUgJOi4vbVVWNw01yCgh4F5y0z6eVckhoXh9dyFAhnjKHgHpcrMr1gfXm645Lfaikb+yPaWPDoqjkVfuQ4Ti6BrrZ3fVpd9v69t/dNe88jjkkEMyj8b005do49IpejuMwCFTFD4zjboq0yFA9uhWJUDa1WyDNtbIYO2LOydApJk6OfbYY7vXrq6XRYsWxU+PwrLj6K7tJJuOUcQ/eTRa38XXNk3YjJ83bLjKPsav1zC/z0ntaxEgh726hz/P/f51zeZZhGb4HMd75hZbbBHcd1Tvk046aSyFQoAsFnvrBUhNffYf3PRlPovTaB2/U8oyRcGlq1EtTrzMmp87ly0EIACBLASqEiC/853vBPdCjSqPO/dQlPRSpBFo7l6qaYT9nB4sXFxtBzk39dudo5W4y3TxlyLlq5e33/3ud6nZSnxx9jFdObOMzIqfM8geZlIB3Muoy1ej+rUwTz8nEVfx1W+mTduukkO/siYdQ4AMqVQlQCpXiY165nHXW7+t4g1a5T6sSXrIfZBWfrJnp4Vs/Lwl5siGYh6ne4lW4/7yl79c2N+JJ57YGUY8lHjr6qNnyyRhKk/dBsVFgOwRqkqAVI5xe4LxUT6uv0sydaI+SFPz3XUyaODDqAJk1o9ZPZL5fFX1MeoPHTNtZZphGDeJfS0C5DBXymjnuGdtXattFyB33HHH4LepOh9xxBGjARzhbATIEeAlnDr4DS/hpDrscg+c+jEOcvvss09wEadN//PTia+Afemll/qH+/rdC5x+LHqAxUEAAhAomkBVAqRedg8++ODgHqoHz5deeqlbpbSXIt1n/ZecLCYsTjnllCCfQcziU7DLtgmT9FKk+7wEj6SRkJoaGhdk9JKYJCZqn5hKsFR/o3T9P9n8kngh3nrZTEojzktx3KI/Li3Z8Uxa6EMfzjRF1MWTPc40VyaHtDyz7keADElVKUAqZ11HegbSdR6/9hXWBwyNpuon2oc1GBzy7T86oVG/k0996lPR9SxBPek3Ojj18cfwR4bnMfswbMkRIHvkqhQgJYbFR75LhHSCszN1st9++0UF1DH9npwtVZlJcb+BKFKCZ+utt45+G8NMwdbvq0xXZh+je5TuBWpbZyvW9Xvanm1HaqvvlsiqKaCOf7/6TmJfiwDZ74oo59ikCJB77bVXdH9yv83Pf/7z5UDNmCoCZEZQGaNNhAApw+b+KEi9kPVzegn0H5z1cpnH+R17nmnbefIgLgQgMNkEqhIgHeVzzjkneCDQS7+m6rrp15qqrZHjenj3hUeNKIgvqODSjG/PP//8II/48Xj4iSeeCOLfeOON8SiFhuMvRbKj5WwFy1amXmbmz//EwL8AABJCSURBVJ/fFWD0kuhGwusBSv60KeoqpD9S1D1w9dvq4T+ri6et/lCLFMiul0a4Snh0L7A6phfdfq5MDv3yzXIMATKkVLUAGeb+x5D7WJF0bNR9v/jFL6J7gK5diQu+85/l9Nt0TiK8pmjrHlJ359t/7GfCoqh6IED2SFYpQCpXXb/+AjHqA9THHH300R1nR1j3c92DZSvUHykvcwZJsxB6ten5ZGPS9S9ZZnhdcsklUXyd56/Q3ku1OF+ZfYymWbu6Z9nmMe0ySX0tAmRx13vWlCZBgIwPeNBvNM0mblZuRcRDgCyCYi+NiRAgVd24jSC9eKU5deJ+p6QvYVmdPyJHDws4CEAAAmUQqFqAVB00skKjz/0POv690vdrKmTeKZY33XRTcO8dNEpKC134efZb+KKINoi/FO27777dUYvxF0a/TPLr4WnQi6HsZLrzxFeCpUReCSj6k1+jWxz7c889N1eV9CLtbDu6fOJbicVZGJbJIVelEiIjQIZQ6iBAhiUqNnTBBRdEv5ukZy5/RJkvrJ955pnd87KMFiu2xPlS08gq95vX7/UnP/lJvgSGiI0A2YNWtQDpcr7iiiuCD3nxe7Uf1qjiLPdtl7a2msro0tCo+EFO/Y2Lr76pbFdmH6MPD6qL62fVr7q+Vlv9qY7udzdo4ag4i0npaxEg4y1ffrjtAqRmjbr7jNsOY5e1jJZAgCyW6sQIkMKmBWjcBa2tHkD9r+WaUhB/kfQfWLOg96fK9BvtkiUt4kAAAhBIIzAOAdKVRaMfNB1YdtLcPXXOnDkd3f+uv/76jhaHGcbJZq9LT9sHH3ywbzK33HJLFF8vC2W7pJcil+eTTz7ZHeGoUSkaraKRoBpdWOboL5d3nq0Ya1EcCTcyNaLyasVfzRTI6urMAQEybMW2C5D+atpJq0drZLK7p/gfk/UiJ+Hh9ddfD4HVLBS3/1hF8RAge5THJUC6Euh+rWvA3dd0zcre4Omnn95dYGnQRzqXTnzrf/BSmoOcFpRyvyON/C/b1bmPyVr3tve1CJBZr4Ti4rVZgDzjjDOie4y71wxrk7U44r2UECB7LIrwTZQAKWD+13Jd4PrSpS/ksoHivnZpv0acDGMs3J/GVvYUhSIuANKAAASaSWCcAqQj5gy46yW/KOc/YGlEZD/n3881TbFs1++lqOy865R+nTm4F3X3AKspcZPs2i5A6hnOtbWE9bjzp1tKEJBzI62PO+64ePTahf2P2jvttFMl5UOA7GEetwDpSuJsy8umfRFOHwnd70bbQe8rzu6+4uqaLNvVuY8pu+5++nXmgADpt1Q1fv/5uE2L0OgjuH8/kn+99dZLtFdeDempuSBATmUyyp6JEyAFSx2vXko23njjQHTUV0A9rMqg86DOOAm6Hn7dD0h20XAQgAAEyiJQBwHSjaIo6qVIrPxFw+KrgMZZ+qMyqljwq84vA3E2ZYbrzAEBMmz5NguQvjikD8j+jBZHwbddq0WuNGpa0yv1Ivfyyy+7aLXd+vZ0Naq6CocA2aPsX2N6vs+yYEvv7OJ8btpwP/NReXPzRwcPmm2gkUju/eaOO+7Im1Xu+HXuY3JXZoQT6swBAXKEhh3y1DYKkO49wt1ftNUgsEceeWRISuWchgBZLNeJFCDjCDVFLsuKovHz4uG999476qB/8IMfxA8ThgAEIFAYgToIkO4BVPaqinKLFi2K7qP9jONrZUo9pLiHFr0olu3q/DJQdt399OvMAQHSb6lOp80CpG9zW4br09yhhx4a3Sfcy81Pf/rTtOi12R+3//jAAw9UUjYEyB7mugiQ66+/fvcaHmRLuFfywT5/dG2/0cD+Qk+a5VWF2YI69zGDyRYXo84c3POfewbLa7KsOEqTk1LbBMg777yz8+Y3vznon5dffvnOvffeW7tGRYAstkkQIAviKRHTTeHWgwIOAhCAQJkE6iBAuhU4n3766UKrKhtT7qH21ltvTUzbn7JR1YjzOr8MJEIqaWedOSBAho3eZgFSNdUCEbfffntY6YTQb3/7286NN97Y0f1kWLt5CcmWusv/GFPFwh+uMgiQjkSnUwcB0k2XlvhXpNN7i2Z+qa/V9SVBP8n5gyuqEpnq3MckMSprX505IECW1erp6bZJgNQHtVVXXTV61td9SO81eRevTKdV7BEEyGJ5IkAWxPPCCy+MfkQypIqDAAQgUCaBcQuQ7qVID0RFO9mWdA9a+rAj+1fOafSFb/tRoySHMZnh0suz1aIyThjV9lOf+lSe01sTt84cECDDy6ztAmRY23aFjjnmmOh+s9tuu1VWOQTIHuo6CJAS/dTfaCHNop1ma7nBE+pzfdv3spl64IEHRtegVs6uytW5j6mKgfKpMwcEyCqvhD/m5Z6LdT9osg1ILdro1szwn6mvvPLK6qFmzBEBMiOojNEQIDOCGhTtwx/+cNRJ68UcBwEIQKBMAuMWIN0K2GWNPtRUM710u4cTTbeW2OgvOnHAAQd03MISZbJW2pryvd9++0XlUblUpueee67srGuVft05IECGlwsCZMijbqHnn3++c9JJJ3U0yswfSa4PLf69TiM9q3IIkD3SdRAgnQgo+/RluO9///sd38bjBz/4wY7eaZwwqdGRZ555ZhlZJ6ZZ9z4msdAl7Kw7BwTIEhp9QJJtECA1YGDDDTcMnqX1PH3++ecPqP14DyNAFssfAbIAng899FD0Q6pqlcICik0SEIBAgwmMW4B0D59lT8nSNI1zzz23o/w++clPdg477LDON7/5zc6jjz5aSetpsTJ9qXUvY04Q9bcSIvXSppfVtrqmcECADK9ABMiQR91Ce+65Z/T8KFuVzskmn7vHbL311m53JVsEyB7mOgiQzv5j2YMbZJ7g1FNP7ey7777d0f0agatFb6r6yNeUPqZ3dZTjawoH9wzo7lNlPwuWQ7tZqbZBgNxiiy2ivs1dO7JHW3eHAFlsCyFAFsBT0xLcj2jBggUFpEgSEIAABPoTGLcAqYdk3feeeeaZ/gVt+FFnI8vd4/tttZpfW11TOCBAhlcgAmTIo24hjS5z95QTTjihW7zTTz892ic7u0888USlxUaA7OEetwCpldp1fUh4aLtrSh9Tdjs0hQMCZNlXwtT0my5A7rDDDlHf5vq9Kk07TCWafQ8CZHZWWWIupkj2Imic22OPPcwpp5xi7I/RLFy4cGzlt9NkzGqrrWbsKnHGdhrm4YcfNtOmTRtbecgYAhCYDAKLL764eeWVV7qVnTVrlrGrxlVa8cMPP9zYxRzMUUcdVWm+VWdmX/6NFVmNFXyNmM+cOdPMmDHD2OlRXf52OkmXg7bqC5Zaaqmqi1hJfk3hYG0wm1133TVicvLJJ5vdd989Ck+aZ9111zV2MZNutadPn27sysqThqDW9d1ll13MWWed1S3jzjvvbO6+++7oXq7w3LlzzZJLLllpHT72sY+ZSy+9NMrTzvIxdrGAKDxJnscee8ysuOKKUZU333xzM2/evChctkd9vK6Df/mXfzHbbLNN2dmNNf2m9DFlQ2oKh4MPPthY8SjCYUdAGmsmJwrjKZ6AFcG6fYRStjYgu8+hxedSXop2FLfZaqutzPz587uZWLNG5thjjy0vwwJTnj17dqA3NVQ+K5DIaEkhQI7Gz9gRj2aTTTbppnLkkUeagw46aMQUOR0CEIDAYALjFiAHl5AYEKieAAJkyBwBMuRRt5AEpuuvv97YlT/NnXfeaVZYYQXzrne9y2y33Xbdj9rjKC8CZI/6uAXIXknwQaBeBBAgq2+PpguQIqaP9xIhl1tuOWNH+1cPccgcESCHBJdyGgJkCpisu3fccUdz3nnndaNr9OMqq6yS9VTiQQACEBiaAALk0Og4scUEECDDxkWADHkQGkwAAbLHCAGyxwIfBHwCCJA+jWr8bRAgqyFVfC4IkMUybawA+bnPfc585StfMdbwv7nllluKpZIjteWXX97Y5eSNXTHOXHPNNTnOJCoEIACB4QkgQA7PjjPbSwABMmxbBMiQB6HBBBAge4wQIHss8EHAJ4AA6dOoxo8AWQ3npFwQIJOoDL+vsQLkd7/7XSM7kPvss0/XPsrwCEY7c86cOebiiy82p512mrEr1Y2WGGdDAAIQyEgAATIjKKJNFAEEyLC5ESBDHoQGE0CA7DFCgOyxwAcBnwACpE+jGj8CZDWck3JBgEyiMvy+xgqQw1eZMyEAAQg0nwACZPPbkBoUTwABMmSKABnyIDSYAAJkjxECZI8FPgj4BBAgfRrV+BEgq+GclAsCZBKV4fchQA7PjjMhAAEIjI0AAuTY0JNxjQkgQIaNgwAZ8iA0mAACZI8RAmSPBT4I+AQQIH0a1fgRIKvhnJQLAmQSleH3IUAOz44zIQABCIyNAALk2NCTcY0JIECGjYMAGfIgNJgAAmSPEQJkjwU+CPgEECB9GtX4ESCr4ZyUCwJkEpXh9yFADs+OMyEAAQiMjQAC5NjQk3GNCSBAho2DABnyIDSYAAJkjxECZI8FPgj4BBAgfRrV+BEgq+GclAsCZBKV4fchQA7PjjMhAAEIjI0AAuTY0JNxjQkgQIaNgwAZ8iA0mAACZI8RAmSPBT4I+AQQIH0a1fgRIKvhnJQLAmQSleH3IUAOz44zIQABCIyNAALk2NCTcY0JIECGjYMAGfIgNJgAAmSPEQJkjwU+CPgEECB9GtX4ESCr4ZyUCwJkEpXh9yFADs+OMyEAAQiMjQAC5NjQk3GNCSBAho2DABnyIDSYAAJkjxECZI8FPgj4BBAgfRrV+BEgq+GclAsCZBKV4fchQA7PjjMhAAEIjI0AAuTY0JNxjQkgQIaNgwAZ8iA0mAACZI8RAmSPBT4I+AQQIH0a1fjjAuTRRx9dTcbkYi666CKzcOHCiESn04n8ePITQIDMz4wzIAABCIydAALk2JuAAtSQAAJk2CgIkCEPQoMJIED2GCFA9ljgg4BPAAHSp1GN3xcgq8mRXNIIIECmkcm2HwEyGydiQQACEKgVAQTIWjUHhakJAQTIsCEQIEMehAYTQIDsMUKA7LHABwGfAAKkT6MaPwJkNZyz5IIAmYVSehwEyHQ2HIEABCBQWwIIkLVtGgo2RgIIkCF8BMiQB6HBBBAge4wQIHss8EHAJ4AA6dOoxo8AWQ3nLLkgQGahlB4HATKdDUcgAAEI1JYAAmRtm4aCjZEAAmQIHwEy5EFoMAEEyB4jBMgeC3wQ8AkgQPo0qvFfeOGF1WRELgMJbL311gPjECGdAAJkOhuOQAACEKgtAV+AnDlzZm3LScEgUDWBV199Ncry5JNPNrvvvnsUnjQPAuSktfjo9UWA7DGMC5D0tT02+CDg97VXXXWV2WyzzYACAQhAYCABBMiBiIgAAQhAoH4EfAGyfqWjRBCoBwEEyHXNokWLuo0xffp089RTT9WjYShFbQnssssu5tJLL43K99BDD5lVV101Ck+SJy5ATlLdqSsE8hBAgMxDi7gQmGwCCJCT3f7UHgIQaCgBBMiGNhzFrpQAAmRPgKwUPJm1hgAC5IqtaUsqAoGyCCBAlkWWdCHQPgIIkO1rU2oEAQhMAIG11157AmpJFSEwGgFNv2YK9h9HQI5GkrMnlcCkC5CbbrrppDY99YZAZgLHHHMMU7Az0yIiBCabAALkZLc/tYcABCAAAQhAoKUEfBuQLa0i1SqZwCQLkCWjJXkIQAACEIDAxBFAgJy4JqfCEIAABCAAAQhMAoG///u/n4RqUscSCZx55pkTawOyRKwkDQEIQAACEJhIAgiQE9nsVBoCEIAABCAAAQhAAAIQgAAEIAABCEAAAtUQQICshjO5QAACEIAABCAAAQhAAAIQgAAEIAABCEBgIgkgQE5ks1NpCEAAAhCAAAQgAAEIQAACEIAABCAAAQhUQwABshrO5AIBCEAAAhCAAAQgAAEIQAACEIAABCAAgYkkgAA5kc1OpSEAAQh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+ } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize circuits and operators\n", + "\n", + "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", + "\n", + "\n", + "![optimized_H_test.png](attachment:optimized_H_test.png)\n", + "\n", + "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", + "This is satisfied when the Hamiltonian preserves the U(1) symmetry.\n", + "Assume that the gate $\\psi_0-prep$ prepares our desired reference state $\\ket{\\psi_0}$, e.g., to prepare the HF state for chemistry $\\psi_0-prep$ would be a product of single-qubit NOTs, so controlled-$\\psi_0-prep$ is just a product of CNOTs.\n", + "Then the circuit above implements the following state prior to measurement:\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\ket{0} \\ket{0}^N\\xrightarrow{H}&\\frac{1}{\\sqrt{2}}\n", + " \\left(\n", + " \\ket{0}\\ket{0}^N+ \\ket{1} \\ket{0}^N\n", + " \\right)\\\\\n", + " \\xrightarrow{\\text{1-ctrl-init}}&\\frac{1}{\\sqrt{2}}\\left(|0\\rangle|0\\rangle^N+|1\\rangle|\\psi_0\\rangle\\right)\\\\\n", + " \\xrightarrow{U}&\\frac{1}{\\sqrt{2}}\\left(e^{i\\phi}\\ket{0}\\ket{0}^N+\\ket{1} U\\ket{\\psi_0}\\right)\\\\\n", + " \\xrightarrow{\\text{0-ctrl-init}}&\\frac{1}{\\sqrt{2}}\n", + " \\left(\n", + " e^{i\\phi}\\ket{0} \\ket{\\psi_0}\n", + " +\\ket{1} U\\ket{\\psi_0}\n", + " \\right)\\\\\n", + " =&\\frac{1}{2}\n", + " \\left(\n", + " \\ket{+}\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", + " +\\ket{-}\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", + " \\right)\\\\\n", + " =&\\frac{1}{2}\n", + " \\left(\n", + " \\ket{+i}\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", + " +\\ket{-i}\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", + " \\right)\n", + "\\end{split}\n", + "\\end{equation}\n", + "\n", + "where we have used the classical simulable phase shift $ U\\ket{0}^N = e^{i\\phi}\\ket{0}$ in the third line. Therefore the expectation values are obtained as\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\langle X\\otimes P\\rangle&=\\frac{1}{4}\n", + " \\Big(\n", + " \\left(e^{-i\\phi}\\bra{\\psi_0}+\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", + " \\\\\n", + " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", + " \\Big)\\\\\n", + " &=\\text{Re}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right],\n", + "\\end{split}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\langle Y\\otimes P\\rangle&=\\frac{1}{4}\n", + " \\Big(\n", + " \\left(e^{-i\\phi}\\bra{\\psi_0}+i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", + " \\\\\n", + " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", + " \\Big)\\\\\n", + " &=\\text{Im}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right].\n", + "\\end{split}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", + "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + "# ## Create the time-evo op circuit\n", + "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "# Create instruction for rotation about XX+YY-ZZ:\n", + "Rxyz_circ = QuantumCircuit(2)\n", + "Rxyz_circ.rxx(t,0,1)\n", + "Rxyz_circ.ryy(t,0,1)\n", + "Rxyz_circ.rzz(-t,0,1)\n", + "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", + "\n", + "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "trotter_step_circ = QuantumCircuit(qr)\n", + "for i, color in enumerate(interaction_list):\n", + " for interaction in color:\n", + " trotter_step_circ.append(Rxyz_instr, interaction)\n", + "\n", + "\n", + "qc_evol = QuantumCircuit(qr)\n", + "for _ in range(num_trotter_steps):\n", + " qc_evol.compose(trotter_step_circ, inplace=True)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use an optimized circuit for state preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", + "for idx in range(n_qubits):\n", + " if idx % 2 == 0:\n", + " controlled_state_prep.swap(idx, idx+1)\n", + " else:\n", + " controlled_state_prep.cx(idx+1, idx)\n", + " controlled_state_prep.cx(idx, idx+1)\n", + "\n", + "\n", + "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(n_qubits)\n", + "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(0)\n", + "qc_real.h(0)\n", + "\n", + "S_real_circ = qc_real.decompose().copy()\n", + "\n", + "# # Create hadamard test circuit for imaginary part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag = QuantumCircuit(qr)\n", + "qc_imag.h(0)\n", + "qc_imag.sdg(0)\n", + "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(n_qubits)\n", + "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(0)\n", + "qc_imag.h(0)\n", + "\n", + "\n", + "S_imag_circ = qc_imag.decompose().copy()\n", + "\n", + "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 96\n" + ] + } + ], + "source": [ + "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", + "The only difference between the circuits used in the Hadamard test will be the phase in the time-evolution operator and the observables measured. Therefore we can prepare a template circuit which represent the generic circuit for the Hadamard test, with placeholders for the gates that depend on the time-evolution operator.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Hamiltonian terms to measure\n", + "observable_list = []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " # print(pauli)\n", + " observable = pauli[::-1].to_label() + 'Z'\n", + " observable_list.append(observable)\n", + "\n", + "\n", + "\n", + "# Real part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_1 = QuantumCircuit(qr)\n", + "qc_real_1.h(0)\n", + "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real_1.x(n_qubits)\n", + "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_real_circ_1 = qc_real_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_2 = QuantumCircuit(qr)\n", + "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real_2.x(0)\n", + "qc_real_2.h(0)\n", + "H_real_circ_2 = qc_real_2.decompose().copy()\n", + "\n", + "# Imaginary part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_1 = QuantumCircuit(qr)\n", + "qc_imag_1.h(0)\n", + "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_1.x(n_qubits)\n", + "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_2 = QuantumCircuit(qr)\n", + "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_2.x(0)\n", + "qc_imag_2.sdg(0)\n", + "qc_imag_2.h(0)\n", + "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Execute using a quantum primitive" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate circuits to calculate all matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "S_real_circuits, S_imag_circuits = [], []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " \n", + "\n", + " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " S_real_circuits.append(circuit_real)\n", + " S_imag_circuits.append(circuit_imag)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "count = 0\n", + "H_real_circuits, H_imag_circuits = [], [] \n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " H_real_circuits.append(circuit_real)\n", + " H_imag_circuits.append(circuit_imag)\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Execute circuits for $\\tilde{S}$ with the Estimator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "210 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs = {'S': {'real':[], 'imag':[]},\n", + " 'H': {'real':[], 'imag':[]}\n", + " } # store executed jobs\n", + "\n", + "\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size_S = 20\n", + "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", + "\n", + "\n", + "\n", + "print(len(S_real_circuits), 'circuits to run')\n", + "\n", + "S_real_results_list, S_imag_results_list = [], []\n", + "for i in range(len(job_idxs_S)-1):\n", + "\n", + " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['real'].append(job.job_id())\n", + " S_real_results = job.result()\n", + "\n", + " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['imag'].append(job.job_id())\n", + " S_imag_results = job.result()\n", + "\n", + "\n", + " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", + "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5670 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs['H']['real'], jobs['H']['imag'] = [], []\n", + "shots = 100000\n", + "\n", + "\n", + "job_size = 50\n", + "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", + "\n", + "print(len(H_imag_circuits), 'circuits to run')\n", + "\n", + "H_real_results_list, H_imag_results_list = [], []\n", + "for i in range(len(job_idxs)-1):\n", + " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", + "\n", + "\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " # print(f\"job id: {job_real.job_id()}\")\n", + " jobs['H']['real'].append(job_real.job_id())\n", + " H_real_results = job_real.result()\n", + "\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " # print(f\"job id: {job_imag.job_id()}\")\n", + " jobs['H']['imag'].append(job_imag.job_id())\n", + " H_imag_results = job_imag.result()\n", + "\n", + "\n", + " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", + " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process and analyze results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + "\n", + " eff_count = count % (job_size_S)\n", + " res_idx = count // (job_size_S)\n", + "\n", + " S_real_results = S_real_results_list[res_idx]\n", + " S_imag_results = S_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = S_real_results.values[eff_count]\n", + " expval_imag = S_imag_results.values[eff_count]\n", + "\n", + " # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + " # Fill-in matrix elements\n", + " S_circ[idx_bra, idx_ket] = expval\n", + " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", + "\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the matrix elements of $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " eff_count = count % (job_size)\n", + " res_idx = count // (job_size)\n", + "\n", + " H_real_results = H_real_results_list[res_idx]\n", + " H_imag_results = H_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = H_real_results.values[eff_count]\n", + " expval_imag = H_imag_results.values[eff_count]\n", + "\n", + " # # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + "\n", + " # Fill-in matrix elements\n", + " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", + " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", + " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", + "\n", + "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", + "\n", + "and get an estimate of the ground state energy $c_{min}$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The estimated ground state energy is: 8.975147310913348\n", + "The estimated ground state energy is: 0.6699145941880671\n", + "The estimated ground state energy is: 1.3257378975608196\n", + "The estimated ground state energy is: -3.3030639423840706\n", + "The estimated ground state energy is: -3.9934796043575798\n", + "The estimated ground state energy is: -3.003872747466045\n", + "The estimated ground state energy is: -2.5086442931004727\n", + "The estimated ground state energy is: -5.48481710169914\n", + "The estimated ground state energy is: -5.545506988684572\n", + "The estimated ground state energy is: -6.98377741561271\n", + "The estimated ground state energy is: -6.676634627880108\n", + "The estimated ground state energy is: -7.6408885159105715\n", + "The estimated ground state energy is: -7.524234968608674\n", + "The estimated ground state energy is: -7.093259720004493\n", + "The estimated ground state energy is: -7.282617495801976\n", + "The estimated ground state energy is: -8.530915996980566\n", + "The estimated ground state energy is: -7.592245638927923\n", + "The estimated ground state energy is: -7.973568152294788\n", + "The estimated ground state energy is: -8.215496239766923\n", + "The estimated ground state energy is: -8.346530278432619\n" + ] + } + ], + "source": [ + "gnd_en_circ_est_list = []\n", + "for d in range(1, krylov_dim+1):\n", + " # Solve generalized eigenvalue problem\n", + " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", + " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", + " print('The estimated ground state energy is: ', gnd_en_circ_est)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", + "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", + "plt.legend()\n", + "plt.xlabel('Krylov space dimension')\n", + "plt.ylabel('Energy')\n", + "plt.title('Estimating Ground state energy with Quantum Krylov')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-9.000000000000009" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Take home exercise:\n", + "Compute ground state energy with other methods" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.17" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb deleted file mode 100644 index b84b268..0000000 --- a/docs/krylov-subspace-demo.ipynb +++ /dev/null @@ -1,1315 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Krylov subspace expansion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 1: Map problem to quantum native format\n", - "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", - "\n", - "\n", - "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", - "\n", - "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", - "\n", - "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", - "\n", - "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", - "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", - "\n", - "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", - "\n", - "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Imports and definitions\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 108, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import numpy as np\n", - "import scipy as sp\n", - "import matplotlib.pylab as plt\n", - "import warnings\n", - "warnings.filterwarnings('ignore')\n", - "\n", - "from qiskit.quantum_info import SparsePauliOp, Operator\n", - "from qiskit.circuit import Parameter\n", - "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n", - "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", - "from qiskit.providers.fake_provider import FakePrague\n", - "from qiskit.primitives import Estimator, Sampler\n", - "\n", - "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", - " s_vals, s_vecs = sp.linalg.eigh(s)\n", - " s_vecs = s_vecs.T\n", - " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", - " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", - " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", - " if k==1:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", - " else:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Define Hamiltonian\n", - "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SparsePauliOp(['ZZIIII', 'IZZIII', 'IIZZII', 'IIIZZI', 'IIIIZZ', 'XXIIII', 'IXXIII', 'IIXXII', 'IIIXXI', 'IIIIXX', 'YYIIII', 'IYYIII', 'IIYYII', 'IIIYYI', 'IIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Define problem Hamiltonian. Kicked Ising in this case\n", - "n_qubits = 6\n", - "J = 1 # coupling strength for ZZ interaction\n", - "\n", - "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", - "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", - "for i in range(n_qubits-1):\n", - " H_int[i][i] = 'Z'\n", - " H_int[i][i+1] = 'Z'\n", - "for i in range(n_qubits-1):\n", - " H_int[n_qubits-1+i][i] = 'X'\n", - " H_int[n_qubits-1+i][i+1] = 'X'\n", - "for i in range(n_qubits-1):\n", - " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", - " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", - "H_int = [''.join(term) for term in H_int]\n", - "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", - "\n", - "# Get operator\n", - "H_op = SparsePauliOp.from_list(H_tot)\n", - "H_op" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Set parameters for the algorithm" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Set parameters for quantum Krylov algorithm\n", - "krylov_dim = 20 # size of krylov subspace\n", - "dt = 0.1 # time step\n", - "num_trotter_steps = 4\n", - "dt_circ = dt/num_trotter_steps" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### State preparation\n", - "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_state_prep = QuantumCircuit(n_qubits)\n", - "for i in range(n_qubits):\n", - " if i%2 != 0:\n", - " qc_state_prep.x(i)\n", - "qc_state_prep.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Time evolution\n", - "\n", - "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - " ## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "qc_evol = QuantumCircuit(qr)\n", - "qc_evol.append(evol_gate, qargs=qr)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" - ] - }, - { - "attachments": { - "H_test.PNG": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Hadamard test\n", - "\n", - "![H_test.PNG](attachment:H_test.PNG)\n", - "\n", - "\n", - "\\begin{equation}\n", - " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", - "\\begin{equation}\n", - " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "... then measure:\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", - " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{split}\n", - "\\end{equation}\n", - "Similarly, measuring $Y$ yields\n", - "\\begin{equation}\n", - " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{equation}" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit for calculating the real part of the overlap in S via Hadamard test\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "## Create the time-evo op dagger circuit\n", - "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", - "evol_gate_d = evol_gate_d.inverse()\n", - "\n", - "# Put pieces together\n", - "qc_temp = QuantumCircuit(n_qubits)\n", - "qc_temp.compose(qc_state_prep, inplace=True)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", - "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", - "\n", - "# Create controlled version of the circuit\n", - "controlled_U = qc_temp.to_gate().control(1)\n", - "\n", - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", - "qc_real.h(0)\n", - "\n", - "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", - "qc_real.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 4447\n" - ] - } - ], - "source": [ - "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" - ] - }, - { - "attachments": { - "optimized_H_test.PNG": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize circuits and operators\n", - "\n", - "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", - "\n", - "\n", - "![optimized_H_test.PNG](attachment:optimized_H_test.PNG)\n", - "\n", - "\n", - "This works provided the operator $\\hat{O}$ preserves Hamming weight.\n", - "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " |0\\rangle_a|0\\rangle^N\\quad&\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|0\\rangle^N+|1\\rangle_a|\\psi_0\\rangle\\Big) \\\\\n", - " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|0\\rangle^N+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", - " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", - "\\end{split}\n", - "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", - "\\begin{equation}\n", - " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "... then measure:\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\|e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\|e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", - " &= \\text{Re}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", - "\\end{split}\n", - "\\end{equation}\n", - "Similarly, measuring $Y$ yields\n", - "\\begin{equation}\n", - " \\langle Y\\rangle_a = \\text{Im}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", - "\\end{equation}\n", - "Hence the desired matrix element is\n", - "\\begin{equation}\n", - " \\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle=e^{i\\phi}\\big(\\langle X\\rangle_a+i\\langle Y\\rangle_a\\big).\n", - "\\end{equation}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", - "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - "# ## Create the time-evo op circuit\n", - "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "# Create instruction for rotation about XX+YY-ZZ:\n", - "Rxyz_circ = QuantumCircuit(2)\n", - "Rxyz_circ.rxx(t,0,1)\n", - "Rxyz_circ.ryy(t,0,1)\n", - "Rxyz_circ.rzz(-t,0,1)\n", - "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", - "\n", - "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "trotter_step_circ = QuantumCircuit(qr)\n", - "for i, color in enumerate(interaction_list):\n", - " for interaction in color:\n", - " trotter_step_circ.append(Rxyz_instr, interaction)\n", - "\n", - "\n", - "qc_evol = QuantumCircuit(qr)\n", - "for _ in range(num_trotter_steps):\n", - " qc_evol.compose(trotter_step_circ, inplace=True)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Use an optimized circuit for state preparation" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", - "for idx in range(n_qubits):\n", - " if idx % 2 == 0:\n", - " controlled_state_prep.swap(idx, idx+1)\n", - " else:\n", - " controlled_state_prep.cx(idx+1, idx)\n", - " controlled_state_prep.cx(idx, idx+1)\n", - "\n", - "\n", - "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(n_qubits)\n", - "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(0)\n", - "qc_real.h(0)\n", - "\n", - "S_real_circ = qc_real.decompose().copy()\n", - "\n", - "# # Create hadamard test circuit for imaginary part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag = QuantumCircuit(qr)\n", - "qc_imag.h(0)\n", - "qc_imag.sdg(0)\n", - "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(n_qubits)\n", - "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(0)\n", - "qc_imag.h(0)\n", - "\n", - "\n", - "S_imag_circ = qc_imag.decompose().copy()\n", - "\n", - "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 76\n" - ] - } - ], - "source": [ - "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", - "The derivation of the Hadamard test assumes that the operator $\\hat{O}$ which represents a collection of terms in $H$ preserves Hamming weight. For this reason, we decompose $H$ into ZZ:\n", - "\n", - "$$ \\text{ZZ} = \\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & -1 & 0 & 0\\\\\n", - "0 & 0 & -1 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "\n", - "$$ \\text{SWAP} = \\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "\n", - " $$ \\text{mSWAP} = \\begin{pmatrix}\n", - "-1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & -1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "instead of ZZ, XX, and YY.\n", - "Using the former decomposition yields terms that are all unitary AND number conserving." - ] - }, - { - "cell_type": "code", - "execution_count": 98, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['IZZIII', 'IIZZII', 'IIIZZI', 'ZZIIII', 'IIIIZZ']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IZZIII\n", - "['I', 'Z', 'Z', 'I', 'I', 'I']\n", - "IIZZII\n", - "['I', 'Z', 'Z', 'Z', 'I', 'I']\n", - "IIIZZI\n", - "['I', 'Z', 'Z', 'Z', 'Z', 'I']\n", - "ZZIIII\n", - "['Z', 'Z', 'Z', 'Z', 'Z', 'I']\n", - "IIIIZZ\n", - "['Z', 'Z', 'Z', 'Z', 'Z', 'Z']\n", - "['IXXIII', 'IIXXII', 'IIIXXI', 'XXIIII', 'IIIIXX']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IXXIII\n", - "['I', 'X', 'X', 'I', 'I', 'I']\n", - "IIXXII\n", - "['I', 'X', 'X', 'X', 'I', 'I']\n", - "IIIXXI\n", - "['I', 'X', 'X', 'X', 'X', 'I']\n", - "XXIIII\n", - "['X', 'X', 'X', 'X', 'X', 'I']\n", - "IIIIXX\n", - "['X', 'X', 'X', 'X', 'X', 'X']\n", - "['IYYIII', 'IIYYII', 'IIIYYI', 'YYIIII', 'IIIIYY']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IYYIII\n", - "['I', 'Y', 'Y', 'I', 'I', 'I']\n", - "IIYYII\n", - "['I', 'Y', 'Y', 'Y', 'I', 'I']\n", - "IIIYYI\n", - "['I', 'Y', 'Y', 'Y', 'Y', 'I']\n", - "YYIIII\n", - "['Y', 'Y', 'Y', 'Y', 'Y', 'I']\n", - "IIIIYY\n", - "['Y', 'Y', 'Y', 'Y', 'Y', 'Y']\n" - ] - }, - { - "data": { - "text/plain": [ - "['ZZZZZZ', 'XXXXXX', 'YYYYYY']" - ] - }, - "execution_count": 98, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "non_commuting_ops_list = []\n", - "paulis_to_non_commuting_ops_dict = {}\n", - "for grp_idx, paulis in enumerate(H_op.paulis.group_commuting(qubit_wise=True)):\n", - " print(paulis)\n", - "\n", - " total_op = ['I' for _ in range(len(paulis[0]))]\n", - " print(total_op)\n", - " for pauli in paulis:\n", - " pauli = pauli.to_label()\n", - " print(pauli)\n", - "\n", - " for idx, term in enumerate(pauli):\n", - " if total_op[idx] == 'I':\n", - " total_op[idx] = term\n", - " print(total_op)\n", - "\n", - " non_commuting_ops_list.append(\"\".join(total_op))\n", - "\n", - " for pauli in paulis:\n", - " pauli = pauli.to_label()\n", - " paulis_to_non_commuting_ops_dict[pauli] = \"\".join(total_op)\n", - "\n", - "non_commuting_ops_list\n" - ] - }, - { - "cell_type": "code", - "execution_count": 99, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'IZZIII': 'ZZZZZZ',\n", - " 'IIZZII': 'ZZZZZZ',\n", - " 'IIIZZI': 'ZZZZZZ',\n", - " 'ZZIIII': 'ZZZZZZ',\n", - " 'IIIIZZ': 'ZZZZZZ',\n", - " 'IXXIII': 'XXXXXX',\n", - " 'IIXXII': 'XXXXXX',\n", - " 'IIIXXI': 'XXXXXX',\n", - " 'XXIIII': 'XXXXXX',\n", - " 'IIIIXX': 'XXXXXX',\n", - " 'IYYIII': 'YYYYYY',\n", - " 'IIYYII': 'YYYYYY',\n", - " 'IIIYYI': 'YYYYYY',\n", - " 'YYIIII': 'YYYYYY',\n", - " 'IIIIYY': 'YYYYYY'}" - ] - }, - "execution_count": 99, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "paulis_to_non_commuting_ops_dict" - ] - }, - { - "cell_type": "code", - "execution_count": 104, - "metadata": {}, - "outputs": [], - "source": [ - "# mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", - "# mswap = mswap_op.to_instruction()\n", - "# mswap.label = 'mswap'\n", - "\n", - "# # Hamiltonian terms\n", - "# hamiltonian_circuits = []\n", - "# for idx_ket in range(krylov_dim):\n", - "# for idx_bra in range(idx_ket + 1):\n", - "# for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "# qr = QuantumRegister(n_qubits)\n", - "# qc_ham = QuantumCircuit(qr)\n", - "# active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", - "# if 'X' in pauli.to_label():\n", - "# qc_ham.swap(*active_qubits)\n", - "# if 'Y' in pauli.to_label():\n", - "# qc_ham.append(mswap,qargs=active_qubits)\n", - "# for i in active_qubits:\n", - "# qc_ham.z(i)\n", - "# if 'Z' in pauli.to_label():\n", - "# for i in active_qubits:\n", - "# qc_ham.z(i)\n", - "# hamiltonian_circuits.append(qc_ham)\n", - "\n", - "# ## TODO: how does runtime estimator group commuting observables?\n", - "# # Hamiltonian terms to measure\n", - "# observable_list = []\n", - "# for idx_ket in range(krylov_dim):\n", - "# for idx_bra in range(idx_ket + 1):\n", - "# for pauli in non_commuting_ops_list:\n", - "# # print(pauli)\n", - "# observable = pauli + 'Z'\n", - "# observable_list.append(observable)\n", - "\n", - "# Measurement of Hamiltonian terms\n", - "hamiltonian_measurement_circs = {}\n", - "for obs in non_commuting_ops_list:\n", - " qr = QuantumRegister(n_qubits+1)\n", - " cr = ClassicalRegister(n_qubits+1)\n", - " qc_meas = QuantumCircuit(qr, cr)\n", - " qc_meas.measure(0, 0)\n", - " for idx, term in enumerate(obs):\n", - " if term == 'Z':\n", - " qc_meas.measure(idx+1, idx+1)\n", - " if term == 'X':\n", - " qc_meas.h(idx+1)\n", - " qc_meas.measure(idx+1, idx+1)\n", - " if term == 'Y':\n", - " qc_meas.sdg(idx+1)\n", - " qc_meas.h(idx+1)\n", - " qc_meas.measure(idx+1, idx+1)\n", - " hamiltonian_measurement_circs[obs] = qc_meas.copy()\n", - "\n", - "\n", - "\n", - "\n", - "# Real part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_1 = QuantumCircuit(qr)\n", - "qc_real_1.h(0)\n", - "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real_1.x(n_qubits)\n", - "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_real_circ_1 = qc_real_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_2 = QuantumCircuit(qr)\n", - "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real_2.x(0)\n", - "qc_real_2.h(0)\n", - "H_real_circ_2 = qc_real_2.decompose().copy()\n", - "\n", - "# Imaginary part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_1 = QuantumCircuit(qr)\n", - "qc_imag_1.h(0)\n", - "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_1.x(n_qubits)\n", - "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_2 = QuantumCircuit(qr)\n", - "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_2.x(0)\n", - "qc_imag_2.sdg(0)\n", - "qc_imag_2.h(0)\n", - "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 3: Execute using a quantum primitive" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate circuits to calculate all matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 105, - "metadata": {}, - "outputs": [], - "source": [ - "S_real_circuits, S_imag_circuits = [], []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " \n", - "\n", - " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " S_real_circuits.append(circuit_real)\n", - " S_imag_circuits.append(circuit_imag)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 106, - "metadata": {}, - "outputs": [], - "source": [ - "count = 0\n", - "H_real_circuits, H_imag_circuits = [], [] \n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", - " for pauli in non_commuting_ops_list:\n", - "\n", - " circuit_real = H_real_circ_1.compose(H_real_circ_2, list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " circuit_imag = H_imag_circ_1.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " H_real_circuits.append(circuit_real)\n", - " H_imag_circuits.append(circuit_imag)\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Execute circuits for $\\tilde{S}$ with the Estimator" - ] - }, - { - "cell_type": "code", - "execution_count": 107, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "210 circuits to run\n" - ] - } - ], - "source": [ - "\n", - "\n", - "estimator = Estimator()\n", - "\n", - "jobs = {'S': {'real':[], 'imag':[]},\n", - " 'H': {'real':[], 'imag':[]}\n", - " } # store executed jobs\n", - "\n", - "\n", - "shots = 100000\n", - "observable = 'I'*(n_qubits) + 'Z'\n", - "\n", - "job_size_S = 20\n", - "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", - "\n", - "\n", - "\n", - "print(len(S_real_circuits), 'circuits to run')\n", - "\n", - "S_real_results_list, S_imag_results_list = [], []\n", - "for i in range(len(job_idxs_S)-1):\n", - "\n", - " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['real'].append(job.job_id())\n", - " S_real_results = job.result()\n", - "\n", - " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['imag'].append(job.job_id())\n", - " S_imag_results = job.result()\n", - "\n", - "\n", - " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And use Sampler for $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 109, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "630 circuits to run\n" - ] - } - ], - "source": [ - "sampler = Sampler()\n", - "\n", - "jobs['H']['real'], jobs['H']['imag'] = [], []\n", - "shots = 100000\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "job_size = 50\n", - "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", - "\n", - "print(len(H_imag_circuits), 'circuits to run')\n", - "\n", - "H_real_results_list, H_imag_results_list = [], []\n", - "for i in range(len(job_idxs)-1):\n", - " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", - "\n", - "\n", - " job_real = sampler.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_real.job_id()}\")\n", - " jobs['H']['real'].append(job_real.job_id())\n", - " H_real_results = job_real.result()\n", - "\n", - " job_imag = sampler.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_imag.job_id()}\")\n", - " jobs['H']['imag'].append(job_imag.job_id())\n", - " H_imag_results = job_imag.result()\n", - "\n", - "\n", - " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process and analyze results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 110, - "metadata": {}, - "outputs": [], - "source": [ - "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - "\n", - " eff_count = count % (job_size_S)\n", - " res_idx = count // (job_size_S)\n", - "\n", - " S_real_results = S_real_results_list[res_idx]\n", - " S_imag_results = S_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = S_real_results.values[eff_count]\n", - " expval_imag = S_imag_results.values[eff_count]\n", - "\n", - " # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - " # Fill-in matrix elements\n", - " S_circ[idx_bra, idx_ket] = expval\n", - " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", - "\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And the matrix elements of $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 130, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: 0.01561,\n", - " 2: 0.01528,\n", - " 4: 0.01528,\n", - " 6: 0.01556,\n", - " 8: 0.01563,\n", - " 10: 0.01563,\n", - " 12: 0.01572,\n", - " 14: 0.01533,\n", - " 16: 0.01513,\n", - " 18: 0.01622,\n", - " 20: 0.01547,\n", - " 22: 0.01542,\n", - " 24: 0.01513,\n", - " 26: 0.01537,\n", - " 28: 0.01517,\n", - " 30: 0.01564,\n", - " 32: 0.01577,\n", - " 34: 0.01568,\n", - " 36: 0.0154,\n", - " 38: 0.01654,\n", - " 40: 0.01548,\n", - " 42: 0.01613,\n", - " 44: 0.01552,\n", - " 46: 0.01565,\n", - " 48: 0.01558,\n", - " 50: 0.01567,\n", - " 52: 0.01529,\n", - " 54: 0.01524,\n", - " 56: 0.01575,\n", - " 58: 0.01561,\n", - " 60: 0.01569,\n", - " 62: 0.01569,\n", - " 64: 0.01575,\n", - " 66: 0.01506,\n", - " 68: 0.01534,\n", - " 70: 0.01512,\n", - " 72: 0.01614,\n", - " 74: 0.01672,\n", - " 76: 0.01553,\n", - " 78: 0.01572,\n", - " 80: 0.01526,\n", - " 82: 0.01591,\n", - " 84: 0.01572,\n", - " 86: 0.01563,\n", - " 88: 0.016,\n", - " 90: 0.01579,\n", - " 92: 0.01547,\n", - " 94: 0.01604,\n", - " 96: 0.01549,\n", - " 98: 0.01629,\n", - " 100: 0.01544,\n", - " 102: 0.01589,\n", - " 104: 0.01479,\n", - " 106: 0.01599,\n", - " 108: 0.01586,\n", - " 110: 0.01574,\n", - " 112: 0.01576,\n", - " 114: 0.01567,\n", - " 116: 0.01526,\n", - " 118: 0.01532,\n", - " 120: 0.01529,\n", - " 122: 0.01624,\n", - " 124: 0.01545,\n", - " 126: 0.01604}" - ] - }, - "execution_count": 130, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H_real_results_list[0].quasi_dists[1]" - ] - }, - { - "cell_type": "code", - "execution_count": 131, - "metadata": {}, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "'int' object has no attribute 'replace'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[131], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mqiskit\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mresult\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m marginal_distribution\n\u001b[0;32m----> 2\u001b[0m \u001b[43mmarginal_distribution\u001b[49m\u001b[43m(\u001b[49m\u001b[43mH_real_results_list\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mquasi_dists\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n", - "File \u001b[0;32m~/opt/miniconda3/envs/krylov-sk/lib/python3.10/site-packages/qiskit/result/utils.py:224\u001b[0m, in \u001b[0;36mmarginal_distribution\u001b[0;34m(counts, indices, format_marginal)\u001b[0m\n\u001b[1;32m 199\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmarginal_distribution\u001b[39m(\n\u001b[1;32m 200\u001b[0m counts: \u001b[38;5;28mdict\u001b[39m,\n\u001b[1;32m 201\u001b[0m indices: Optional[Sequence[\u001b[38;5;28mint\u001b[39m]] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 202\u001b[0m format_marginal: \u001b[38;5;28mbool\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m,\n\u001b[1;32m 203\u001b[0m ) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m Dict[\u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28mint\u001b[39m]:\n\u001b[1;32m 204\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"Marginalize counts from an experiment over some indices of interest.\u001b[39;00m\n\u001b[1;32m 205\u001b[0m \n\u001b[1;32m 206\u001b[0m \u001b[38;5;124;03m Unlike :func:`~.marginal_counts` this function respects the order of\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[38;5;124;03m is invalid.\u001b[39;00m\n\u001b[1;32m 223\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m--> 224\u001b[0m num_clbits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcounts\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkeys\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreplace\u001b[49m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[1;32m 225\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m indices \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m (\u001b[38;5;28mlen\u001b[39m(indices) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mset\u001b[39m(indices)\u001b[38;5;241m.\u001b[39missubset(\u001b[38;5;28mrange\u001b[39m(num_clbits))):\n\u001b[1;32m 226\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m QiskitError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mindices must be in range [0, \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnum_clbits\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;250m \u001b[39m\u001b[38;5;241m1\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m].\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", - "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'replace'" - ] - } - ], - "source": [ - "from qiskit.result import marginal_distribution\n", - "marginal_distribution(H_real_results_list[0].quasi_dists[1], [0])" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " ## TODO: process results according to the non-commuting op that was measured (remember to marginalize to get original ops)\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " eff_count = count % (job_size)\n", - " res_idx = count // (job_size)\n", - "\n", - " H_real_results = H_real_results_list[res_idx]\n", - " H_imag_results = H_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = H_real_results.values[eff_count]\n", - " expval_imag = H_imag_results.values[eff_count]\n", - "\n", - " # # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - "\n", - " # Fill-in matrix elements\n", - " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", - " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", - " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", - "\n", - "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", - "\n", - "and get an estimate of the ground state energy $c_{min}$" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The estimated ground state energy is: 4.996846612987735\n", - "The estimated ground state energy is: -2.0169805323125676\n", - "The estimated ground state energy is: -1.2544170610566237\n", - "The estimated ground state energy is: -1.1598799405018336\n", - "The estimated ground state energy is: -0.9582267795672128\n", - "The estimated ground state energy is: -3.7140982342407463\n", - "The estimated ground state energy is: -4.007699282777389\n", - "The estimated ground state energy is: -3.838242692778295\n", - "The estimated ground state energy is: -4.096162385313948\n", - "The estimated ground state energy is: -4.363812874300807\n", - "The estimated ground state energy is: -4.52896248339562\n", - "The estimated ground state energy is: -4.630593705244608\n", - "The estimated ground state energy is: -4.708647040966806\n", - "The estimated ground state energy is: -4.550912411928362\n", - "The estimated ground state energy is: -4.6168766143968\n", - "The estimated ground state energy is: -4.677402157138201\n", - "The estimated ground state energy is: -4.813755791046398\n", - "The estimated ground state energy is: -4.997815001632314\n", - "The estimated ground state energy is: -5.056110423013211\n", - "The estimated ground state energy is: -4.957529560835039\n" - ] - } - ], - "source": [ - "gnd_en_circ_est_list = []\n", - "for d in range(1, krylov_dim+1):\n", - " # Solve generalized eigenvalue problem\n", - " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", - " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", - " print('The estimated ground state energy is: ', gnd_en_circ_est)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", - "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", - "plt.legend()\n", - "plt.xlabel('Krylov space dimension')\n", - "plt.ylabel('Energy')\n", - "plt.title('Estimating Ground state energy with Quantum Krylov')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-5.000000000000002" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Take home exercise:\n", - "Compute ground state energy with other methods" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.13" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From e311c874a404057a9e53d968bf08750d83be5c9d Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:26:14 -0700 Subject: [PATCH 05/22] small text fixes --- ...s with the quantum krylov subspace method.ipynb | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index b7636b7..94d8da8 100644 --- a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -20,7 +20,7 @@ "\n", "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", "\n", - "Is the krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", + "Is the Krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", "\n", "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", "\n", @@ -30,14 +30,14 @@ "\n", "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n", "\n", - "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $A^{-1}$.\n", + "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $H^{-1}$.\n", "\n", "Why is it useful for ground state energy problems?\n", "\n", "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", "\n", "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}$ which can be shown to give similar convergence guarantess as the power method. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", "\n", "\n", "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", @@ -48,14 +48,14 @@ "\n", "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi \\rangle$. \n", "\n", "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", "\n", "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + "$$\\langle \\psi \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi \\rangle$$" ] }, { From 8880b006e6a86339d176bccda11bc6d1437f3e26 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:27:02 -0700 Subject: [PATCH 06/22] delete classical gs en calculation --- ...h the quantum krylov subspace method.ipynb | 28 ------------------- 1 file changed, 28 deletions(-) diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index 94d8da8..16a24fb 100644 --- a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -1013,34 +1013,6 @@ "plt.title('Estimating Ground state energy with Quantum Krylov')\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-9.000000000000009" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Take home exercise:\n", - "Compute ground state energy with other methods" - ] } ], "metadata": { From 7e55745ac33305326457b129a3c1789095df3bc7 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 1 Feb 2024 11:51:36 -0700 Subject: [PATCH 07/22] adding PF version of krylov demo --- docs/krylov-subspace-demo.ipynb | 1044 +++++++++++++++++++++++++++++++ 1 file changed, 1044 insertions(+) create mode 100644 docs/krylov-subspace-demo.ipynb diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb new file mode 100644 index 0000000..aa7e11a --- /dev/null +++ b/docs/krylov-subspace-demo.ipynb @@ -0,0 +1,1044 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Krylov subspace expansion" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map problem to quantum native format\n", + "\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "\n", + "\n", + "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", + "\n", + "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", + "\n", + "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", + "\n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "\n", + "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", + "\n", + "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Imports and definitions\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pylab as plt\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", + "from qiskit.quantum_info import SparsePauliOp, Operator\n", + "from qiskit.circuit import Parameter\n", + "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit.circuit.library import PauliEvolutionGate\n", + "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", + "from qiskit.providers.fake_provider import FakePrague\n", + "from qiskit.primitives import Estimator\n", + "\n", + "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", + " s_vals, s_vecs = sp.linalg.eigh(s)\n", + " s_vecs = s_vecs.T\n", + " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", + " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", + " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", + " if k==1:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", + " else:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define Hamiltonian\n", + "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['ZZIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIZZ', 'XXIIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIXX', 'YYIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Define problem Hamiltonian. Kicked Ising in this case\n", + "n_qubits = 20\n", + "J = 1 # coupling strength for ZZ interaction\n", + "\n", + "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", + "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", + "for i in range(n_qubits-1):\n", + " H_int[i][i] = 'Z'\n", + " H_int[i][i+1] = 'Z'\n", + "for i in range(n_qubits-1):\n", + " H_int[n_qubits-1+i][i] = 'X'\n", + " H_int[n_qubits-1+i][i+1] = 'X'\n", + "for i in range(n_qubits-1):\n", + " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", + " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", + "H_int = [''.join(term) for term in H_int]\n", + "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", + "\n", + "# Get operator\n", + "H_op = SparsePauliOp.from_list(H_tot)\n", + "H_op" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set parameters for the algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set parameters for quantum Krylov algorithm\n", + "krylov_dim = 20 # size of krylov subspace\n", + "dt = 0.1 # time step\n", + "num_trotter_steps = 4\n", + "dt_circ = dt/num_trotter_steps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### State preparation\n", + "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_state_prep = QuantumCircuit(n_qubits)\n", + "for i in range(n_qubits):\n", + " if i%2 != 0:\n", + " qc_state_prep.x(i)\n", + "qc_state_prep.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time evolution\n", + "\n", + "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + " ## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "qc_evol = QuantumCircuit(qr)\n", + "qc_evol.append(evol_gate, qargs=qr)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" + ] + }, + { + "attachments": { + "H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hadamard test\n", + "\n", + "![H_test.PNG](attachment:H_test.PNG)\n", + "\n", + "\n", + "\\begin{equation}\n", + " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit for calculating the real part of the overlap in S via Hadamard test\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "## Create the time-evo op dagger circuit\n", + "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", + "evol_gate_d = evol_gate_d.inverse()\n", + "\n", + "# Put pieces together\n", + "qc_temp = QuantumCircuit(n_qubits)\n", + "qc_temp.compose(qc_state_prep, inplace=True)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", + "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", + "\n", + "# Create controlled version of the circuit\n", + "controlled_U = qc_temp.to_gate().control(1)\n", + "\n", + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", + "qc_real.h(0)\n", + "\n", + "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", + "qc_real.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 16644\n" + ] + } + ], + "source": [ + "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" + ] + }, + { + "attachments": { + "optimized_H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize circuits and operators\n", + "\n", + "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", + "\n", + "\n", + "![optimized_H_test.PNG](attachment:optimized_H_test.PNG)\n", + "\n", + "\n", + "This works provided the operator $\\hat{O}$ preserves Hamming weight.\n", + "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " |0\\rangle_a|0\\rangle^N\\quad&\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|0\\rangle^N+|1\\rangle_a|\\psi_0\\rangle\\Big) \\\\\n", + " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|0\\rangle^N+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", + " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", + "\\end{split}\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\|e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\|e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}\n", + "Hence the desired matrix element is\n", + "\\begin{equation}\n", + " \\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle=e^{i\\phi}\\big(\\langle X\\rangle_a+i\\langle Y\\rangle_a\\big).\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", + "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + "# ## Create the time-evo op circuit\n", + "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "# Create instruction for rotation about XX+YY-ZZ:\n", + "Rxyz_circ = QuantumCircuit(2)\n", + "Rxyz_circ.rxx(t,0,1)\n", + "Rxyz_circ.ryy(t,0,1)\n", + "Rxyz_circ.rzz(-t,0,1)\n", + "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", + "\n", + "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "trotter_step_circ = QuantumCircuit(qr)\n", + "for i, color in enumerate(interaction_list):\n", + " for interaction in color:\n", + " trotter_step_circ.append(Rxyz_instr, interaction)\n", + "\n", + "\n", + "qc_evol = QuantumCircuit(qr)\n", + "for _ in range(num_trotter_steps):\n", + " qc_evol.compose(trotter_step_circ, inplace=True)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use an optimized circuit for state preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", + "for idx in range(n_qubits):\n", + " if idx % 2 == 0:\n", + " controlled_state_prep.swap(idx, idx+1)\n", + " else:\n", + " controlled_state_prep.cx(idx+1, idx)\n", + " controlled_state_prep.cx(idx, idx+1)\n", + "\n", + "\n", + "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(n_qubits)\n", + "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(0)\n", + "qc_real.h(0)\n", + "\n", + "S_real_circ = qc_real.decompose().copy()\n", + "\n", + "# # Create hadamard test circuit for imaginary part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag = QuantumCircuit(qr)\n", + "qc_imag.h(0)\n", + "qc_imag.sdg(0)\n", + "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(n_qubits)\n", + "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(0)\n", + "qc_imag.h(0)\n", + "\n", + "\n", + "S_imag_circ = qc_imag.decompose().copy()\n", + "\n", + "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 146\n" + ] + } + ], + "source": [ + "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", + "The derivation of the Hadamard test assumes that the operator $\\hat{O}$ which represents a collection of terms in $H$ preserves Hamming weight. For this reason, we decompose $H$ into ZZ:\n", + "\n", + "$$ \\text{ZZ} = \\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & -1 & 0 & 0\\\\\n", + "0 & 0 & -1 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "\n", + "$$ \\text{SWAP} = \\begin{pmatrix}\n", + "1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & 1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "\n", + " $$ \\text{mSWAP} = \\begin{pmatrix}\n", + "-1 & 0 & 0 & 0\\\\\n", + "0 & 0 & 1 & 0\\\\\n", + "0 & 1 & 0 & 0\\\\\n", + "0 & 0 & 0 & -1\\\\\n", + "\\end{pmatrix}$$\n", + "\n", + "instead of ZZ, XX, and YY.\n", + "Using the former decomposition yields terms that are all unitary AND number conserving." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", + "mswap = mswap_op.to_instruction()\n", + "mswap.label = 'mswap'\n", + "\n", + "# Hamiltonian terms\n", + "hamiltonian_circuits = []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " qr = QuantumRegister(n_qubits)\n", + " qc_ham = QuantumCircuit(qr)\n", + " active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", + " if 'X' in pauli.to_label():\n", + " qc_ham.swap(*active_qubits)\n", + " if 'Y' in pauli.to_label():\n", + " qc_ham.append(mswap,qargs=active_qubits)\n", + " for i in active_qubits:\n", + " qc_ham.z(i)\n", + " if 'Z' in pauli.to_label():\n", + " for i in active_qubits:\n", + " qc_ham.z(i)\n", + " hamiltonian_circuits.append(qc_ham)\n", + "\n", + "\n", + "\n", + "# Real part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_1 = QuantumCircuit(qr)\n", + "qc_real_1.h(0)\n", + "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real_1.x(n_qubits)\n", + "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_real_circ_1 = qc_real_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_2 = QuantumCircuit(qr)\n", + "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real_2.x(0)\n", + "qc_real_2.h(0)\n", + "H_real_circ_2 = qc_real_2.decompose().copy()\n", + "\n", + "# Imaginary part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_1 = QuantumCircuit(qr)\n", + "qc_imag_1.h(0)\n", + "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_1.x(n_qubits)\n", + "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_2 = QuantumCircuit(qr)\n", + "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_2.x(0)\n", + "qc_imag_2.sdg(0)\n", + "qc_imag_2.h(0)\n", + "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Execute using a quantum primitive" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate circuits to calculate all matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "S_real_circuits, S_imag_circuits = [], []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " \n", + "\n", + " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " S_real_circuits.append(circuit_real)\n", + " S_imag_circuits.append(circuit_imag)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "count = 0\n", + "H_real_circuits, H_imag_circuits = [], [] \n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " circuit_real = H_real_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " circuit_imag = H_imag_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " H_real_circuits.append(circuit_real)\n", + " H_imag_circuits.append(circuit_imag)\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Execute circuits for $\\tilde{S}$ with the Estimator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "210 circuits to run\n" + ] + } + ], + "source": [ + "\n", + "\n", + "estimator = Estimator()\n", + "\n", + "jobs = {'S': {'real':[], 'imag':[]},\n", + " 'H': {'real':[], 'imag':[]}\n", + " } # store executed jobs\n", + "\n", + "\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size_S = 20\n", + "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", + "\n", + "\n", + "\n", + "print(len(S_real_circuits), 'circuits to run')\n", + "\n", + "S_real_results_list, S_imag_results_list = [], []\n", + "for i in range(len(job_idxs_S)-1):\n", + "\n", + " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['real'].append(job.job_id())\n", + " S_real_results = job.result()\n", + "\n", + " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['imag'].append(job.job_id())\n", + " S_imag_results = job.result()\n", + "\n", + "\n", + " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", + " np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "11970 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs['H']['real'], jobs['H']['imag'] = [], []\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size = 50\n", + "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", + "\n", + "print(len(H_imag_circuits), 'circuits to run')\n", + "\n", + "H_real_results_list, H_imag_results_list = [], []\n", + "for i in range(len(job_idxs)-1):\n", + " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", + "\n", + "\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " # print(f\"job id: {job_real.job_id()}\")\n", + " jobs['H']['real'].append(job_real.job_id())\n", + " H_real_results = job_real.result()\n", + "\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " # print(f\"job id: {job_imag.job_id()}\")\n", + " jobs['H']['imag'].append(job_imag.job_id())\n", + " H_imag_results = job_imag.result()\n", + "\n", + "\n", + " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", + " np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process and analyze results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + "\n", + " eff_count = count % (job_size_S)\n", + " res_idx = count // (job_size_S)\n", + "\n", + " S_real_results = S_real_results_list[res_idx]\n", + " S_imag_results = S_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = S_real_results.values[eff_count]\n", + " expval_imag = S_imag_results.values[eff_count]\n", + "\n", + " # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + " # Fill-in matrix elements\n", + " S_circ[idx_bra, idx_ket] = expval\n", + " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", + "\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the matrix elements of $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " eff_count = count % (job_size)\n", + " res_idx = count // (job_size)\n", + "\n", + " H_real_results = H_real_results_list[res_idx]\n", + " H_imag_results = H_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = H_real_results.values[eff_count]\n", + " expval_imag = H_imag_results.values[eff_count]\n", + "\n", + " # # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + "\n", + " # Fill-in matrix elements\n", + " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", + " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", + " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", + "\n", + "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", + "\n", + "and get an estimate of the ground state energy $c_{min}$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The estimated ground state energy is: 19.001772561386353\n", + "The estimated ground state energy is: 8.886186757411066\n", + "The estimated ground state energy is: 1.7414658785731836\n", + "The estimated ground state energy is: 2.6407110576585704\n", + "The estimated ground state energy is: -2.1789120241090623\n", + "The estimated ground state energy is: -1.802298672047528\n", + "The estimated ground state energy is: -5.394027756861737\n", + "The estimated ground state energy is: -3.7933471412719424\n", + "The estimated ground state energy is: -6.680804698251523\n", + "The estimated ground state energy is: -5.256784025157172\n", + "The estimated ground state energy is: -7.286989741211739\n", + "The estimated ground state energy is: -6.081949425638568\n", + "The estimated ground state energy is: -7.753950647115604\n", + "The estimated ground state energy is: -6.611646116146415\n", + "The estimated ground state energy is: -6.618399572796952\n", + "The estimated ground state energy is: -7.40844667021687\n", + "The estimated ground state energy is: -8.136604965075088\n", + "The estimated ground state energy is: -8.59843083841513\n", + "The estimated ground state energy is: -8.372146644647229\n", + "The estimated ground state energy is: -9.600091507679045\n" + ] + } + ], + "source": [ + "gnd_en_circ_est_list = []\n", + "for d in range(1, krylov_dim+1):\n", + " # Solve generalized eigenvalue problem\n", + " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", + " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", + " print('The estimated ground state energy is: ', gnd_en_circ_est)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", + "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", + "plt.legend()\n", + "plt.xlabel('Krylov space dimension')\n", + "plt.ylabel('Energy')\n", + "plt.title('Estimating Ground state energy with Quantum Krylov')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Take home exercise:\n", + "Compute ground state energy with other methods" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.17" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From f525525568b502148d5639bd9e9cefd1fd0882d9 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 8 Feb 2024 11:30:57 -0700 Subject: [PATCH 08/22] switch to Hadamard test with pauli measurements --- docs/krylov-subspace-demo.ipynb | 180 ++++++++++++++++++-------------- 1 file changed, 103 insertions(+), 77 deletions(-) diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb index aa7e11a..a410ee1 100644 --- a/docs/krylov-subspace-demo.ipynb +++ b/docs/krylov-subspace-demo.ipynb @@ -97,15 +97,9 @@ { "data": { "text/plain": [ - "SparsePauliOp(['ZZIIIIIIIIIIIIIIIIII', 'IZZIIIIIIIIIIIIIIIII', 'IIZZIIIIIIIIIIIIIIII', 'IIIZZIIIIIIIIIIIIIII', 'IIIIZZIIIIIIIIIIIIII', 'IIIIIZZIIIIIIIIIIIII', 'IIIIIIZZIIIIIIIIIIII', 'IIIIIIIZZIIIIIIIIIII', 'IIIIIIIIZZIIIIIIIIII', 'IIIIIIIIIZZIIIIIIIII', 'IIIIIIIIIIZZIIIIIIII', 'IIIIIIIIIIIZZIIIIIII', 'IIIIIIIIIIIIZZIIIIII', 'IIIIIIIIIIIIIZZIIIII', 'IIIIIIIIIIIIIIZZIIII', 'IIIIIIIIIIIIIIIZZIII', 'IIIIIIIIIIIIIIIIZZII', 'IIIIIIIIIIIIIIIIIZZI', 'IIIIIIIIIIIIIIIIIIZZ', 'XXIIIIIIIIIIIIIIIIII', 'IXXIIIIIIIIIIIIIIIII', 'IIXXIIIIIIIIIIIIIIII', 'IIIXXIIIIIIIIIIIIIII', 'IIIIXXIIIIIIIIIIIIII', 'IIIIIXXIIIIIIIIIIIII', 'IIIIIIXXIIIIIIIIIIII', 'IIIIIIIXXIIIIIIIIIII', 'IIIIIIIIXXIIIIIIIIII', 'IIIIIIIIIXXIIIIIIIII', 'IIIIIIIIIIXXIIIIIIII', 'IIIIIIIIIIIXXIIIIIII', 'IIIIIIIIIIIIXXIIIIII', 'IIIIIIIIIIIIIXXIIIII', 'IIIIIIIIIIIIIIXXIIII', 'IIIIIIIIIIIIIIIXXIII', 'IIIIIIIIIIIIIIIIXXII', 'IIIIIIIIIIIIIIIIIXXI', 'IIIIIIIIIIIIIIIIIIXX', 'YYIIIIIIIIIIIIIIIIII', 'IYYIIIIIIIIIIIIIIIII', 'IIYYIIIIIIIIIIIIIIII', 'IIIYYIIIIIIIIIIIIIII', 'IIIIYYIIIIIIIIIIIIII', 'IIIIIYYIIIIIIIIIIIII', 'IIIIIIYYIIIIIIIIIIII', 'IIIIIIIYYIIIIIIIIIII', 'IIIIIIIIYYIIIIIIIIII', 'IIIIIIIIIYYIIIIIIIII', 'IIIIIIIIIIYYIIIIIIII', 'IIIIIIIIIIIYYIIIIIII', 'IIIIIIIIIIIIYYIIIIII', 'IIIIIIIIIIIIIYYIIIII', 'IIIIIIIIIIIIIIYYIIII', 'IIIIIIIIIIIIIIIYYIII', 'IIIIIIIIIIIIIIIIYYII', 'IIIIIIIIIIIIIIIIIYYI', 'IIIIIIIIIIIIIIIIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j])" + "SparsePauliOp(['ZZIIII', 'IZZIII', 'IIZZII', 'IIIZZI', 'IIIIZZ', 'XXIIII', 'IXXIII', 'IIXXII', 'IIIXXI', 'IIIIXX', 'YYIIII', 'IYYIII', 'IIYYII', 'IIIYYI', 'IIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" ] }, "execution_count": 2, @@ -115,7 +109,7 @@ ], "source": [ "# Define problem Hamiltonian. Kicked Ising in this case\n", - "n_qubits = 20\n", + "n_qubits = 6\n", "J = 1 # coupling strength for ZZ interaction\n", "\n", "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", @@ -172,9 +166,9 @@ "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 4, @@ -206,9 +200,9 @@ "outputs": [ { "data": { - "image/png": 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", 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" + "
" ] }, "execution_count": 5, @@ -277,9 +271,9 @@ }, { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 6, @@ -334,7 +328,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 16644\n" + "The circuit has 2Q gates depth: 4447\n" ] } ], @@ -406,9 +400,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, "execution_count": 8, @@ -459,9 +453,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" + "
" ] }, "execution_count": 9, @@ -496,9 +490,9 @@ "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, "execution_count": 10, @@ -547,7 +541,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 146\n" + "The circuit has 2Q gates depth: 76\n" ] } ], @@ -604,28 +598,38 @@ "metadata": {}, "outputs": [], "source": [ - "mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", - "mswap = mswap_op.to_instruction()\n", - "mswap.label = 'mswap'\n", - "\n", - "# Hamiltonian terms\n", - "hamiltonian_circuits = []\n", + "# mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", + "# mswap = mswap_op.to_instruction()\n", + "# mswap.label = 'mswap'\n", + "\n", + "# # Hamiltonian terms\n", + "# hamiltonian_circuits = []\n", + "# for idx_ket in range(krylov_dim):\n", + "# for idx_bra in range(idx_ket + 1):\n", + "# for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "# qr = QuantumRegister(n_qubits)\n", + "# qc_ham = QuantumCircuit(qr)\n", + "# active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", + "# if 'X' in pauli.to_label():\n", + "# qc_ham.swap(*active_qubits)\n", + "# if 'Y' in pauli.to_label():\n", + "# qc_ham.append(mswap,qargs=active_qubits)\n", + "# for i in active_qubits:\n", + "# qc_ham.z(i)\n", + "# if 'Z' in pauli.to_label():\n", + "# for i in active_qubits:\n", + "# qc_ham.z(i)\n", + "# hamiltonian_circuits.append(qc_ham)\n", + "\n", + "#TODO: can make a compact list of non-commuting observables to measure separately \n", + "# Hamiltonian terms to measure\n", + "observable_list = []\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " qr = QuantumRegister(n_qubits)\n", - " qc_ham = QuantumCircuit(qr)\n", - " active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", - " if 'X' in pauli.to_label():\n", - " qc_ham.swap(*active_qubits)\n", - " if 'Y' in pauli.to_label():\n", - " qc_ham.append(mswap,qargs=active_qubits)\n", - " for i in active_qubits:\n", - " qc_ham.z(i)\n", - " if 'Z' in pauli.to_label():\n", - " for i in active_qubits:\n", - " qc_ham.z(i)\n", - " hamiltonian_circuits.append(qc_ham)\n", + " # print(pauli)\n", + " observable = pauli[::-1].to_label() + 'Z'\n", + " observable_list.append(observable)\n", "\n", "\n", "\n", @@ -716,13 +720,14 @@ "H_real_circuits, H_imag_circuits = [], [] \n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", + " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", "\n", - " circuit_real = H_real_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", - " circuit_imag = H_imag_circ_1.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", @@ -785,7 +790,7 @@ "\n", "\n", " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - " np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" ] }, { @@ -804,7 +809,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "11970 circuits to run\n" + "3150 circuits to run\n" ] } ], @@ -813,7 +818,10 @@ "\n", "jobs['H']['real'], jobs['H']['imag'] = [], []\n", "shots = 100000\n", - "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "\n", + "\n", + "\n", "\n", "job_size = 50\n", "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", @@ -825,19 +833,19 @@ " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", "\n", "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_real.job_id()}\")\n", " jobs['H']['real'].append(job_real.job_id())\n", " H_real_results = job_real.result()\n", "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = [observable]*len(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size]), shots=shots)\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_imag.job_id()}\")\n", " jobs['H']['imag'].append(job_imag.job_id())\n", " H_imag_results = job_imag.result()\n", "\n", "\n", " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" ] }, { @@ -951,26 +959,26 @@ "name": "stdout", "output_type": "stream", "text": [ - "The estimated ground state energy is: 19.001772561386353\n", - "The estimated ground state energy is: 8.886186757411066\n", - "The estimated ground state energy is: 1.7414658785731836\n", - "The estimated ground state energy is: 2.6407110576585704\n", - "The estimated ground state energy is: -2.1789120241090623\n", - "The estimated ground state energy is: -1.802298672047528\n", - "The estimated ground state energy is: -5.394027756861737\n", - "The estimated ground state energy is: -3.7933471412719424\n", - "The estimated ground state energy is: -6.680804698251523\n", - "The estimated ground state energy is: -5.256784025157172\n", - "The estimated ground state energy is: -7.286989741211739\n", - "The estimated ground state energy is: -6.081949425638568\n", - "The estimated ground state energy is: -7.753950647115604\n", - "The estimated ground state energy is: -6.611646116146415\n", - "The estimated ground state energy is: -6.618399572796952\n", - "The estimated ground state energy is: -7.40844667021687\n", - "The estimated ground state energy is: -8.136604965075088\n", - "The estimated ground state energy is: -8.59843083841513\n", - "The estimated ground state energy is: -8.372146644647229\n", - "The estimated ground state energy is: -9.600091507679045\n" + "The estimated ground state energy is: 4.996846612987735\n", + "The estimated ground state energy is: -2.0169805323125676\n", + "The estimated ground state energy is: -1.2544170610566237\n", + "The estimated ground state energy is: -1.1598799405018336\n", + "The estimated ground state energy is: -0.9582267795672128\n", + "The estimated ground state energy is: -3.7140982342407463\n", + "The estimated ground state energy is: -4.007699282777389\n", + "The estimated ground state energy is: -3.838242692778295\n", + "The estimated ground state energy is: -4.096162385313948\n", + "The estimated ground state energy is: -4.363812874300807\n", + "The estimated ground state energy is: -4.52896248339562\n", + "The estimated ground state energy is: -4.630593705244608\n", + "The estimated ground state energy is: -4.708647040966806\n", + "The estimated ground state energy is: -4.550912411928362\n", + "The estimated ground state energy is: -4.6168766143968\n", + "The estimated ground state energy is: -4.677402157138201\n", + "The estimated ground state energy is: -4.813755791046398\n", + "The estimated ground state energy is: -4.997815001632314\n", + "The estimated ground state energy is: -5.056110423013211\n", + "The estimated ground state energy is: -4.957529560835039\n" ] } ], @@ -990,14 +998,12 @@ "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "
" + "
" ] }, - "metadata": { - "needs_background": "light" - }, + "metadata": {}, "output_type": "display_data" } ], @@ -1011,6 +1017,26 @@ "plt.show()" ] }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-5.000000000000002" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -1036,7 +1062,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.17" + "version": "3.10.13" } }, "nbformat": 4, From dae8f46a74d47d1099ef7fb2884d51296ef5ddb5 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 8 Feb 2024 16:20:52 -0700 Subject: [PATCH 09/22] attempting to measure commuting observables simultaneously --- docs/krylov-subspace-demo.ipynb | 301 +++++++++++++++++++++++++++++--- 1 file changed, 273 insertions(+), 28 deletions(-) diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb index a410ee1..b84b268 100644 --- a/docs/krylov-subspace-demo.ipynb +++ b/docs/krylov-subspace-demo.ipynb @@ -44,7 +44,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 108, "metadata": {}, "outputs": [], "source": [ @@ -57,11 +57,11 @@ "\n", "from qiskit.quantum_info import SparsePauliOp, Operator\n", "from qiskit.circuit import Parameter\n", - "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n", "from qiskit.circuit.library import PauliEvolutionGate\n", "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", "from qiskit.providers.fake_provider import FakePrague\n", - "from qiskit.primitives import Estimator\n", + "from qiskit.primitives import Estimator, Sampler\n", "\n", "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", " s_vals, s_vecs = sp.linalg.eigh(s)\n", @@ -594,7 +594,125 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 98, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "['IZZIII', 'IIZZII', 'IIIZZI', 'ZZIIII', 'IIIIZZ']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IZZIII\n", + "['I', 'Z', 'Z', 'I', 'I', 'I']\n", + "IIZZII\n", + "['I', 'Z', 'Z', 'Z', 'I', 'I']\n", + "IIIZZI\n", + "['I', 'Z', 'Z', 'Z', 'Z', 'I']\n", + "ZZIIII\n", + "['Z', 'Z', 'Z', 'Z', 'Z', 'I']\n", + "IIIIZZ\n", + "['Z', 'Z', 'Z', 'Z', 'Z', 'Z']\n", + "['IXXIII', 'IIXXII', 'IIIXXI', 'XXIIII', 'IIIIXX']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IXXIII\n", + "['I', 'X', 'X', 'I', 'I', 'I']\n", + "IIXXII\n", + "['I', 'X', 'X', 'X', 'I', 'I']\n", + "IIIXXI\n", + "['I', 'X', 'X', 'X', 'X', 'I']\n", + "XXIIII\n", + "['X', 'X', 'X', 'X', 'X', 'I']\n", + "IIIIXX\n", + "['X', 'X', 'X', 'X', 'X', 'X']\n", + "['IYYIII', 'IIYYII', 'IIIYYI', 'YYIIII', 'IIIIYY']\n", + "['I', 'I', 'I', 'I', 'I', 'I']\n", + "IYYIII\n", + "['I', 'Y', 'Y', 'I', 'I', 'I']\n", + "IIYYII\n", + "['I', 'Y', 'Y', 'Y', 'I', 'I']\n", + "IIIYYI\n", + "['I', 'Y', 'Y', 'Y', 'Y', 'I']\n", + "YYIIII\n", + "['Y', 'Y', 'Y', 'Y', 'Y', 'I']\n", + "IIIIYY\n", + "['Y', 'Y', 'Y', 'Y', 'Y', 'Y']\n" + ] + }, + { + "data": { + "text/plain": [ + "['ZZZZZZ', 'XXXXXX', 'YYYYYY']" + ] + }, + "execution_count": 98, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "non_commuting_ops_list = []\n", + "paulis_to_non_commuting_ops_dict = {}\n", + "for grp_idx, paulis in enumerate(H_op.paulis.group_commuting(qubit_wise=True)):\n", + " print(paulis)\n", + "\n", + " total_op = ['I' for _ in range(len(paulis[0]))]\n", + " print(total_op)\n", + " for pauli in paulis:\n", + " pauli = pauli.to_label()\n", + " print(pauli)\n", + "\n", + " for idx, term in enumerate(pauli):\n", + " if total_op[idx] == 'I':\n", + " total_op[idx] = term\n", + " print(total_op)\n", + "\n", + " non_commuting_ops_list.append(\"\".join(total_op))\n", + "\n", + " for pauli in paulis:\n", + " pauli = pauli.to_label()\n", + " paulis_to_non_commuting_ops_dict[pauli] = \"\".join(total_op)\n", + "\n", + "non_commuting_ops_list\n" + ] + }, + { + "cell_type": "code", + "execution_count": 99, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{'IZZIII': 'ZZZZZZ',\n", + " 'IIZZII': 'ZZZZZZ',\n", + " 'IIIZZI': 'ZZZZZZ',\n", + " 'ZZIIII': 'ZZZZZZ',\n", + " 'IIIIZZ': 'ZZZZZZ',\n", + " 'IXXIII': 'XXXXXX',\n", + " 'IIXXII': 'XXXXXX',\n", + " 'IIIXXI': 'XXXXXX',\n", + " 'XXIIII': 'XXXXXX',\n", + " 'IIIIXX': 'XXXXXX',\n", + " 'IYYIII': 'YYYYYY',\n", + " 'IIYYII': 'YYYYYY',\n", + " 'IIIYYI': 'YYYYYY',\n", + " 'YYIIII': 'YYYYYY',\n", + " 'IIIIYY': 'YYYYYY'}" + ] + }, + "execution_count": 99, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "paulis_to_non_commuting_ops_dict" + ] + }, + { + "cell_type": "code", + "execution_count": 104, "metadata": {}, "outputs": [], "source": [ @@ -621,15 +739,35 @@ "# qc_ham.z(i)\n", "# hamiltonian_circuits.append(qc_ham)\n", "\n", - "#TODO: can make a compact list of non-commuting observables to measure separately \n", - "# Hamiltonian terms to measure\n", - "observable_list = []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " # print(pauli)\n", - " observable = pauli[::-1].to_label() + 'Z'\n", - " observable_list.append(observable)\n", + "# ## TODO: how does runtime estimator group commuting observables?\n", + "# # Hamiltonian terms to measure\n", + "# observable_list = []\n", + "# for idx_ket in range(krylov_dim):\n", + "# for idx_bra in range(idx_ket + 1):\n", + "# for pauli in non_commuting_ops_list:\n", + "# # print(pauli)\n", + "# observable = pauli + 'Z'\n", + "# observable_list.append(observable)\n", + "\n", + "# Measurement of Hamiltonian terms\n", + "hamiltonian_measurement_circs = {}\n", + "for obs in non_commuting_ops_list:\n", + " qr = QuantumRegister(n_qubits+1)\n", + " cr = ClassicalRegister(n_qubits+1)\n", + " qc_meas = QuantumCircuit(qr, cr)\n", + " qc_meas.measure(0, 0)\n", + " for idx, term in enumerate(obs):\n", + " if term == 'Z':\n", + " qc_meas.measure(idx+1, idx+1)\n", + " if term == 'X':\n", + " qc_meas.h(idx+1)\n", + " qc_meas.measure(idx+1, idx+1)\n", + " if term == 'Y':\n", + " qc_meas.sdg(idx+1)\n", + " qc_meas.h(idx+1)\n", + " qc_meas.measure(idx+1, idx+1)\n", + " hamiltonian_measurement_circs[obs] = qc_meas.copy()\n", + "\n", "\n", "\n", "\n", @@ -687,7 +825,7 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 105, "metadata": {}, "outputs": [], "source": [ @@ -712,7 +850,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 106, "metadata": {}, "outputs": [], "source": [ @@ -721,14 +859,14 @@ "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " for pauli in non_commuting_ops_list:\n", "\n", - " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = H_real_circ_1.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", - " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = H_imag_circ_1.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", " H_real_circuits.append(circuit_real)\n", @@ -746,7 +884,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 107, "metadata": {}, "outputs": [ { @@ -797,24 +935,24 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "And for $\\tilde{H}$" + "And use Sampler for $\\tilde{H}$" ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 109, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "3150 circuits to run\n" + "630 circuits to run\n" ] } ], "source": [ - "estimator = Estimator()\n", + "sampler = Sampler()\n", "\n", "jobs['H']['real'], jobs['H']['imag'] = [], []\n", "shots = 100000\n", @@ -833,12 +971,12 @@ " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", "\n", "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " job_real = sampler.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_real.job_id()}\")\n", " jobs['H']['real'].append(job_real.job_id())\n", " H_real_results = job_real.result()\n", "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " job_imag = sampler.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", " # print(f\"job id: {job_imag.job_id()}\")\n", " jobs['H']['imag'].append(job_imag.job_id())\n", " H_imag_results = job_imag.result()\n", @@ -864,7 +1002,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 110, "metadata": {}, "outputs": [], "source": [ @@ -903,6 +1041,112 @@ "And the matrix elements of $\\tilde{H}$" ] }, + { + "cell_type": "code", + "execution_count": 130, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "{0: 0.01561,\n", + " 2: 0.01528,\n", + " 4: 0.01528,\n", + " 6: 0.01556,\n", + " 8: 0.01563,\n", + " 10: 0.01563,\n", + " 12: 0.01572,\n", + " 14: 0.01533,\n", + " 16: 0.01513,\n", + " 18: 0.01622,\n", + " 20: 0.01547,\n", + " 22: 0.01542,\n", + " 24: 0.01513,\n", + " 26: 0.01537,\n", + " 28: 0.01517,\n", + " 30: 0.01564,\n", + " 32: 0.01577,\n", + " 34: 0.01568,\n", + " 36: 0.0154,\n", + " 38: 0.01654,\n", + " 40: 0.01548,\n", + " 42: 0.01613,\n", + " 44: 0.01552,\n", + " 46: 0.01565,\n", + " 48: 0.01558,\n", + " 50: 0.01567,\n", + " 52: 0.01529,\n", + " 54: 0.01524,\n", + " 56: 0.01575,\n", + " 58: 0.01561,\n", + " 60: 0.01569,\n", + " 62: 0.01569,\n", + " 64: 0.01575,\n", + " 66: 0.01506,\n", + " 68: 0.01534,\n", + " 70: 0.01512,\n", + " 72: 0.01614,\n", + " 74: 0.01672,\n", + " 76: 0.01553,\n", + " 78: 0.01572,\n", + " 80: 0.01526,\n", + " 82: 0.01591,\n", + " 84: 0.01572,\n", + " 86: 0.01563,\n", + " 88: 0.016,\n", + " 90: 0.01579,\n", + " 92: 0.01547,\n", + " 94: 0.01604,\n", + " 96: 0.01549,\n", + " 98: 0.01629,\n", + " 100: 0.01544,\n", + " 102: 0.01589,\n", + " 104: 0.01479,\n", + " 106: 0.01599,\n", + " 108: 0.01586,\n", + " 110: 0.01574,\n", + " 112: 0.01576,\n", + " 114: 0.01567,\n", + " 116: 0.01526,\n", + " 118: 0.01532,\n", + " 120: 0.01529,\n", + " 122: 0.01624,\n", + " 124: 0.01545,\n", + " 126: 0.01604}" + ] + }, + "execution_count": 130, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "H_real_results_list[0].quasi_dists[1]" + ] + }, + { + "cell_type": "code", + "execution_count": 131, + "metadata": {}, + "outputs": [ + { + "ename": "AttributeError", + "evalue": "'int' object has no attribute 'replace'", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", + "Cell \u001b[0;32mIn[131], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mqiskit\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mresult\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m marginal_distribution\n\u001b[0;32m----> 2\u001b[0m \u001b[43mmarginal_distribution\u001b[49m\u001b[43m(\u001b[49m\u001b[43mH_real_results_list\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mquasi_dists\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n", + "File \u001b[0;32m~/opt/miniconda3/envs/krylov-sk/lib/python3.10/site-packages/qiskit/result/utils.py:224\u001b[0m, in \u001b[0;36mmarginal_distribution\u001b[0;34m(counts, indices, format_marginal)\u001b[0m\n\u001b[1;32m 199\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmarginal_distribution\u001b[39m(\n\u001b[1;32m 200\u001b[0m counts: \u001b[38;5;28mdict\u001b[39m,\n\u001b[1;32m 201\u001b[0m indices: Optional[Sequence[\u001b[38;5;28mint\u001b[39m]] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 202\u001b[0m format_marginal: \u001b[38;5;28mbool\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m,\n\u001b[1;32m 203\u001b[0m ) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m Dict[\u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28mint\u001b[39m]:\n\u001b[1;32m 204\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"Marginalize counts from an experiment over some indices of interest.\u001b[39;00m\n\u001b[1;32m 205\u001b[0m \n\u001b[1;32m 206\u001b[0m \u001b[38;5;124;03m Unlike :func:`~.marginal_counts` this function respects the order of\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[38;5;124;03m is invalid.\u001b[39;00m\n\u001b[1;32m 223\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m--> 224\u001b[0m num_clbits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcounts\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkeys\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreplace\u001b[49m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[1;32m 225\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m indices \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m (\u001b[38;5;28mlen\u001b[39m(indices) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mset\u001b[39m(indices)\u001b[38;5;241m.\u001b[39missubset(\u001b[38;5;28mrange\u001b[39m(num_clbits))):\n\u001b[1;32m 226\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m QiskitError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mindices must be in range [0, \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnum_clbits\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;250m \u001b[39m\u001b[38;5;241m1\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m].\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", + "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'replace'" + ] + } + ], + "source": [ + "from qiskit.result import marginal_distribution\n", + "marginal_distribution(H_real_results_list[0].quasi_dists[1], [0])" + ] + }, { "cell_type": "code", "execution_count": 18, @@ -913,6 +1157,7 @@ "count = 0\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", + " ## TODO: process results according to the non-commuting op that was measured (remember to marginalize to get original ops)\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", "\n", " eff_count = count % (job_size)\n", From 1ef7c6269206374079505bf067a624f379534071 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:21:56 -0700 Subject: [PATCH 10/22] polish notebook with meas based approach --- ...h the quantum krylov subspace method.ipynb | 1067 +++++++++++++ docs/krylov-subspace-demo.ipynb | 1315 ----------------- 2 files changed, 1067 insertions(+), 1315 deletions(-) create mode 100644 docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb delete mode 100644 docs/krylov-subspace-demo.ipynb diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb new file mode 100644 index 0000000..b7636b7 --- /dev/null +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -0,0 +1,1067 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Calculating ground states on large scale systems: Quantum Krylov Subspaces" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 1: Map problem to quantum native format\n", + "\n", + "Given a matrix H that we are interested in, subspace methods use a set of states as a basis for the construction of a smaller representation of H, which captures its properties of interest (e.g. lowest eigenvalue).\n", + "\n", + "\n", + "What is the Krylov subspace? \n", + "\n", + "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "Is the krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", + "\n", + "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", + "\n", + "$$ \\vert \\psi \\rangle = c_1 \\vert \\lambda_1 \\rangle + c_2 \\vert \\lambda_2 \\rangle + ... + c_n \\vert \\lambda_n \\rangle $$\n", + "\n", + "Applying $j^{th}$ power of the matrix $H$ gives:\n", + "\n", + "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n", + "\n", + "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $A^{-1}$.\n", + "\n", + "Why is it useful for ground state energy problems?\n", + "\n", + "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", + "\n", + "\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "\n", + "\n", + "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "\n", + "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", + "\n", + "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", + "\n", + "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", + "\n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "\n", + "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", + "\n", + "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", + "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Imports and definitions\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np\n", + "import scipy as sp\n", + "import matplotlib.pylab as plt\n", + "import warnings\n", + "warnings.filterwarnings('ignore')\n", + "\n", + "from qiskit.quantum_info import SparsePauliOp, Operator\n", + "from qiskit.circuit import Parameter\n", + "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", + "from qiskit.circuit.library import PauliEvolutionGate\n", + "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", + "from qiskit.providers.fake_provider import FakePrague\n", + "from qiskit.primitives import Estimator\n", + "\n", + "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", + " s_vals, s_vecs = sp.linalg.eigh(s)\n", + " s_vecs = s_vecs.T\n", + " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", + " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", + " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", + " if k==1:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", + " else:\n", + " if return_dimn:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", + " else:\n", + " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Define Hamiltonian\n", + "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "SparsePauliOp(['ZZIIIIIIII', 'IZZIIIIIII', 'IIZZIIIIII', 'IIIZZIIIII', 'IIIIZZIIII', 'IIIIIZZIII', 'IIIIIIZZII', 'IIIIIIIZZI', 'IIIIIIIIZZ', 'XXIIIIIIII', 'IXXIIIIIII', 'IIXXIIIIII', 'IIIXXIIIII', 'IIIIXXIIII', 'IIIIIXXIII', 'IIIIIIXXII', 'IIIIIIIXXI', 'IIIIIIIIXX', 'YYIIIIIIII', 'IYYIIIIIII', 'IIYYIIIIII', 'IIIYYIIIII', 'IIIIYYIIII', 'IIIIIYYIII', 'IIIIIIYYII', 'IIIIIIIYYI', 'IIIIIIIIYY'],\n", + " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", + " -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", + " 1.+0.j, 1.+0.j, 1.+0.j])" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Define problem Hamiltonian. Kicked Ising in this case\n", + "n_qubits = 10\n", + "J = 1 # coupling strength for ZZ interaction\n", + "\n", + "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", + "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", + "for i in range(n_qubits-1):\n", + " H_int[i][i] = 'Z'\n", + " H_int[i][i+1] = 'Z'\n", + "for i in range(n_qubits-1):\n", + " H_int[n_qubits-1+i][i] = 'X'\n", + " H_int[n_qubits-1+i][i+1] = 'X'\n", + "for i in range(n_qubits-1):\n", + " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", + " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", + "H_int = [''.join(term) for term in H_int]\n", + "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", + "\n", + "# Get operator\n", + "H_op = SparsePauliOp.from_list(H_tot)\n", + "H_op" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Set parameters for the algorithm" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "# Set parameters for quantum Krylov algorithm\n", + "krylov_dim = 20 # size of krylov subspace\n", + "dt = 0.1 # time step\n", + "num_trotter_steps = 4\n", + "dt_circ = dt/num_trotter_steps" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### State preparation\n", + "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "qc_state_prep = QuantumCircuit(n_qubits)\n", + "for i in range(n_qubits):\n", + " if i%2 != 0:\n", + " qc_state_prep.x(i)\n", + "qc_state_prep.draw('mpl')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Time evolution\n", + "\n", + "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + " ## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "qc_evol = QuantumCircuit(qr)\n", + "qc_evol.append(evol_gate, qargs=qr)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" + ] + }, + { + "attachments": { + "H_test.PNG": { + "image/png": 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" + } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Hadamard test\n", + "\n", + "![H_test.PNG](attachment:H_test.PNG)\n", + "\n", + "\n", + "\\begin{equation}\n", + " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "To measure $X$, first apply $H$...\n", + "\\begin{equation}\n", + " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", + "\\end{equation}\n", + "... then measure:\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", + " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{split}\n", + "\\end{equation}\n", + "Similarly, measuring $Y$ yields\n", + "\\begin{equation}\n", + " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", + "\\end{equation}" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Circuit for calculating the real part of the overlap in S via Hadamard test\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "## Create the time-evo op circuit\n", + "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "## Create the time-evo op dagger circuit\n", + "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", + "evol_gate_d = evol_gate_d.inverse()\n", + "\n", + "# Put pieces together\n", + "qc_temp = QuantumCircuit(n_qubits)\n", + "qc_temp.compose(qc_state_prep, inplace=True)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", + "for _ in range(num_trotter_steps):\n", + " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", + "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", + "\n", + "# Create controlled version of the circuit\n", + "controlled_U = qc_temp.to_gate().control(1)\n", + "\n", + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", + "qc_real.h(0)\n", + "\n", + "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", + "qc_real.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 8047\n" + ] + } + ], + "source": [ + "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" + ] + }, + { + "attachments": { + "optimized_H_test.png": { + "image/png": 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+ } + }, + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 2: Optimize circuits and operators\n", + "\n", + "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", + "\n", + "\n", + "![optimized_H_test.png](attachment:optimized_H_test.png)\n", + "\n", + "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", + "This is satisfied when the Hamiltonian preserves the U(1) symmetry.\n", + "Assume that the gate $\\psi_0-prep$ prepares our desired reference state $\\ket{\\psi_0}$, e.g., to prepare the HF state for chemistry $\\psi_0-prep$ would be a product of single-qubit NOTs, so controlled-$\\psi_0-prep$ is just a product of CNOTs.\n", + "Then the circuit above implements the following state prior to measurement:\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\ket{0} \\ket{0}^N\\xrightarrow{H}&\\frac{1}{\\sqrt{2}}\n", + " \\left(\n", + " \\ket{0}\\ket{0}^N+ \\ket{1} \\ket{0}^N\n", + " \\right)\\\\\n", + " \\xrightarrow{\\text{1-ctrl-init}}&\\frac{1}{\\sqrt{2}}\\left(|0\\rangle|0\\rangle^N+|1\\rangle|\\psi_0\\rangle\\right)\\\\\n", + " \\xrightarrow{U}&\\frac{1}{\\sqrt{2}}\\left(e^{i\\phi}\\ket{0}\\ket{0}^N+\\ket{1} U\\ket{\\psi_0}\\right)\\\\\n", + " \\xrightarrow{\\text{0-ctrl-init}}&\\frac{1}{\\sqrt{2}}\n", + " \\left(\n", + " e^{i\\phi}\\ket{0} \\ket{\\psi_0}\n", + " +\\ket{1} U\\ket{\\psi_0}\n", + " \\right)\\\\\n", + " =&\\frac{1}{2}\n", + " \\left(\n", + " \\ket{+}\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", + " +\\ket{-}\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", + " \\right)\\\\\n", + " =&\\frac{1}{2}\n", + " \\left(\n", + " \\ket{+i}\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", + " +\\ket{-i}\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", + " \\right)\n", + "\\end{split}\n", + "\\end{equation}\n", + "\n", + "where we have used the classical simulable phase shift $ U\\ket{0}^N = e^{i\\phi}\\ket{0}$ in the third line. Therefore the expectation values are obtained as\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\langle X\\otimes P\\rangle&=\\frac{1}{4}\n", + " \\Big(\n", + " \\left(e^{-i\\phi}\\bra{\\psi_0}+\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", + " \\\\\n", + " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", + " \\Big)\\\\\n", + " &=\\text{Re}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right],\n", + "\\end{split}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\begin{split}\n", + " \\langle Y\\otimes P\\rangle&=\\frac{1}{4}\n", + " \\Big(\n", + " \\left(e^{-i\\phi}\\bra{\\psi_0}+i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", + " \\\\\n", + " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", + " \\Big)\\\\\n", + " &=\\text{Im}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right].\n", + "\\end{split}\n", + "\\end{equation}\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", + "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "t = Parameter('t')\n", + "\n", + "# ## Create the time-evo op circuit\n", + "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "\n", + "# Create instruction for rotation about XX+YY-ZZ:\n", + "Rxyz_circ = QuantumCircuit(2)\n", + "Rxyz_circ.rxx(t,0,1)\n", + "Rxyz_circ.ryy(t,0,1)\n", + "Rxyz_circ.rzz(-t,0,1)\n", + "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", + "\n", + "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", + "\n", + "qr = QuantumRegister(n_qubits)\n", + "trotter_step_circ = QuantumCircuit(qr)\n", + "for i, color in enumerate(interaction_list):\n", + " for interaction in color:\n", + " trotter_step_circ.append(Rxyz_instr, interaction)\n", + "\n", + "\n", + "qc_evol = QuantumCircuit(qr)\n", + "for _ in range(num_trotter_steps):\n", + " qc_evol.compose(trotter_step_circ, inplace=True)\n", + "\n", + "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Use an optimized circuit for state preparation" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", + "for idx in range(n_qubits):\n", + " if idx % 2 == 0:\n", + " controlled_state_prep.swap(idx, idx+1)\n", + " else:\n", + " controlled_state_prep.cx(idx+1, idx)\n", + " controlled_state_prep.cx(idx, idx+1)\n", + "\n", + "\n", + "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", 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" + ] + }, + "execution_count": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Create hadamard test circuit for real part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real = QuantumCircuit(qr)\n", + "qc_real.h(0)\n", + "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(n_qubits)\n", + "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real.x(0)\n", + "qc_real.h(0)\n", + "\n", + "S_real_circ = qc_real.decompose().copy()\n", + "\n", + "# # Create hadamard test circuit for imaginary part\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag = QuantumCircuit(qr)\n", + "qc_imag.h(0)\n", + "qc_imag.sdg(0)\n", + "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(n_qubits)\n", + "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", + "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag.x(0)\n", + "qc_imag.h(0)\n", + "\n", + "\n", + "S_imag_circ = qc_imag.decompose().copy()\n", + "\n", + "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The circuit has 2Q gates depth: 96\n" + ] + } + ], + "source": [ + "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", + "\n", + "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", + "The only difference between the circuits used in the Hadamard test will be the phase in the time-evolution operator and the observables measured. Therefore we can prepare a template circuit which represent the generic circuit for the Hadamard test, with placeholders for the gates that depend on the time-evolution operator.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [], + "source": [ + "# Hamiltonian terms to measure\n", + "observable_list = []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " # print(pauli)\n", + " observable = pauli[::-1].to_label() + 'Z'\n", + " observable_list.append(observable)\n", + "\n", + "\n", + "\n", + "# Real part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_1 = QuantumCircuit(qr)\n", + "qc_real_1.h(0)\n", + "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_real_1.x(n_qubits)\n", + "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_real_circ_1 = qc_real_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_real_2 = QuantumCircuit(qr)\n", + "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_real_2.x(0)\n", + "qc_real_2.h(0)\n", + "H_real_circ_2 = qc_real_2.decompose().copy()\n", + "\n", + "# Imaginary part\n", + "# First half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_1 = QuantumCircuit(qr)\n", + "qc_imag_1.h(0)\n", + "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_1.x(n_qubits)\n", + "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", + "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", + "\n", + "# Second half hadamard test\n", + "qr = QuantumRegister(n_qubits+1)\n", + "qc_imag_2 = QuantumCircuit(qr)\n", + "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", + "qc_imag_2.x(0)\n", + "qc_imag_2.sdg(0)\n", + "qc_imag_2.h(0)\n", + "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 3: Execute using a quantum primitive" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Generate circuits to calculate all matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "S_real_circuits, S_imag_circuits = [], []\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " \n", + "\n", + " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " S_real_circuits.append(circuit_real)\n", + " S_imag_circuits.append(circuit_imag)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "count = 0\n", + "H_real_circuits, H_imag_circuits = [], [] \n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", + " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + "\n", + " H_real_circuits.append(circuit_real)\n", + " H_imag_circuits.append(circuit_imag)\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Execute circuits for $\\tilde{S}$ with the Estimator" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "210 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs = {'S': {'real':[], 'imag':[]},\n", + " 'H': {'real':[], 'imag':[]}\n", + " } # store executed jobs\n", + "\n", + "\n", + "shots = 100000\n", + "observable = 'I'*(n_qubits) + 'Z'\n", + "\n", + "job_size_S = 20\n", + "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", + "\n", + "\n", + "\n", + "print(len(S_real_circuits), 'circuits to run')\n", + "\n", + "S_real_results_list, S_imag_results_list = [], []\n", + "for i in range(len(job_idxs_S)-1):\n", + "\n", + " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['real'].append(job.job_id())\n", + " S_real_results = job.result()\n", + "\n", + " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", + " jobs['S']['imag'].append(job.job_id())\n", + " S_imag_results = job.result()\n", + "\n", + "\n", + " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", + "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And for $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "5670 circuits to run\n" + ] + } + ], + "source": [ + "estimator = Estimator()\n", + "\n", + "jobs['H']['real'], jobs['H']['imag'] = [], []\n", + "shots = 100000\n", + "\n", + "\n", + "job_size = 50\n", + "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", + "\n", + "print(len(H_imag_circuits), 'circuits to run')\n", + "\n", + "H_real_results_list, H_imag_results_list = [], []\n", + "for i in range(len(job_idxs)-1):\n", + " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", + "\n", + "\n", + " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " # print(f\"job id: {job_real.job_id()}\")\n", + " jobs['H']['real'].append(job_real.job_id())\n", + " H_real_results = job_real.result()\n", + "\n", + " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", + " # print(f\"job id: {job_imag.job_id()}\")\n", + " jobs['H']['imag'].append(job_imag.job_id())\n", + " H_imag_results = job_imag.result()\n", + "\n", + "\n", + " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", + " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Step 4: Post-process and analyze results" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + "\n", + " eff_count = count % (job_size_S)\n", + " res_idx = count // (job_size_S)\n", + "\n", + " S_real_results = S_real_results_list[res_idx]\n", + " S_imag_results = S_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = S_real_results.values[eff_count]\n", + " expval_imag = S_imag_results.values[eff_count]\n", + "\n", + " # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + " # Fill-in matrix elements\n", + " S_circ[idx_bra, idx_ket] = expval\n", + " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", + "\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "And the matrix elements of $\\tilde{H}$" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [], + "source": [ + "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", + "count = 0\n", + "for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", + " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + "\n", + " eff_count = count % (job_size)\n", + " res_idx = count // (job_size)\n", + "\n", + " H_real_results = H_real_results_list[res_idx]\n", + " H_imag_results = H_imag_results_list[res_idx]\n", + "\n", + " # Get expectation values from experiment\n", + " expval_real = H_real_results.values[eff_count]\n", + " expval_imag = H_imag_results.values[eff_count]\n", + "\n", + " # # Get expectation values\n", + " expval = expval_real + 1j*expval_imag\n", + "\n", + "\n", + " # Fill-in matrix elements\n", + " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", + " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", + " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", + "\n", + "\n", + "\n", + " count+=1" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", + "\n", + "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", + "\n", + "and get an estimate of the ground state energy $c_{min}$" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The estimated ground state energy is: 8.975147310913348\n", + "The estimated ground state energy is: 0.6699145941880671\n", + "The estimated ground state energy is: 1.3257378975608196\n", + "The estimated ground state energy is: -3.3030639423840706\n", + "The estimated ground state energy is: -3.9934796043575798\n", + "The estimated ground state energy is: -3.003872747466045\n", + "The estimated ground state energy is: -2.5086442931004727\n", + "The estimated ground state energy is: -5.48481710169914\n", + "The estimated ground state energy is: -5.545506988684572\n", + "The estimated ground state energy is: -6.98377741561271\n", + "The estimated ground state energy is: -6.676634627880108\n", + "The estimated ground state energy is: -7.6408885159105715\n", + "The estimated ground state energy is: -7.524234968608674\n", + "The estimated ground state energy is: -7.093259720004493\n", + "The estimated ground state energy is: -7.282617495801976\n", + "The estimated ground state energy is: -8.530915996980566\n", + "The estimated ground state energy is: -7.592245638927923\n", + "The estimated ground state energy is: -7.973568152294788\n", + "The estimated ground state energy is: -8.215496239766923\n", + "The estimated ground state energy is: -8.346530278432619\n" + ] + } + ], + "source": [ + "gnd_en_circ_est_list = []\n", + "for d in range(1, krylov_dim+1):\n", + " # Solve generalized eigenvalue problem\n", + " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", + " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", + " print('The estimated ground state energy is: ', gnd_en_circ_est)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", + "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", + "plt.legend()\n", + "plt.xlabel('Krylov space dimension')\n", + "plt.ylabel('Energy')\n", + "plt.title('Estimating Ground state energy with Quantum Krylov')\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "-9.000000000000009" + ] + }, + "execution_count": 21, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Take home exercise:\n", + "Compute ground state energy with other methods" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.17" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/docs/krylov-subspace-demo.ipynb b/docs/krylov-subspace-demo.ipynb deleted file mode 100644 index b84b268..0000000 --- a/docs/krylov-subspace-demo.ipynb +++ /dev/null @@ -1,1315 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Krylov subspace expansion" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 1: Map problem to quantum native format\n", - "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", - "\n", - "\n", - "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", - "\n", - "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", - "\n", - "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", - "\n", - "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", - "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", - "\n", - "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", - "\n", - "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Imports and definitions\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 108, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import numpy as np\n", - "import scipy as sp\n", - "import matplotlib.pylab as plt\n", - "import warnings\n", - "warnings.filterwarnings('ignore')\n", - "\n", - "from qiskit.quantum_info import SparsePauliOp, Operator\n", - "from qiskit.circuit import Parameter\n", - "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile\n", - "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", - "from qiskit.providers.fake_provider import FakePrague\n", - "from qiskit.primitives import Estimator, Sampler\n", - "\n", - "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", - " s_vals, s_vecs = sp.linalg.eigh(s)\n", - " s_vecs = s_vecs.T\n", - " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", - " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", - " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", - " if k==1:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", - " else:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Define Hamiltonian\n", - "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SparsePauliOp(['ZZIIII', 'IZZIII', 'IIZZII', 'IIIZZI', 'IIIIZZ', 'XXIIII', 'IXXIII', 'IIXXII', 'IIIXXI', 'IIIIXX', 'YYIIII', 'IYYIII', 'IIYYII', 'IIIYYI', 'IIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j])" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Define problem Hamiltonian. Kicked Ising in this case\n", - "n_qubits = 6\n", - "J = 1 # coupling strength for ZZ interaction\n", - "\n", - "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", - "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", - "for i in range(n_qubits-1):\n", - " H_int[i][i] = 'Z'\n", - " H_int[i][i+1] = 'Z'\n", - "for i in range(n_qubits-1):\n", - " H_int[n_qubits-1+i][i] = 'X'\n", - " H_int[n_qubits-1+i][i+1] = 'X'\n", - "for i in range(n_qubits-1):\n", - " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", - " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", - "H_int = [''.join(term) for term in H_int]\n", - "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", - "\n", - "# Get operator\n", - "H_op = SparsePauliOp.from_list(H_tot)\n", - "H_op" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Set parameters for the algorithm" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Set parameters for quantum Krylov algorithm\n", - "krylov_dim = 20 # size of krylov subspace\n", - "dt = 0.1 # time step\n", - "num_trotter_steps = 4\n", - "dt_circ = dt/num_trotter_steps" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### State preparation\n", - "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_state_prep = QuantumCircuit(n_qubits)\n", - "for i in range(n_qubits):\n", - " if i%2 != 0:\n", - " qc_state_prep.x(i)\n", - "qc_state_prep.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Time evolution\n", - "\n", - "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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- "text/plain": [ - "
" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - " ## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "qc_evol = QuantumCircuit(qr)\n", - "qc_evol.append(evol_gate, qargs=qr)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" - ] - }, - { - "attachments": { - "H_test.PNG": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Hadamard test\n", - "\n", - "![H_test.PNG](attachment:H_test.PNG)\n", - "\n", - "\n", - "\\begin{equation}\n", - " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", - "\\begin{equation}\n", - " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "... then measure:\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", - " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{split}\n", - "\\end{equation}\n", - "Similarly, measuring $Y$ yields\n", - "\\begin{equation}\n", - " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{equation}" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit for calculating the real part of the overlap in S via Hadamard test\n" - ] - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "## Create the time-evo op dagger circuit\n", - "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", - "evol_gate_d = evol_gate_d.inverse()\n", - "\n", - "# Put pieces together\n", - "qc_temp = QuantumCircuit(n_qubits)\n", - "qc_temp.compose(qc_state_prep, inplace=True)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", - "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", - "\n", - "# Create controlled version of the circuit\n", - "controlled_U = qc_temp.to_gate().control(1)\n", - "\n", - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", - "qc_real.h(0)\n", - "\n", - "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", - "qc_real.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 4447\n" - ] - } - ], - "source": [ - "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" - ] - }, - { - "attachments": { - "optimized_H_test.PNG": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize circuits and operators\n", - "\n", - "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", - "\n", - "\n", - "![optimized_H_test.PNG](attachment:optimized_H_test.PNG)\n", - "\n", - "\n", - "This works provided the operator $\\hat{O}$ preserves Hamming weight.\n", - "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " |0\\rangle_a|0\\rangle^N\\quad&\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|0\\rangle^N+|1\\rangle_a|\\psi_0\\rangle\\Big) \\\\\n", - " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|0\\rangle^N+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", - " &\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(e^{i\\phi}|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) \\\\\n", - "\\end{split}\n", - "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", - "\\begin{equation}\n", - " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "... then measure:\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\|e^{i\\phi}|\\psi_0\\rangle+U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\|e^{i\\phi}|\\psi_0\\rangle-U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", - " &= \\text{Re}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", - "\\end{split}\n", - "\\end{equation}\n", - "Similarly, measuring $Y$ yields\n", - "\\begin{equation}\n", - " \\langle Y\\rangle_a = \\text{Im}\\Big[e^{-i\\phi}\\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle\\Big].\n", - "\\end{equation}\n", - "Hence the desired matrix element is\n", - "\\begin{equation}\n", - " \\langle\\psi_0|U_j^\\dagger\\hat{O}U_k|\\psi_0\\rangle=e^{i\\phi}\\big(\\langle X\\rangle_a+i\\langle Y\\rangle_a\\big).\n", - "\\end{equation}" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", - "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - "# ## Create the time-evo op circuit\n", - "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "# Create instruction for rotation about XX+YY-ZZ:\n", - "Rxyz_circ = QuantumCircuit(2)\n", - "Rxyz_circ.rxx(t,0,1)\n", - "Rxyz_circ.ryy(t,0,1)\n", - "Rxyz_circ.rzz(-t,0,1)\n", - "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", - "\n", - "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "trotter_step_circ = QuantumCircuit(qr)\n", - "for i, color in enumerate(interaction_list):\n", - " for interaction in color:\n", - " trotter_step_circ.append(Rxyz_instr, interaction)\n", - "\n", - "\n", - "qc_evol = QuantumCircuit(qr)\n", - "for _ in range(num_trotter_steps):\n", - " qc_evol.compose(trotter_step_circ, inplace=True)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Use an optimized circuit for state preparation" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", - "for idx in range(n_qubits):\n", - " if idx % 2 == 0:\n", - " controlled_state_prep.swap(idx, idx+1)\n", - " else:\n", - " controlled_state_prep.cx(idx+1, idx)\n", - " controlled_state_prep.cx(idx, idx+1)\n", - "\n", - "\n", - "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(n_qubits)\n", - "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(0)\n", - "qc_real.h(0)\n", - "\n", - "S_real_circ = qc_real.decompose().copy()\n", - "\n", - "# # Create hadamard test circuit for imaginary part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag = QuantumCircuit(qr)\n", - "qc_imag.h(0)\n", - "qc_imag.sdg(0)\n", - "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(n_qubits)\n", - "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(0)\n", - "qc_imag.h(0)\n", - "\n", - "\n", - "S_imag_circ = qc_imag.decompose().copy()\n", - "\n", - "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 76\n" - ] - } - ], - "source": [ - "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", - "The derivation of the Hadamard test assumes that the operator $\\hat{O}$ which represents a collection of terms in $H$ preserves Hamming weight. For this reason, we decompose $H$ into ZZ:\n", - "\n", - "$$ \\text{ZZ} = \\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & -1 & 0 & 0\\\\\n", - "0 & 0 & -1 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "\n", - "$$ \\text{SWAP} = \\begin{pmatrix}\n", - "1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & 1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "\n", - " $$ \\text{mSWAP} = \\begin{pmatrix}\n", - "-1 & 0 & 0 & 0\\\\\n", - "0 & 0 & 1 & 0\\\\\n", - "0 & 1 & 0 & 0\\\\\n", - "0 & 0 & 0 & -1\\\\\n", - "\\end{pmatrix}$$\n", - "\n", - "instead of ZZ, XX, and YY.\n", - "Using the former decomposition yields terms that are all unitary AND number conserving." - ] - }, - { - "cell_type": "code", - "execution_count": 98, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "['IZZIII', 'IIZZII', 'IIIZZI', 'ZZIIII', 'IIIIZZ']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IZZIII\n", - "['I', 'Z', 'Z', 'I', 'I', 'I']\n", - "IIZZII\n", - "['I', 'Z', 'Z', 'Z', 'I', 'I']\n", - "IIIZZI\n", - "['I', 'Z', 'Z', 'Z', 'Z', 'I']\n", - "ZZIIII\n", - "['Z', 'Z', 'Z', 'Z', 'Z', 'I']\n", - "IIIIZZ\n", - "['Z', 'Z', 'Z', 'Z', 'Z', 'Z']\n", - "['IXXIII', 'IIXXII', 'IIIXXI', 'XXIIII', 'IIIIXX']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IXXIII\n", - "['I', 'X', 'X', 'I', 'I', 'I']\n", - "IIXXII\n", - "['I', 'X', 'X', 'X', 'I', 'I']\n", - "IIIXXI\n", - "['I', 'X', 'X', 'X', 'X', 'I']\n", - "XXIIII\n", - "['X', 'X', 'X', 'X', 'X', 'I']\n", - "IIIIXX\n", - "['X', 'X', 'X', 'X', 'X', 'X']\n", - "['IYYIII', 'IIYYII', 'IIIYYI', 'YYIIII', 'IIIIYY']\n", - "['I', 'I', 'I', 'I', 'I', 'I']\n", - "IYYIII\n", - "['I', 'Y', 'Y', 'I', 'I', 'I']\n", - "IIYYII\n", - "['I', 'Y', 'Y', 'Y', 'I', 'I']\n", - "IIIYYI\n", - "['I', 'Y', 'Y', 'Y', 'Y', 'I']\n", - "YYIIII\n", - "['Y', 'Y', 'Y', 'Y', 'Y', 'I']\n", - "IIIIYY\n", - "['Y', 'Y', 'Y', 'Y', 'Y', 'Y']\n" - ] - }, - { - "data": { - "text/plain": [ - "['ZZZZZZ', 'XXXXXX', 'YYYYYY']" - ] - }, - "execution_count": 98, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "non_commuting_ops_list = []\n", - "paulis_to_non_commuting_ops_dict = {}\n", - "for grp_idx, paulis in enumerate(H_op.paulis.group_commuting(qubit_wise=True)):\n", - " print(paulis)\n", - "\n", - " total_op = ['I' for _ in range(len(paulis[0]))]\n", - " print(total_op)\n", - " for pauli in paulis:\n", - " pauli = pauli.to_label()\n", - " print(pauli)\n", - "\n", - " for idx, term in enumerate(pauli):\n", - " if total_op[idx] == 'I':\n", - " total_op[idx] = term\n", - " print(total_op)\n", - "\n", - " non_commuting_ops_list.append(\"\".join(total_op))\n", - "\n", - " for pauli in paulis:\n", - " pauli = pauli.to_label()\n", - " paulis_to_non_commuting_ops_dict[pauli] = \"\".join(total_op)\n", - "\n", - "non_commuting_ops_list\n" - ] - }, - { - "cell_type": "code", - "execution_count": 99, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{'IZZIII': 'ZZZZZZ',\n", - " 'IIZZII': 'ZZZZZZ',\n", - " 'IIIZZI': 'ZZZZZZ',\n", - " 'ZZIIII': 'ZZZZZZ',\n", - " 'IIIIZZ': 'ZZZZZZ',\n", - " 'IXXIII': 'XXXXXX',\n", - " 'IIXXII': 'XXXXXX',\n", - " 'IIIXXI': 'XXXXXX',\n", - " 'XXIIII': 'XXXXXX',\n", - " 'IIIIXX': 'XXXXXX',\n", - " 'IYYIII': 'YYYYYY',\n", - " 'IIYYII': 'YYYYYY',\n", - " 'IIIYYI': 'YYYYYY',\n", - " 'YYIIII': 'YYYYYY',\n", - " 'IIIIYY': 'YYYYYY'}" - ] - }, - "execution_count": 99, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "paulis_to_non_commuting_ops_dict" - ] - }, - { - "cell_type": "code", - "execution_count": 104, - "metadata": {}, - "outputs": [], - "source": [ - "# mswap_op = Operator([[-1,0,0,0],[0,0,1,0],[0,1,0,0],[0,0,0,-1]])\n", - "# mswap = mswap_op.to_instruction()\n", - "# mswap.label = 'mswap'\n", - "\n", - "# # Hamiltonian terms\n", - "# hamiltonian_circuits = []\n", - "# for idx_ket in range(krylov_dim):\n", - "# for idx_bra in range(idx_ket + 1):\n", - "# for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "# qr = QuantumRegister(n_qubits)\n", - "# qc_ham = QuantumCircuit(qr)\n", - "# active_qubits = [i for i, op in enumerate(pauli.to_label()) if op != 'I']\n", - "# if 'X' in pauli.to_label():\n", - "# qc_ham.swap(*active_qubits)\n", - "# if 'Y' in pauli.to_label():\n", - "# qc_ham.append(mswap,qargs=active_qubits)\n", - "# for i in active_qubits:\n", - "# qc_ham.z(i)\n", - "# if 'Z' in pauli.to_label():\n", - "# for i in active_qubits:\n", - "# qc_ham.z(i)\n", - "# hamiltonian_circuits.append(qc_ham)\n", - "\n", - "# ## TODO: how does runtime estimator group commuting observables?\n", - "# # Hamiltonian terms to measure\n", - "# observable_list = []\n", - "# for idx_ket in range(krylov_dim):\n", - "# for idx_bra in range(idx_ket + 1):\n", - "# for pauli in non_commuting_ops_list:\n", - "# # print(pauli)\n", - "# observable = pauli + 'Z'\n", - "# observable_list.append(observable)\n", - "\n", - "# Measurement of Hamiltonian terms\n", - "hamiltonian_measurement_circs = {}\n", - "for obs in non_commuting_ops_list:\n", - " qr = QuantumRegister(n_qubits+1)\n", - " cr = ClassicalRegister(n_qubits+1)\n", - " qc_meas = QuantumCircuit(qr, cr)\n", - " qc_meas.measure(0, 0)\n", - " for idx, term in enumerate(obs):\n", - " if term == 'Z':\n", - " qc_meas.measure(idx+1, idx+1)\n", - " if term == 'X':\n", - " qc_meas.h(idx+1)\n", - " qc_meas.measure(idx+1, idx+1)\n", - " if term == 'Y':\n", - " qc_meas.sdg(idx+1)\n", - " qc_meas.h(idx+1)\n", - " qc_meas.measure(idx+1, idx+1)\n", - " hamiltonian_measurement_circs[obs] = qc_meas.copy()\n", - "\n", - "\n", - "\n", - "\n", - "# Real part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_1 = QuantumCircuit(qr)\n", - "qc_real_1.h(0)\n", - "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real_1.x(n_qubits)\n", - "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_real_circ_1 = qc_real_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_2 = QuantumCircuit(qr)\n", - "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real_2.x(0)\n", - "qc_real_2.h(0)\n", - "H_real_circ_2 = qc_real_2.decompose().copy()\n", - "\n", - "# Imaginary part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_1 = QuantumCircuit(qr)\n", - "qc_imag_1.h(0)\n", - "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_1.x(n_qubits)\n", - "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_2 = QuantumCircuit(qr)\n", - "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_2.x(0)\n", - "qc_imag_2.sdg(0)\n", - "qc_imag_2.h(0)\n", - "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 3: Execute using a quantum primitive" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate circuits to calculate all matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 105, - "metadata": {}, - "outputs": [], - "source": [ - "S_real_circuits, S_imag_circuits = [], []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " \n", - "\n", - " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " S_real_circuits.append(circuit_real)\n", - " S_imag_circuits.append(circuit_imag)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 106, - "metadata": {}, - "outputs": [], - "source": [ - "count = 0\n", - "H_real_circuits, H_imag_circuits = [], [] \n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " ## TODO: remove the following step which duplicates the circuit for each term of the Hamiltonian to measure\n", - " for pauli in non_commuting_ops_list:\n", - "\n", - " circuit_real = H_real_circ_1.compose(H_real_circ_2, list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " circuit_imag = H_imag_circ_1.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.compose(hamiltonian_measurement_circs[pauli], list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " H_real_circuits.append(circuit_real)\n", - " H_imag_circuits.append(circuit_imag)\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Execute circuits for $\\tilde{S}$ with the Estimator" - ] - }, - { - "cell_type": "code", - "execution_count": 107, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "210 circuits to run\n" - ] - } - ], - "source": [ - "\n", - "\n", - "estimator = Estimator()\n", - "\n", - "jobs = {'S': {'real':[], 'imag':[]},\n", - " 'H': {'real':[], 'imag':[]}\n", - " } # store executed jobs\n", - "\n", - "\n", - "shots = 100000\n", - "observable = 'I'*(n_qubits) + 'Z'\n", - "\n", - "job_size_S = 20\n", - "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", - "\n", - "\n", - "\n", - "print(len(S_real_circuits), 'circuits to run')\n", - "\n", - "S_real_results_list, S_imag_results_list = [], []\n", - "for i in range(len(job_idxs_S)-1):\n", - "\n", - " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['real'].append(job.job_id())\n", - " S_real_results = job.result()\n", - "\n", - " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['imag'].append(job.job_id())\n", - " S_imag_results = job.result()\n", - "\n", - "\n", - " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And use Sampler for $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 109, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "630 circuits to run\n" - ] - } - ], - "source": [ - "sampler = Sampler()\n", - "\n", - "jobs['H']['real'], jobs['H']['imag'] = [], []\n", - "shots = 100000\n", - "\n", - "\n", - "\n", - "\n", - "\n", - "job_size = 50\n", - "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", - "\n", - "print(len(H_imag_circuits), 'circuits to run')\n", - "\n", - "H_real_results_list, H_imag_results_list = [], []\n", - "for i in range(len(job_idxs)-1):\n", - " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", - "\n", - "\n", - " job_real = sampler.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_real.job_id()}\")\n", - " jobs['H']['real'].append(job_real.job_id())\n", - " H_real_results = job_real.result()\n", - "\n", - " job_imag = sampler.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_imag.job_id()}\")\n", - " jobs['H']['imag'].append(job_imag.job_id())\n", - " H_imag_results = job_imag.result()\n", - "\n", - "\n", - " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process and analyze results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 110, - "metadata": {}, - "outputs": [], - "source": [ - "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - "\n", - " eff_count = count % (job_size_S)\n", - " res_idx = count // (job_size_S)\n", - "\n", - " S_real_results = S_real_results_list[res_idx]\n", - " S_imag_results = S_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = S_real_results.values[eff_count]\n", - " expval_imag = S_imag_results.values[eff_count]\n", - "\n", - " # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - " # Fill-in matrix elements\n", - " S_circ[idx_bra, idx_ket] = expval\n", - " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", - "\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And the matrix elements of $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 130, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "{0: 0.01561,\n", - " 2: 0.01528,\n", - " 4: 0.01528,\n", - " 6: 0.01556,\n", - " 8: 0.01563,\n", - " 10: 0.01563,\n", - " 12: 0.01572,\n", - " 14: 0.01533,\n", - " 16: 0.01513,\n", - " 18: 0.01622,\n", - " 20: 0.01547,\n", - " 22: 0.01542,\n", - " 24: 0.01513,\n", - " 26: 0.01537,\n", - " 28: 0.01517,\n", - " 30: 0.01564,\n", - " 32: 0.01577,\n", - " 34: 0.01568,\n", - " 36: 0.0154,\n", - " 38: 0.01654,\n", - " 40: 0.01548,\n", - " 42: 0.01613,\n", - " 44: 0.01552,\n", - " 46: 0.01565,\n", - " 48: 0.01558,\n", - " 50: 0.01567,\n", - " 52: 0.01529,\n", - " 54: 0.01524,\n", - " 56: 0.01575,\n", - " 58: 0.01561,\n", - " 60: 0.01569,\n", - " 62: 0.01569,\n", - " 64: 0.01575,\n", - " 66: 0.01506,\n", - " 68: 0.01534,\n", - " 70: 0.01512,\n", - " 72: 0.01614,\n", - " 74: 0.01672,\n", - " 76: 0.01553,\n", - " 78: 0.01572,\n", - " 80: 0.01526,\n", - " 82: 0.01591,\n", - " 84: 0.01572,\n", - " 86: 0.01563,\n", - " 88: 0.016,\n", - " 90: 0.01579,\n", - " 92: 0.01547,\n", - " 94: 0.01604,\n", - " 96: 0.01549,\n", - " 98: 0.01629,\n", - " 100: 0.01544,\n", - " 102: 0.01589,\n", - " 104: 0.01479,\n", - " 106: 0.01599,\n", - " 108: 0.01586,\n", - " 110: 0.01574,\n", - " 112: 0.01576,\n", - " 114: 0.01567,\n", - " 116: 0.01526,\n", - " 118: 0.01532,\n", - " 120: 0.01529,\n", - " 122: 0.01624,\n", - " 124: 0.01545,\n", - " 126: 0.01604}" - ] - }, - "execution_count": 130, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "H_real_results_list[0].quasi_dists[1]" - ] - }, - { - "cell_type": "code", - "execution_count": 131, - "metadata": {}, - "outputs": [ - { - "ename": "AttributeError", - "evalue": "'int' object has no attribute 'replace'", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", - "Cell \u001b[0;32mIn[131], line 2\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;28;01mfrom\u001b[39;00m \u001b[38;5;21;01mqiskit\u001b[39;00m\u001b[38;5;21;01m.\u001b[39;00m\u001b[38;5;21;01mresult\u001b[39;00m \u001b[38;5;28;01mimport\u001b[39;00m marginal_distribution\n\u001b[0;32m----> 2\u001b[0m \u001b[43mmarginal_distribution\u001b[49m\u001b[43m(\u001b[49m\u001b[43mH_real_results_list\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mquasi_dists\u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m1\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43m[\u001b[49m\u001b[38;5;241;43m0\u001b[39;49m\u001b[43m]\u001b[49m\u001b[43m)\u001b[49m\n", - "File \u001b[0;32m~/opt/miniconda3/envs/krylov-sk/lib/python3.10/site-packages/qiskit/result/utils.py:224\u001b[0m, in \u001b[0;36mmarginal_distribution\u001b[0;34m(counts, indices, format_marginal)\u001b[0m\n\u001b[1;32m 199\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mmarginal_distribution\u001b[39m(\n\u001b[1;32m 200\u001b[0m counts: \u001b[38;5;28mdict\u001b[39m,\n\u001b[1;32m 201\u001b[0m indices: Optional[Sequence[\u001b[38;5;28mint\u001b[39m]] \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mNone\u001b[39;00m,\n\u001b[1;32m 202\u001b[0m format_marginal: \u001b[38;5;28mbool\u001b[39m \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mFalse\u001b[39;00m,\n\u001b[1;32m 203\u001b[0m ) \u001b[38;5;241m-\u001b[39m\u001b[38;5;241m>\u001b[39m Dict[\u001b[38;5;28mstr\u001b[39m, \u001b[38;5;28mint\u001b[39m]:\n\u001b[1;32m 204\u001b[0m \u001b[38;5;250m \u001b[39m\u001b[38;5;124;03m\"\"\"Marginalize counts from an experiment over some indices of interest.\u001b[39;00m\n\u001b[1;32m 205\u001b[0m \n\u001b[1;32m 206\u001b[0m \u001b[38;5;124;03m Unlike :func:`~.marginal_counts` this function respects the order of\u001b[39;00m\n\u001b[0;32m (...)\u001b[0m\n\u001b[1;32m 222\u001b[0m \u001b[38;5;124;03m is invalid.\u001b[39;00m\n\u001b[1;32m 223\u001b[0m \u001b[38;5;124;03m \"\"\"\u001b[39;00m\n\u001b[0;32m--> 224\u001b[0m num_clbits \u001b[38;5;241m=\u001b[39m \u001b[38;5;28mlen\u001b[39m(\u001b[38;5;28;43mmax\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43mcounts\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mkeys\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mreplace\u001b[49m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m \u001b[39m\u001b[38;5;124m\"\u001b[39m, \u001b[38;5;124m\"\u001b[39m\u001b[38;5;124m\"\u001b[39m))\n\u001b[1;32m 225\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m indices \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m \u001b[38;5;129;01mand\u001b[39;00m (\u001b[38;5;28mlen\u001b[39m(indices) \u001b[38;5;241m==\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;129;01mor\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mset\u001b[39m(indices)\u001b[38;5;241m.\u001b[39missubset(\u001b[38;5;28mrange\u001b[39m(num_clbits))):\n\u001b[1;32m 226\u001b[0m \u001b[38;5;28;01mraise\u001b[39;00m QiskitError(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mindices must be in range [0, \u001b[39m\u001b[38;5;132;01m{\u001b[39;00mnum_clbits\u001b[38;5;250m \u001b[39m\u001b[38;5;241m-\u001b[39m\u001b[38;5;250m \u001b[39m\u001b[38;5;241m1\u001b[39m\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m].\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n", - "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'replace'" - ] - } - ], - "source": [ - "from qiskit.result import marginal_distribution\n", - "marginal_distribution(H_real_results_list[0].quasi_dists[1], [0])" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " ## TODO: process results according to the non-commuting op that was measured (remember to marginalize to get original ops)\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " eff_count = count % (job_size)\n", - " res_idx = count // (job_size)\n", - "\n", - " H_real_results = H_real_results_list[res_idx]\n", - " H_imag_results = H_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = H_real_results.values[eff_count]\n", - " expval_imag = H_imag_results.values[eff_count]\n", - "\n", - " # # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - "\n", - " # Fill-in matrix elements\n", - " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", - " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", - " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", - "\n", - "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", - "\n", - "and get an estimate of the ground state energy $c_{min}$" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The estimated ground state energy is: 4.996846612987735\n", - "The estimated ground state energy is: -2.0169805323125676\n", - "The estimated ground state energy is: -1.2544170610566237\n", - "The estimated ground state energy is: -1.1598799405018336\n", - "The estimated ground state energy is: -0.9582267795672128\n", - "The estimated ground state energy is: -3.7140982342407463\n", - "The estimated ground state energy is: -4.007699282777389\n", - "The estimated ground state energy is: -3.838242692778295\n", - "The estimated ground state energy is: -4.096162385313948\n", - "The estimated ground state energy is: -4.363812874300807\n", - "The estimated ground state energy is: -4.52896248339562\n", - "The estimated ground state energy is: -4.630593705244608\n", - "The estimated ground state energy is: -4.708647040966806\n", - "The estimated ground state energy is: -4.550912411928362\n", - "The estimated ground state energy is: -4.6168766143968\n", - "The estimated ground state energy is: -4.677402157138201\n", - "The estimated ground state energy is: -4.813755791046398\n", - "The estimated ground state energy is: -4.997815001632314\n", - "The estimated ground state energy is: -5.056110423013211\n", - "The estimated ground state energy is: -4.957529560835039\n" - ] - } - ], - "source": [ - "gnd_en_circ_est_list = []\n", - "for d in range(1, krylov_dim+1):\n", - " # Solve generalized eigenvalue problem\n", - " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", - " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", - " print('The estimated ground state energy is: ', gnd_en_circ_est)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", - "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", - "plt.legend()\n", - "plt.xlabel('Krylov space dimension')\n", - "plt.ylabel('Energy')\n", - "plt.title('Estimating Ground state energy with Quantum Krylov')\n", - "plt.show()" - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-5.000000000000002" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Take home exercise:\n", - "Compute ground state energy with other methods" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.10.13" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 52c691b82f2b73a0d72565ec85b3419ce522a72f Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:26:14 -0700 Subject: [PATCH 11/22] small text fixes --- ...s with the quantum krylov subspace method.ipynb | 14 +++++++------- 1 file changed, 7 insertions(+), 7 deletions(-) diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index b7636b7..94d8da8 100644 --- a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -20,7 +20,7 @@ "\n", "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", "\n", - "Is the krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", + "Is the Krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", "\n", "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", "\n", @@ -30,14 +30,14 @@ "\n", "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n", "\n", - "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $A^{-1}$.\n", + "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $H^{-1}$.\n", "\n", "Why is it useful for ground state energy problems?\n", "\n", "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", "\n", "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}\\sim \\sum_j \\frac{(-it)^j}{j!}H^j$ which is equivalent for small times $t$. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}$ which can be shown to give similar convergence guarantess as the power method. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", "\n", "\n", "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", @@ -48,14 +48,14 @@ "\n", "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi_0 \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi_0 \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi_0 \\rangle$. \n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi \\rangle$. \n", "\n", "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", "\n", "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi_0 \\rangle$$\n", - "$$\\langle \\psi_0 \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi_0 \\rangle$$" + "$$\\langle \\psi \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi \\rangle$$" ] }, { From 959d1016cdd5f0777950aa604a1990eed6bb449e Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 9 Feb 2024 15:27:02 -0700 Subject: [PATCH 12/22] delete classical gs en calculation --- ...h the quantum krylov subspace method.ipynb | 28 ------------------- 1 file changed, 28 deletions(-) diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index 94d8da8..16a24fb 100644 --- a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -1013,34 +1013,6 @@ "plt.title('Estimating Ground state energy with Quantum Krylov')\n", "plt.show()" ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "-9.000000000000009" - ] - }, - "execution_count": 21, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "np.min(np.linalg.eigh(H_op.to_matrix()).eigenvalues)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Take home exercise:\n", - "Compute ground state energy with other methods" - ] } ], "metadata": { From a804a51b930321fbe71d3e66c07b148289e1b868 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 19 Feb 2024 10:53:22 -0700 Subject: [PATCH 13/22] move nb --- ...ge scale systems with the quantum krylov subspace method.ipynb | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename docs/{ => notebooks}/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb (100%) diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb similarity index 100% rename from docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb rename to docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb From 497869ebb4b5cd3f95138b67ba818ae75ea81a8e Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 19 Feb 2024 11:22:57 -0700 Subject: [PATCH 14/22] update notebook to work on qiskit1.0 --- ...h the quantum krylov subspace method.ipynb | 160 +++++++++--------- 1 file changed, 79 insertions(+), 81 deletions(-) diff --git a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index 16a24fb..43a7eb0 100644 --- a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -68,7 +68,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -84,7 +84,7 @@ "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", "from qiskit.circuit.library import PauliEvolutionGate\n", "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", - "from qiskit.providers.fake_provider import FakePrague\n", + "from qiskit.providers.fake_provider import Fake20QV1\n", "from qiskit.primitives import Estimator\n", "\n", "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", @@ -115,7 +115,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [ { @@ -128,7 +128,7 @@ " 1.+0.j, 1.+0.j, 1.+0.j])" ] }, - "execution_count": 2, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -166,7 +166,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ @@ -187,17 +187,17 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 5, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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", 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" ] }, - "execution_count": 4, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -221,17 +221,17 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 16, "metadata": {}, "outputs": [ { "data": { - "image/png": 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Sk6PvQCZDedm7z7GK8sqirtmp19rI6AnKyyoYOfk2Fy1cwcmxd1i2eHWINoCRk2+z8IIlnDg5zLJFq3nljQFqV159ztoKuT/Hx8dYumgVzw0+wbo1H6LsX/a32Gs2ZV7FfKovvJjJyUnKysoZPvE6b48cD9G2dNEqyjLllJWVc+Clx6hduZ6jxwfJZMqoqlzABs7/fk51TV37J0dPnPbcW7xgWSprFm7g8bO9/42jxwe56tINDAztp/rCiykvq2DFkloumLeQ/hf38vLRgyxesIxli1czMnqCT3/kr1gwfzHPD/Zy5aW/l3XgMSWTKWNk9O1z3lZRXsn8eRdy+8Yvs2bFOp547pdsvObPsm74+WybcnH1+7j12k9z2aqrefy5XXzi5k3s7v1uam1JuwAuWVbHNZd/mOUXXcqvn/kZjR/5Sx7ef18qXWfbBrBm5XqeH+zl2ituZfcTXXz6I39F7/O7Q7QB09fcrdc28viBXdy+8cscemXfWbWl0QWwetn7+dXTP+ETN29i4JV93Hrtp8lkMom70mybMnzidRo/8pe8deIY11z+YS6uvpSjx18u2ppNqayo4o3hoTOee7ufmPm+TbPtrXeOccUl13HVmpvY3vVF/vqzd2cdeEw5n/u5oGoRk5MTrF1zE//5fzbxH//9/0r9eZt0Py9dfiX9hx+hZsVV/OMv/pYtn/oWD+y7N7Wus2kDqH//H/C93X/Prdc28sM9d3HHh1vYN/BgiDaA6z/wselr7okDu7jikuvOGGYV65l26vX2+vArTE5OMDE5cVZdabXBu8/b//FPf8OWT32LZ196lP7Dj7D8oktDtAFUllfRf3gvd3y4hbKycr63+++5qmZDiOdtWVnFjM+9Qy8/VVBXoW1rVqzl/ie/T+OtX+UnD3+L267/LI8+2zPrzxid4X+opd029ffbodcHuO36z9L7/P9lzYr1HH716dTbkuxnZUUVFeXzWLNiPaPjI7z51mu8PfJmql1J26bUrlzPm2+9Rt0HPsaDT93LwgVnfqNlsdoANqz9Ex586l7+9Y1f4N49d7Gu9vdTaUvj/vzwB+/g3j130XRbK3f/vI0/uvE/cPT4y2fVlVYbwC1X387dP2/j83/0N/z3n/0nvvDHbdN/Dyl2G8D7Lv4A9z20ky/8cRv3/OJvabz1qzzw1A+Ltp+/a9/Ag6c99x4/8M8Fd80k3D9pmWSS2pVXMzJ2gkymjPHxMSBDWaZsekK2csllTE5O8uobL7Lv0AMcHHySrl/+HQsvWMLLRw/N/jMmJ5j3O5PytNsAJibG2f3Ed3nl9QHue2gnC+YvZuCVvhBtU370wNd45+Rb/Pw3dzMxMc6B3z6WalvSLoCu3X/HvIr59L3wK155fYDnXpq57Xyv2XTfv1xzTx3cM30dRmkDpq+5Qy/vm74OJybGz6otjS6AB566d/p6m7oGp44v5ppN+e1rz01fc1PX4RvDQ0VdsykTE2NnPPcGX3v+nK/ZWyeOsXTxal488gx7nvw+n7jlz+k//OvZf8Z52s/x8THeOfkWI6Mn+FVfN00faeWRp/9P6m1J9/OFoT6WLX4fTzy3m09s/POsw46kXWfTBvDr/p+xYe2f8MRzu7lp7b/h0QO/CNMGTF9zTzy3e/o6TKMtjftz6np7aP9909fg2T5r02oDePqFR6avuanrMNLz9uWjB6evuanrcOiNF0I8b0fHRs547j39wiPnZc0uWXYF8yqqqF64nOoLL87rZ1SWVxXclaQNmO5avGApSxetOidtSfdzqmnJwpUsWrA09a6zaQOmu5YtXp112FGsNmC6a/68BaxcellqbWncn1NNmUzmtN/6PpuutNqA07rWrFwXqm3KVNfUMyZpW9pdpzZNPV+SrtnvSvVbWpKY7RNfdz3+HW677jPn7OefzSflFqstn0/JPZdtc3HNIG6b+5mda1a4udjmfmY3F9vcz+xKcc0gbtt79f50P9Ptgrht7mf6XfDebJur90A+wv2Gx+86l/+hOlu2FS5qF9iWRNQuiNsWtQtsSyJqF9iWRNQusC2JqF1gWxJRu8C2JKJ2gW1JRO2COTDwkCRJkiRJKlTqA4+uri7a2tro68v9WRWSJEmSJEnnSmoDj56eHrZv386mTZvYunUru3bt4tvf/jb79u2b/WDgxw/+V546uCetnFRFbYvaBbYlEbULbEsiahfYlkTULojbFrULbEsiahfYlkTULrAtiahdYFsSUbsgdls2qX0tbX9/P83NzVRVvftpqplMhpUrVzI8PHzGezs7OxkYGACgurKGjcu3sGzxJbwx/GpaOXnbseNOjo0envG1qG1Ru8C2XNzPws22ZkBR2ubimkHcNvczu7nYFrUL4rZ5D2RnW+l0Qdy2XF0Qt839TN4FPm/z7YJ4bbW1tbS0tOR1fGoDj+HhYTo6Oqirq6O9vZ3GxkbeeOMNBgYG+NCHPnTae0+Nm/rE14sWruDJg/enlZO3zZu3zPpJudHaonaBbbm4n4Wbbc2gOG1zcc0gbpv7md1cbIvaBXHbvAeys610uiBuW64uiNvmfibvgrht0bogdttsUht4tLa20t3dTX19PU1NTdN/fvPNN+d1/NWX3cLVl92SVk6qorZF7QLbkojaBbYlEbULbEsiahfEbYvaBbYlEbULbEsiahfYlkTULrAtiahdELstm9QGHgANDQ1pnk6SJEmSJCkRv5ZWkiRJkiSVHAcekiRJkiSp5DjwkCRJkiRJJceBhyRJkiRJKjkOPCRJkiRJUslx4CFJkiRJkkqOAw9JkiRJklRyUh94dHV10dbWRl9fX9qnliRJkiRJyktqA4+enh62b9/Opk2b2Lp1K7t27eKHP/whDz/8cF7H39/7fX7V95O0clIVtS1qF9iWRNQusC2JqF0Qty1qF9iWRNQusC2JqF1gWxJRu8C2JKJ2gW1JRO2C2G3ZVKR1ov7+fpqbm6mqqgIgk8lw6NAhli1bdsZ7Ozs7GRgYAKC6soaNy7cw8Mp+PnDp76WVk7cdO+7k2OjhGV+L2ha1C2zLxf0s3GxrBhSlbS6uGcRti9oFtuXifhbOZ1rhbCudLojblqsL4ra5n8m7wOdtvl0Qr622tpaWlpa8jk9t4DE8PExHRwd1dXW0t7fT2NjI888/Pz3YONWpcccGYe89ULPiKn772gHGJ8YpLytPK2tWmzdvoXr1zK9FbYvaZVuytqhdkdumuqA4bXNxzSK3Re2yLVlb1K7IbT7TbHsvdEVuy9UVuc39TN4FcduidUVvm01qA4/W1la6u7upr6+nqakJgHXr1uV9/K3XfjqtlNRFbYvaBbYlEbULbEsiahfEbYvaBbYlEbULbEsiahfYlkTULrAtiahdYFsSUbsgdls2qQ08ABoaGtI8nSRJkiRJUiJ+La0kSZIkSSo5DjwkSZIkSVLJceAhSZIkSZJKjgMPSZIkSZJUchx4SJIkSZKkkuPAQ5IkSZIklRwHHpIkSZIkqeSkPvDo6uqira2Nvr6+go7rP7yXb/z4L9LOSYVthYvaBXHbonaBbUlE7QLbkojaBXHbonaBbUlE7QLbkojaBbYlEbULbEsiahfEbsumIq0T9fT00Nvby7Zt2xgaGmLnzp0cP36c+++/n6985SuzHn9VzQYOvbwvrZxU2Va4qF0Qty1qF9iWRNQusC2JqF0Qty1qF9iWRNQusC2JqF1gWxJRu8C2JKJ2Qey2bDKTk5OTaZzo61//Ol/60pf45je/yaZNm/jGN77BF7/4RX7605/y8Y9//LT3dnZ2MjAwAEB1ZQ0bl29h4JU+TowcZ+2am9LIydsDr97JsdHDM74WtW2qCyhK21xcs8htUbsit3kPlFab+1labVG7Ird5D9j2XuiK3JarK3Kb+5m8C3ze5tsVsa22tpaWlpa8jk9t4NHR0cHY2Bh1dXX09/fT2NjIkSNHWL9+PcuWLct63LFB2HtPGgXJbPgcVK+e+bWobVG7wLZc3M/CuWaFm4ttUbvAtlzcz8K5ZoWzrXBRuyBuW64uiNvmfs4sahfEbZur90A+UvsnLa2trXR3d1NfX09TU1Nap5UkSZIkSSpYagMPgIaGhjRPJ0mSJEmSlIhfSytJkiRJkkqOAw9JkiRJklRyHHhIkiRJkqSS48BDkiRJkiSVHAcekiRJkiSp5DjwkCRJkiRJJceBhyRJkiRJKjmpDzy6urpoa2ujr6+voON2Pf4d7n3ga2nnpCJqW9QusC2JqF1gWxJRuyBuW9QusC2JqF1gWxJRu8C2JKJ2gW1JRO0C25KI2gWx27KpSOtEPT099Pb2sm3bNoaGhti5cye9vb3MmzePT37yk6e9t7Ozk4GBAQCqK2vYuHwLI6MneOvEG2nl5G3Hjjs5Nnp4xteitkXtAttycT8LN9uaAUVpm4trBnHbonaBbbm4n4XzmVY420qnC+K25eqCuG3uZ/Iu8HmbbxfEa6utraWlpSWv41MbePT399Pc3ExVVRUAmUyGkZERRkdHz3jvqXHHBmHvPTCvYj4XVC1kYmKCsrLz9y9tNm/eQvXqmV+L2ha1y7ZkbVG7IrdNdUFx2ubimkVui9plW7K2qF2R23ym2fZe6Irclqsrcpv7mbwL4rZF64reNpvUBh7Dw8N0dHRQV1dHe3s7jY2N7Nu3j/Hx8byO/+j1n00rJXVR26J2gW1JRO0C25KI2gVx26J2gW1JRO0C25KI2gW2JRG1C2xLImoX2JZE1C6I3ZZNagOP1tZWuru7qa+vp6mpCYB169aldXpJkiRJkqS8pTbwAGhoaEjzdJIkSZIkSYn4tbSSJEmSJKnkOPCQJEmSJEklx4GHJEmSJEkqOQ48JEmSJElSyXHgIUmSJEmSSo4DD0mSJEmSVHIceEiSJEmSpJKT+sCjq6uLtrY2+vr6Cjpu9xPf5d4HvpZ2TiqitkXtAtuSiNoFtiURtQvitkXtAtuSiNoFtiURtQtsSyJqF9iWRNQusC2JqF0Quy2birRO1NPTQ29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" ] }, - "execution_count": 5, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" } @@ -240,7 +240,7 @@ "t = Parameter('t')\n", "\n", " ## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", + "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=num_trotter_steps) )\n", "\n", "qr = QuantumRegister(n_qubits)\n", "qc_evol = QuantumCircuit(qr)\n", @@ -285,7 +285,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 17, "metadata": {}, "outputs": [ { @@ -297,31 +297,32 @@ }, { "data": { - "image/png": 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", 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", 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" ] }, - "execution_count": 6, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } ], "source": [ "## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", + "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=num_trotter_steps) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", "\n", "## Create the time-evo op dagger circuit\n", - "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", + "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=num_trotter_steps) )\n", "evol_gate_d = evol_gate_d.inverse()\n", "\n", "# Put pieces together\n", - "qc_temp = QuantumCircuit(n_qubits)\n", + "qc_reg = QuantumRegister(n_qubits)\n", + "qc_temp = QuantumCircuit(qc_reg)\n", "qc_temp.compose(qc_state_prep, inplace=True)\n", "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", + " qc_temp.append(evol_gate, qargs=qc_reg)\n", "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", + " qc_temp.append(evol_gate_d, qargs=qc_reg)\n", "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", "\n", "# Create controlled version of the circuit\n", @@ -347,21 +348,21 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 8047\n" + "The circuit has 2Q gates depth: 79349\n" ] } ], "source": [ - "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", + "circuit_trans = transpile(circuits=qc_real.decompose().decompose(), backend=Fake20QV1())\n", "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" + "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits == 2))\n" ] }, { @@ -448,17 +449,17 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 20, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", 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" + "
" ] }, - "execution_count": 8, + "execution_count": 20, "metadata": {}, "output_type": "execute_result" } @@ -501,17 +502,17 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 21, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] }, - "execution_count": 9, + "execution_count": 21, "metadata": {}, "output_type": "execute_result" } @@ -538,17 +539,17 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 22, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "
" + "
" ] }, - "execution_count": 10, + "execution_count": 22, "metadata": {}, "output_type": "execute_result" } @@ -587,7 +588,7 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 23, "metadata": {}, "outputs": [ { @@ -599,7 +600,7 @@ } ], "source": [ - "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", + "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), Fake20QV1())\n", "\n", "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" ] @@ -621,7 +622,7 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 24, "metadata": {}, "outputs": [], "source": [ @@ -690,17 +691,16 @@ }, { "cell_type": "code", - "execution_count": 13, + "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "S_real_circuits, S_imag_circuits = [], []\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", - " \n", "\n", - " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_real = S_real_circ.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = S_imag_circ.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", " S_real_circuits.append(circuit_real)\n", " S_imag_circuits.append(circuit_imag)" @@ -715,7 +715,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 27, "metadata": {}, "outputs": [], "source": [ @@ -725,13 +725,13 @@ " for idx_bra in range(idx_ket + 1):\n", " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", "\n", - " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_real = H_real_circ_1\n", " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_real = circuit_real.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", - " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", + " circuit_imag = H_imag_circ_1\n", " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", + " circuit_imag = circuit_imag.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", "\n", " H_real_circuits.append(circuit_real)\n", " H_imag_circuits.append(circuit_imag)\n", @@ -748,7 +748,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 28, "metadata": {}, "outputs": [ { @@ -789,8 +789,7 @@ " S_imag_results = job.result()\n", "\n", "\n", - " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" + " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n" ] }, { @@ -802,7 +801,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 29, "metadata": {}, "outputs": [ { @@ -841,8 +840,7 @@ " H_imag_results = job_imag.result()\n", "\n", "\n", - " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" + " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n" ] }, { @@ -861,7 +859,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 30, "metadata": {}, "outputs": [], "source": [ @@ -902,7 +900,7 @@ }, { "cell_type": "code", - "execution_count": 18, + "execution_count": 31, "metadata": {}, "outputs": [], "source": [ @@ -949,33 +947,33 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The estimated ground state energy is: 8.975147310913348\n", - "The estimated ground state energy is: 0.6699145941880671\n", - "The estimated ground state energy is: 1.3257378975608196\n", - "The estimated ground state energy is: -3.3030639423840706\n", - "The estimated ground state energy is: -3.9934796043575798\n", - "The estimated ground state energy is: -3.003872747466045\n", - "The estimated ground state energy is: -2.5086442931004727\n", - "The estimated ground state energy is: -5.48481710169914\n", - "The estimated ground state energy is: -5.545506988684572\n", - "The estimated ground state energy is: -6.98377741561271\n", - "The estimated ground state energy is: -6.676634627880108\n", - "The estimated ground state energy is: -7.6408885159105715\n", - "The estimated ground state energy is: -7.524234968608674\n", - "The estimated ground state energy is: -7.093259720004493\n", - "The estimated ground state energy is: -7.282617495801976\n", - "The estimated ground state energy is: -8.530915996980566\n", - "The estimated ground state energy is: -7.592245638927923\n", - "The estimated ground state energy is: -7.973568152294788\n", - "The estimated ground state energy is: -8.215496239766923\n", - "The estimated ground state energy is: -8.346530278432619\n" + "The estimated ground state energy is: 9.02350357851545\n", + "The estimated ground state energy is: 1.3661212194478773\n", + "The estimated ground state energy is: 1.5519667772645285\n", + "The estimated ground state energy is: -2.433030660377216\n", + "The estimated ground state energy is: -3.8243769047376768\n", + "The estimated ground state energy is: -3.093617946223878\n", + "The estimated ground state energy is: -5.141259443945021\n", + "The estimated ground state energy is: -6.327974564731133\n", + "The estimated ground state energy is: -6.219471601689204\n", + "The estimated ground state energy is: -6.585432430537937\n", + "The estimated ground state energy is: -6.995995439961133\n", + "The estimated ground state energy is: -7.193648275003521\n", + "The estimated ground state energy is: -7.577746195049643\n", + "The estimated ground state energy is: -7.375626245886178\n", + "The estimated ground state energy is: -7.633870979679662\n", + "The estimated ground state energy is: -7.765358735198269\n", + "The estimated ground state energy is: -8.061082731107005\n", + "The estimated ground state energy is: -7.880387217614935\n", + "The estimated ground state energy is: -8.43591065997732\n", + "The estimated ground state energy is: -8.441669993329537\n" ] } ], @@ -990,12 +988,12 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 33, "metadata": {}, "outputs": [ { "data": { - "image/png": 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fPk1ERATvv/8+QK4OtT5w4ECaaSdPnuTiiy923Q8JCUm323rXrl0XbD/lw7d06dJpHnv88cdp3bo1DzzwQLrLJiQkpMkvJCSEQ4cOpSmsUnYv5Oaw5PP/PydPngRwvRYhISEkJSWleS22b9+epfY//PBDzpw5w5o1a9ixYwfDhw+nRYsWWc4vt9vAFVdcQfv27d2Kz4iICH755RcAKlWqlOmy4DznyfnL33777WmWjYmJce3aS3Hy5EnKly/v1ma5cuU4duxYmjYdDkeaNsPCwtLklZ1tc9KkScTGxrq2tzJlynDXXXcxfvz4DJ93imXLlhEcHEzNmjVp0aIFZsaqVavcCqQbb7yRFStW4Oy0yJnzt0FI+35MT1aKnJTHjh49mu28Lr74Yj777DOOHDlCbGwsERER7NmzB0h/27vQe8mTsvO5mp0cHn/8ceLj45k3bx61a9fOcL70Pqcg59tbSEgIO3fuTLMdnf8Zl5SUxNSpU+nUqRNBQUEAdOnShaCgoAJXCGmMkA86duwYjRs35vbbb6d9+/a0b9+ehx9+mHHjxtG7d+8ct5uUlJSt6X5+foDzF8wvv/zCtm3beOGFF9i/fz/x8fHccccdvPDCC/j757zevtC6cysyMpJDhw7RoEGDNI+ljBnKqHiJi4vL8ZdKRstl9lrl9Wuxbds26tSpw1133UW7du245557ePrpp3nrrbd48803M13WE9uAv78/CxYs4KOPPkr38R07dmS6LDjHdpx/1B/g1tMJGb+W57cZHh6eYSGcMjYqRUxMzAXbzMypU6f46aefeOCBB3j77bfp2rUrJUqUcOsRzUhKL81NN91EjRo1WL9+PdHR0SxbtoznnnuOUqVKcfXVV/Pqq6/mKsecboN///03nTt3plGjRixbtizdeRo1agQ4e9Yg4/dI6p7oFJMnT6ZFixYMGTKEDRs2cObMGfz9/Zk/f366215u3kvZySuzdeX2/fz3339zxx138Msvv7Bw4UJatmyZbsGT0edUbra3rJo4cSJPPPEE7du3Z+bMmdx7771s3bqVTZs2eWwdnqBCyEclJCTw008/8dNPP+Hn58eXX37JE088wdtvv83u3btz9asvuzp06ECJEiXo2LGj26+c9HZH5EVee/fupX79+mmm16pVK0vLz5kzh759+3LdddexZs2aXOfSunVrSpcu7dYrVLduXdfj8O8v0HLlyrktn5seo71791KsWDFq1qzpVjTUqVMny21ER0czefJkJk+eTGBgINOmTePVV1/l/fffz7Tw88Q2sHv3bkqXLu3qAcqOlF6Xo0eP5mj5jNps3bo1K1asyPFh8NndNr/77jtmzZrFtddeywMPPMD69eszHYScYv/+/ezdu5cbb7yRGjVquIqNpUuXMnToULp160ZAQABLly7NtJ28+tyYPXs2r776Kg899FC6hZC/vz89evTgyJEjrhyz+h4pV64crVu35o033nA7gCOr7/+MZPRanDx5Mk1O6eWVH9asWcPdd9/NnDlzWLhwITfeeGOans7M5GR727t3L40aNcLPz8/tNTr/Mw6c29+hQ4fo3r07y5cv59Zbb3UdJFGQaNeYD0rdfQ/ON2xKhV28eHEAzp49C6T9EMkLKb9sUv+SKVOmDH369Ekz79mzZz2e0/z587n00kvp2LGja1rx4sXp27dvlpb/6KOPOHv2LGPHjk1390t2elx+/vlnAgICeOaZZ9ymP//885w7d465c+cCzl0Fx44dSzPu5amnnsryus6X0vZzzz3nNv2///1vlpY/f7tKSEjg77//xs/Pj8DAQCDj7coT20DKr/q2bdumeaxs2bIZ/uIG5zZw+vRpXnnlFQIC0v6+q1ixYobLZmTy5MkEBATw+uuvp3ns/F3DmeWVnW1z7ty5HDt2jAEDBtCqVats/TpftmwZt956K9dff72r2NiwYQORkZEMHDiQ6OjoC56fLK8+N1avXs38+fPp06cPd955Z5rH3333XerUqcNHH33k2pb27t1LYmLiBd8j6W17kPXtPiMZbae7d++mXLlybmebr1KlCp07d87V+nLq119/5f7776dWrVrMmzcvW+OccrK9/fzzz1xyySVuY3+KFSvGs88+S1RUlNv4IjPjxx9/pEOHDjz44IMEBgYWuN1ioB6hAql9+/au6jq1lStXEhYWxujRoylfvjy//vorBw4cICQkhGeffZY///zTtZ92w4YNJCYmMmDAAMqWLUtcXJxr8JqnLViwgLi4OGbPns3IkSMpXbq063DU4OBgt3nXrVvHk08+yauvvsquXbs4evRorq9jM3LkSJ555hkmTJjA559/zuHDh3nggQdcv+Iv9Ct3165d9OjRgwkTJrB9+3bGjx/Pxo0b8fPzo3r16vTo0YOkpKR0u53PN3v2bH799VfeffddLr/8cjZu3Ejbtm25++67GTp0qKvbH5yHug8aNIhRo0axdu1abrrppkz39V/Ixo0b+d///sfTTz9N2bJlWblyJbfddluWfxkvWLCAI0eOsGLFCsLDw6lXrx7PPPMMc+bMcfVupXyRvvvuu0ycOJGEhARmz57tkW1gyJAhdOzYkZ9++sl1SHapUqVo2LAhXbt25fLLL+f48ePp5h4VFcWTTz7J999/z/r165k4cSLHjh2jWrVq3HnnnaxYsYJnn302W6/n0qVL+frrr3nllVdo3LgxCxYsICEhgSuuuIJu3brRr18/pk6dmmkb2d02ExMTmThxIs8++yyJiYluA1IvZNmyZfTs2ZNz5865dpWdO3eOlStX0q5dOxYvXnzBk6nm5efGQw89xK+//srMmTP53//+x7JlyyhevDhdunThlltu4fvvv2fo0KGu+SMjI5kyZQrPPvssZsbu3bu566670vxYSfnyffnllwkMDOTgwYO0bduW6tWr5yrfdevW0bp1a55//nkOHTpEWFgYf/zxBxMnTuTDDz9k+vTpfPHFF67TNOzYsSPNZS/yy4wZM+jbty+hoaHMmjWLdu3aZekEtTnZ3r755hsef/xxvv32W6655hr27NlD165dueGGG+jXr1+a8ZGTJk3iueee46233mLTpk1s27Ytx88zL3n90DWFMzI7fD714aJdunSxefPm2ZEjRyw2Ntb27NljX331lVWuXNmtvUceecR27dplCQkJbodEZnT4/D333JNuPuef4DHlMNHUl/y46667bMOGDRYdHW3//POP9e/f33r37p3mcNBKlSrZ7Nmz7fTp02aWtRMqnv86pXf46uWXX26zZ8+2s2fPWnh4uA0ZMsQ6d+5sZlk/UWKNGjVsxIgRtmPHDouOjrazZ8/a33//bV9++aU1atQoTQ5RUVHptlOqVCn75JNP7MCBAxYXF2fbt29Pc0JFcB7yO2rUKDt58qSdPn3aJk6caBUrVjSz9A+fP/8SKyn/n9Svb/Hixe2zzz6zY8eOWVRUVLZOqNi3b19bsmSJHTt2zGJiYmznzp324YcfmsPhcJvv1Vdftf3791tiYqLb+nO7DaS8du+++67t2LHDYmNj7ejRo7Z8+XJ74YUX3E7tkFG0atXK5s6daydPnrTo6GjbuXOnjR071po0aXLB/116hz8D9uijj9qaNWvs7Nmzdvr0adu4caN98MEHVqVKFdc8mV1+Irvb5rXXXmtmZvPmzcvW50e9evXMzGzLli1u01955RUzM3vrrbfSLHP+4fOZfW5k9ByzcwmGUqVK2euvv26bN2+26Oho12dberkBVqFCBZsyZYqdOXPGjh8/bl999ZXVr1/f7fMQsODgYJs6daqdOHHCTp48aZMmTbIqVark6r1Uu3ZtW7JkiZ09e9bMzO11at26tW3atMliY2Nt69at1qNHj0xPqJh6Wsrh/+d/JmT0OXx+ZHbi3RdeeMHMzGbNmmXFihXL9HMqq9tbRidUHDNmjB09etRiY2Nt48aN6Z4KJCX27t1rZmlPK1KAwusJKBR5Ev369TMzs+DgYK/nolCkjsy2zZTzQaU+f1ZhjeDgYNuzZ48dOHDALrvsMq/nUxSjKG1vmYTXE1Aoch3nn1At5aR127dv93puiqId2d02hw0bZpGRkVayZEmv554fUbduXYuIiLC//vorzaVLFHkfRW17Sy80RkgKhWnTprFv3z42bNhA2bJl6dmzJ/Xq1aNHjx7eTk2KuKxum3fddRf169fnscceY/jw4UXmwpjbtm3L0WB2yZ2iur1lxOvVmEKR2+jXr59t3rzZoqKiLDo62tauXWv33nuv1/NSKLK6bYaFhVl0dLRNnz7d7dILCkVehLa3f8Mv+YaIiIhIkaPzCImIiEiRpUJIREREiiwNls6C4ODgTK+aLCIiIgWPw+Hg0KFDmc6jQugCgoODOXjwoLfTEBERkRyoWrVqpsWQCqELSOkJqlq1qnqFREREfITD4eDgwYMX/O5WIZRFUVFRKoREREQKGQ2WFhERkSJLhZCIiIgUWSqEREREpMjSGCEREREgICCASy65BH9/9REUdGZGRESER66RpkJIRESKvEqVKvHOO+9QokQJb6ci2bBkyRJCQ0Mxy/nVwlQIiYhIkebn58ejjz7KmTNn+Pjjj4mLi/N2SnIBAQEB1K1bl3vvvReAsWPH5rwtTyUlIiLii8qVK0fdunX58ssv2bFjh7fTkSzavXs3AN27d2fixIk53k2mHaEiIlKkORwOAI4ePerlTCS7tm3bBkDFihVz3IYKIRERKdL8/PwASEpK8nImkl2JiYnAv//DnFAhJCIiIkWWCiEREREBIDQ0lOnTp3s7jXylQkhERKSICQkJwcy46qqr3Kb369eP3r175/n6C1LBpaPGREREBIDIyEhvp5Dv1CPkVcFABW8nISIiPsrPz4+BAwfyzz//EB0dzYYNG7jnnnsA52kBfvjhB44ePUp0dDQ7duxw9fbs2bMHgA0bNmBmLF68GEjbU7N48WK++OILhg4dyokTJzhy5AiPPvooJUuWZOzYsURGRrJz507atWvnWsbf35/Ro0e7ctq2bRvPPfec6/HBgwfTu3dv7r77bswMM6NVq1YAXHrppUyaNImTJ09y/PhxZsyYQUhISF6+hOoR8p5vgV7Ay8AQ76YiIiLpKJmDZeKAlKPPigHFgXNAbBbazf55cAYNGkTPnj154okn2LlzJzfddBM//PADx44do1u3btSvX5/27dsTERFBrVq1uOiiiwC47rrrWLNmDbfddhtbtmwhPj4+w3X06tWLjz76iOuvv57u3bvz1Vdf0blzZ6ZPn857773H888/z/fff0+1atWIiYnB39+fAwcO0K1bN44fP06LFi345ptvOHz4MFOmTOHjjz+mXr16lClThj59+gBw4sQJAgICmD9/PqtWreLGG28kMTGR1157jXnz5tGoUSMSEhKy/fpklSkyDofDYWZmDofDw22/YWAGo7z+HBUKhaIoR0hIiH333XcWEhJy3mOWg+iaavmuydMWn9fu0QyWzV7eQUFBdubMGWvWrJnb9FGjRtn48eNt5syZNmbMmAyfs5nZVVdd5TY9NDTUpk+f7rq/ePFiW7p0qeu+v7+/RUVF2bhx41zTKleubGZmTZs2zTDXYcOG2ZQpUzJcD2APPPCAbd261W1aYGCgnT171tq0aZPN/13Wv7/VI+Q1KWcvre3VLERExDfVqlWLUqVKsXDhQrfpQUFB/Pnnn7z55ptMnTqVJk2asGDBAmbMmMGqVauyvZ5Nmza5bp87d47jx4+zefNm17Tw8HDAeb22FE899RQPP/ww1apV46KLLiIoKIgNGzZkup6rrrqKWrVqERUV5Ta9RIkS1KxZM83z9BQVQl6TUgjV8WoWIiKSkVI5WCb1dcqmJ7dx7rx5Ls9pQm5Kly4NwJ133snBgwfds4iL48CBA4SEhHDHHXfQpk0bfvnlF0aMGEH//v2ztZ7zd0mZWbq7qfz9ncOOu3fvzscff8yLL77IqlWriIqKon///jRt2vSCz2fdunU88MADaR47duxYtnLODhVCXrMz+W9loCxw2ou5iIhIWjm7dtW/kjJoI7ftOv3999/ExsZSrVo1li5dmu48ERERfPfdd3z33XcsW7aMIUOG0L9/f9eYoGLFinkkl9RatmzJypUr+eqrr1zTatas6TZPfHx8mnWvX7+e7t27c/To0TS9QnlJhZDXRAGHgUuAK4C13k1HRER8ypkzZ/j4448ZOnQo/v7+LF++nLJly9KyZUsiIyOpWbMm69atY8uWLRQvXpy77rqLrVu3AriOJGvXrh0HDhwgNjbWY4fO79y5k4ceeoi2bdsSFhbGgw8+yHXXXUdYWJhrnj179nD77bdTu3Ztjh8/zunTpxk/fjz9+/dn5syZvPHGG64erS5duvDRRx+l6fXyFB0+71Xbk/9qnJCIiGTf66+/zttvv82gQYPYunUr8+bN48477yQsLIz4+Hjef/99Nm3axNKlS0lKSuK+++4DnNdVe+6553j88cc5dOgQM2fO9FhOI0eOZNq0aUyaNInVq1dToUIFvvzyS7d5Ro0axfbt21m7di0RERG0bNmSmJgYbrrpJvbt28e0adPYunUrY8aMoUSJEnl+fiOvj9gvyJF3R41hMNLADN70+vNUKBSKohqZHXmkKNjhiaPG1CPkVTpyTERExJtUCHmVCiERERFvUiHkVSqEREREvEmFkFf9g/PwSgdQxcu5iIiIFD0qhLwqAQhLvn2FNxMRESmyzAzIm3PqSN4KCHCeBSjlf5gTKoS8rgPOK9Av83YiIiJFUsrJ+1JfIkJ8Q926dQHniSNzSidU9Lpt3k5ARKRIO3XqFNu2bePee+/lxIkTxMXFXXgh8aqAgADq1q3Lvffey5IlS4iOzvnZuv1wHkcvGXA4HERGRlKmTJl8PeW3iIjkn//85z+8++67lChRwtupSDYsWbKE0NDQdHeNZfX7W4XQBeR9IRQMvIjzwnxP5EH7IiKSFQEBAVSpUkVjhXyAmREREZFpT1BWv7+1a8zrigEv4Bw4/TTOo8hERCS/JSYmcuDAAW+nIflMhZDXHQCGALtw/jtUCImIiOQXFUJeZ8DL3k5CRESkSNLh8yIiIlJkqUeoQHAADYBzwGov5yIiIlJ0qEeoQOgMrATe8XYiIiIiRYoKoQIh5eKrdbyahYiISFHjM4VQWFgYZpYmhg8fnu78vXr1SjNvTExMPmedVSmF0GVASW8mIiIiUqT4zBih6667zu0kVw0aNGDRokVMmTIlw2VOnz5NnTr/9rLk5qJseesEcBznNcdqAZu8m46IiEgR4TOF0PkXVBs4cCC7du3it99+y3AZMyM8PDyvU/OQHUBzoDYqhERERPKHz+waSy0wMJCePXsyduzYTOcrXbo0e/bsYd++fcyYMYP69etfsO2goCAcDodb5I+U3WO182l9IiIi4pOF0N133025cuX49ttvM5xn+/btPPzww3Tq1ImePXvi7+/PypUrqVq1aqZtDxo0iMjISFccPHjQw9lnRIWQiIhIfvPJi67OmzeP+Ph4OnbsmOVlAgIC2Lp1KxMmTOCNN97IcL6goCCKFy/uuu9wODh48GA+XH3+HuBHYBXQIg/XIyIiUvgV2ouuVqtWjdatW9OlS5dsLZeYmMiff/5JrVq1Mp0vPj6e+Pj43KSYQzqEXkREJL/53K6xPn36cPToUebMmZOt5fz9/WnYsCGHDx/Oo8xya1fy3/I4jx4TERGRvOZThZCfnx99+vRh3LhxJCW5X6V93LhxvPfee677r7/+Om3atKF69epcffXV/PDDD4SEhDB69Oj8TjuLYoB9ybc1TkhERCQ/+NSusdatWxMSEpLu0WLVqlXj3LlzrvsXX3wxo0aNokqVKpw8eZJ169bRokULtm7dmp8pZ9MOoBrOQmiVl3MREREp/HxysHR+yupgK88YAfQCXgG+yON1iYiIFF6FdrB04fYi8LS3kxARESkyfGqMUOEX6+0EREREihQVQiIiIlJkqRAqcMYDG4FLvZ2IiIhIoadCqMC5GmgE1PV2IiIiIoWeBksXOAOABGCttxMREREp9FQIFTizvZ2AiIhIkaFdYyIiIlJkqRAqcEoD9wH9vJ2IiIhIoaddYwVOKWACkAR8BcR7Nx0REZFCTD1CBU44EAkUA2p4ORcREZHCTYVQgbQj+a+uQi8iIpKXVAgVSCqERERE8oMKoQJJhZCIiEh+UCFUIKkQEhERyQ8qhAokFUIiIiL5QYVQgZRSCF0COLyZiIiISKGmQqhAigIOJ99Wr5CIiEheUSFUYGn3mIiISF5TIVRgqRASERHJayqECiwVQiIiInlNhVCB9XdyHPJ2IiIiIoWWLrpaYP2cHCIiIpJX1CMkIiIiRZYKIZ9QzNsJiIiIFEoqhAq0z4FTQB8v5yEiIlI4qRAq0Awoi44cExERyRsaLF2gfQaMBP7xch4iIiKFkwqhAm2PtxMQEREp1LRrTERERIosFUIFXj9gDHCptxMREREpdFQIFXgPJ0cDbyciIiJS6KgQKvBSrjlWx6tZiIiIFEYqhAo8XXxVREQkr6gQKvBUCImIiOQVFUIFngohERGRvKJCqMBLKYSqARd5MxEREZFCx2cKocGDB2NmbrF169ZMl+natStbt24lJiaGTZs20b59+3zK1pOOAyeSb9fyZiIiIiKFjs8UQgB//fUXVapUccUNN9yQ4bzNmzdnwoQJjBkzhquvvpoZM2YwY8YMrrzyynzM2FO2J//V7jERERFP8qlCKDExkfDwcFccP348w3n79evHvHnz+Pjjj9m2bRtvvPEG69ev55lnnsnHjD1Fh9CLiIjkBZ8qhK644goOHjzI7t27+eGHH7jssssynLd58+YsWrTIbdr8+fNp3rx5pusICgrC4XC4hfdpwLSIiEhe8JlCaPXq1fTu3Zt27drx5JNPUr16dZYtW0bp0qXTnb9KlSqEh4e7TQsPD6dKlSqZrmfQoEFERka64uDBgx57DjmnQkhERCQv+EwhNG/ePH788Uc2b97MggULuOOOOyhXrhz33nuvR9fz/vvvU6ZMGVdUrVrVo+3njAohERGRvBDg7QRy6vTp0+zYsYNatdI/kurIkSNUrlzZbVrlypU5cuRIpu3Gx8cTHx/vsTw9YxcwH+eg6QAg0bvpiIiIFBI+0yN0vlKlSlGzZk0OHz6c7uOrVq3itttuc5vWpk0bVq1alR/peVg00A7nlehVBImIiHiS+UIMGTLEbrrpJgsJCbHmzZvbggUL7OjRo1axYkUDbNy4cfbee++55m/evLnFx8fbCy+8YHXq1LHBgwdbXFycXXnlldlar8PhMDMzh8Ph9ddAoVAoFApF1iKr398+s2vs0ksvZcKECVSoUIFjx46xfPlymjVrRkREBADVqlXj3LlzrvlXrVpFjx49eOedd3jvvffYuXMnd999N1u2bPHWU/CAskAp4JC3ExERESkU/HBWRJIBh8NBZGQkZcqUISoqyouZPAl8CUwBPDtAXEREpLDJ6ve3z44RKnr2JP8t780kREREChWf2TUmvwAO4Iy3ExERESk0VAj5jPjkEBEREU/RrjEREREpslQI+ZTHgIVAD28nIiIiUiioEPIptYDWwLXeTkRERKRQUCHkU1KuOVbHq1mIiIgUFiqEfIouvioiIuJJKoR8SkohVB0I9GYiIiIihYIKIZ9yBIgCigE1vJyLiIiI71Mh5HO0e0xERMRTVAj5nO3Jf1UIiYiI5JYKIZ+jHiERERFPUSHkc3QIvYiIiKeoEPI56hESERHxFBVCPmdn8t9LcF6NXkRERHJKhZDPicR5GD3AFd5MRERExOcFeDsByYlPgHNAuLcTERER8WkqhHzSx95OQEREpFDQrjEREREpslQI+aRAoBHQ2tuJiIiI+DTtGvNJtYCNOAdOl/VyLiIiIr5LPUI+aTdwFNgClPZyLiIiIr5LPUI+KR6o7O0kREREfJ56hERERKTIUiEkIiIiRZYKIZ91F87rjk3xdiIiIiI+S2OEfFYszktsJHo7EREREZ+lHiGflXIV+ppAMW8mIiIi4rNUCPms/Th7hYKAEC/nIiIi4ptUCPksA3Ym367tzURERER8lgohn5aye0yFkIiISE6oEPJpKoRERERyQ4WQT1MhJCIikhsqhHza9uS/dbyahYiIiK9SIeTTUnqEqgEXeTMRERERn6RCyKcdB04k367lzURERER8ks8UQgMHDuSPP/4gMjKS8PBwpk+fTu3amY+N6dWrF2bmFjExMfmUcX7ROCEREZGc8plCqFWrVowYMYJmzZrRpk0bAgMDWbBgASVLlsx0udOnT1OlShVXhIQUtpMPqhASERHJKZ+51lj79u3d7vfu3Ztjx45xzTXXsGzZsgyXMzPCw8PzOj0v+gaYBazxdiIiIiI+x2cKofOVLVsWgBMnTmQ6X+nSpdmzZw/+/v6sX7+eV155hb///jvD+YOCgihevLjrvsPh8EzCeWaFtxMQERHxWT6zayw1Pz8/PvvsM5YvX86WLVsynG/79u08/PDDdOrUiZ49e+Lv78/KlSupWrVqhssMGjSIyMhIVxw8eDAvnoKIiIgUEOZr8eWXX1pYWJhVrVo1W8sFBATYzp077f/+7/8ynCcoKMgcDocrgoODzczM4XB4/XlnHHcavGhQpgDkolAoFAqF98PhcGTp+9vndo0NGzaMu+66i5tuuinbvTWJiYn8+eef1KqV8aHm8fHxxMfH5zbNfPYVcBmwHFjt5VxERER8h0/tGhs2bBidO3fm1ltvZc+ePdle3t/fn4YNG3L48GHPJ+dVc4CJQKy3ExEREfEpPtMjNGLECHr06EGnTp2IioqicuXKgPPw+NhYZwEwbtw4Dh48yCuvvALA66+/zu+//86uXbsoV64c/fv3JyQkhNGjR3vteeSNJ72dgIiIiE/ymULoqaeeAuC3335zm967d2/GjRsHQLVq1Th37pzrsYsvvphRo0ZRpUoVTp48ybp162jRogVbt27Nv8RFRESkwPLDOVhIMuBwOIiMjKRMmTJERUV5O51M+AFVgMK2209ERCT7svr97VNjhCQjlwHRwE6cBZGIiIhkhQqhQuEQUAwoBQR7ORcRERHfoUKoUEgCdiffruPNRERERHyKCqFCQxdfFRERyS4VQoWGCiEREZHsUiFUaKgQEhERyS4VQoWGCiEREZHsUiFUaKQUQtWBQG8mIiIi4jNUCBUah4EonCcLr+7lXERERHyDCqFCJaVXSIfQi4iIZIUKoUJF44RERESyQ4VQoaJCSEREJDtUCBUqKoRERESyI8DbCYgnzQeu59+CSERERDKjQqhQOZ4c+aE+zou9nsqn9YmIiHhejnaNlSxZ0tN5iM9oAfwGbAGmeDkXERGR3MlRIRQeHs6YMWNo2bKlp/ORXLsb+Bxo5eF2GwKzgBXATcnTbgUqeHg9IiIi+SdHhVDPnj0pX748v/76K9u3b2fAgAFccsklns5NcuQu4Dk8VwhVB74DNgAdgERgJM7xSN8AJTy0HhEREe+wnEbFihXt+eeft40bN1p8fLzNnj3bOnfubMWKFctxmwUtHA6HmZk5HA6v55K1uNvgA4NWuWynssEwgzgDS46JBlcUgOeoUCgUCkXmkY3vb8+s8JlnnrGYmBhLSkqy8PBwe+utt+yiiy7y+guRjy9kIYmyBu8YnDFcBdA8gyYFIDeFQqFQKLIWWf3+ztVRY5UqVaJXr1707t2bkJAQfvzxR8aMGcOll17KgAEDaNasGbfffntuViH57mXgleTbq4FBwOIM5g0ArgN2AcfyPjUREZE8kO0qq3PnzjZr1iyLi4uzP//8055++mkrW7as2zw1atSwuLg4r1eEuQ3f7BGqbHCjQakszFssef6U++UNVhp0ysKycw3M4LEC8JwVCoVCofg38rRHKDQ0lIkTJ9KyZUvWrl2b7jyHDh3i3XffzUnzkmsrgRrAjcDyTOa7HudA6EM4jwADOIHzEPmsWIGzR6hUztIUERHxMj+cFVG2XHTRRcTExORBOgWPw+EgMjKSMmXKEBUV5e10smgu0A54BBibyXyXATuBSOBq4GA213MREEsONiEREZE8ldXv7xz1CAUEBOBwONJMNzPi4uJISEjISbPiMTtwFkLnX3PseqANkNJTtx/oiLMH6UwO1lM0imERESm8clQInTp1CrOMewEOHDjAt99+y1tvvZXpfJJXzr/4aj2cxU/n5PvzgZRdmgs8tM4yOHuWREREfEeOCqHevXvz7rvv8u233/LHH38AcP3119OrVy/eeecd/vOf//DSSy8RFxfH+++/79GEJStSCqHGOHeNPQQUA5KAccBhD67rVuDb5HW29mC7IiIi+SPbI7EXLVpk3bp1SzO9W7dutmjRIgOsZ8+etnXrVq+PGs9t+OZRYyGG6xxAKfGjQd08WFft5PZjDXz/vFEKhUKhKByR1e/vHF1io0WLFvz5559ppv/55580b94cgOXLl1OtWrWcNC+5th+ISL79C86xQV2BbXmwrh3J6ysO3JAH7YuIiOSdHBVC+/fv55FHHkkz/ZFHHmH//v0AVKhQgZMnT+YuO8mhczgPnW+Gc3fVmjxe36Lkv23yeD0iIiKelaMxQi+99BJTpkyhffv2rFnj/JK99tprqVu3Ll27dgXguuuuY9KkSZ7LVLIpL3p/MrIQ6IPGCImIiK/J0XmEAEJCQnj88cepU6cOANu3b2fkyJHs3bvXk/l5nW+eRyi/VQLCk2//h393y4mIiHhHnp1HKCAggHnz5vHEE0/wyiuvXHgBKQKOAhuBq4DbAPUEioiIb8j2GKHExEQaNWqUF7mIT0sZJ6TdYyIi4jtyNFj6hx9+SHewtBRlGjAtIiK+J8eX2Hj44Ydp3bo169at4+zZs26Pv/jiix5JTnzJUiAeCAFqAbu8m46IiEgW5KgQatCgAevXrwegdm3361npkhpFVTTOa5bdjHP3mAohERHxDV4/+2N24qmnnrKwsDCLiYmx33//3a677rpM5+/atatt3brVYmJibNOmTda+ffs8OTOlAoNXDMxgagHIRaFQKBRFOfL0zNIpatasSdu2bSlRokRumsmye++9l08//ZS33nqLJk2asHHjRubPn89//vOfdOdv3rw5EyZMYMyYMVx99dXMmDGDGTNmcOWVV+ZLvkVPyjihql7NQkREJDuyXWWVL1/eFi1aZElJSZaYmGjVq1c3wMaMGWMff/xxnlV3v//+uw0bNsx138/Pzw4cOGADBgxId/6JEyfa7Nmz3aatWrXKvvrqK49XlAoM/A0uKwB5KBQKhaKoR572CA0dOpSEhASqVatGdHS0a/qkSZNo165dTpq8oMDAQK655hoWLVrkmmZmLFq0yHV9s/M1b97cbX6A+fPnZzg/QFBQEA6Hwy0kq87hvO6YiIiIb8hRIdS2bVsGDBjAwYMH3abv3LmTkJAQjyR2vooVKxIQEEB4eLjb9PDwcKpUqZLuMlWqVMnW/ACDBg0iMjLSFec/R8mqXO11FRERyRc5+rYqVaqUW09QivLlyxMXF5frpLzp/fffp0yZMq6oWlXjXbKnFDAb59mmS3o5FxERkczlqBBatmwZDz30kOu+meHn58fLL7/M4sWLPZZcahERESQmJlK5cmW36ZUrV+bIkSPpLnPkyJFszQ8QHx9PVFSUW0h2nAUaAhWAll7ORUREJHM5KoRefvllHnvsMX7++WeCgoL46KOP+Ouvv7jpppsYMGCAp3MEICEhgXXr1nHbbbe5pvn5+XHbbbexatWqdJdZtWqV2/wAbdq0yXB+8ZTHcF53bNGFZhQREfG6HI3GLlOmjL3yyis2adIkmzNnjr399ttWpUqVPB0Bfu+991pMTIw99NBDVrduXfv666/txIkTVqlSJQNs3Lhx9t5777nmb968ucXHx9sLL7xgderUscGDB1tcXJxdeeWVHh91rlAoFAqFouBENr6/vZ9sduLpp5+2PXv2WGxsrP3+++92/fXXux5bvHixhYaGus3ftWtX27Ztm8XGxtrmzZt1QkWFQqFQKIpAZPX72y/5RraVLVuW66+/nkqVKuHv776H7fvvv89JkwWSw+EgMjKSMmXKaLxQtrQH7gOmAD95ORcRESlqsvr9naNrjd11112MHz+e0qVLExkZ6XZ9MTMrVIWQ5NQtwENAIiqERESkoMrRYOlPPvmEsWPHUrp0aS6++GLKly/vigoVKng6R/FJKQOlW3s1CxERkczkqBCqWrUqX3zxBTExMZ7ORwqNZUAcUA2o7eVcRERE0pejQmj+/Plce+21ns5FCpUYYEXybfUKiYhIwZSjMUJz5sxhyJAh1K9fn82bN5OQkOD2+OzZsz2SnPi6RcCtOAuhL72ci4iISFo5OmosKSkpw8fMjICAHNVXBZKOGsuNa4E1wGmcZ5rOeLsRERHxpDw9aqxYsWI5TkyKkvXACaA8zqJotXfTEREROU+2xgjNmTOHMmXKuO4PGDCAsmXLuu6XL1+eLVu2eC478XHngF+Tb2uckIiIFDzZKoRuv/12ihcv7rr/yiuvUL58edf9gIAA6tSp47nspBBIOYy+jVezEBERSU+2CiE/P79M74uklVIINQdKeTMRERGRNHJ0+LxI1u0GwoAg4CYv5yIiIuIuW4WQmbldTiNlmkjmdJZpEREpmLJ11Jifnx/ffvstcXFxAJQoUYKvv/6as2fPAriNHxL51xicZ5pedKEZRURE8lW2ziM0duzYLM338MMP5zSfAkfnERIREfE9eXIeocJU4IiIiIgUnlNASwFXFeiO89xCn3k3FRERkWQ6akzySV3gE+AFbyciIiLioh4hyScrgFnAYpybXaJ30xEREUGFkOSbWKCTt5MQERFxo11jIiIiUmSpEJJ8dinQCyjm7URERES0a0zykx+wAagA7ABWeTUbERER9QhJPjLg1+TbutyGiIh4nwohyWcLk/+28WoWIiIioEJI8l3K9caaAaW9mYiIiIgKIclvYcA/QCBwk5dzERGRok6FkHiBdo+JiEjBoEJIvCBl95gGTIuIiHepEBIv+BXnxVcbAJd4ORcRESnKVAiJF5wA1iffvs2biYiISBGnQki8JGX3mMYJiYiI96gQEi9JGTCtcUIiIuI9KoTES1YAMUAwUM/LuYiISFGla42Jl8QBU3AOmj7n5VxERKSoUiEkXtTL2wmIiEgRp11jIiIiUmSpEBIv8wOuBi7zdiIiIlIE+UQhFBISwujRo/nnn3+Ijo5m165dvPnmmwQGBma63OLFizEzt/jqq6/yKWvJmtE4zynUx9uJiIhIEeQTY4Tq1q2Lv78/jz/+OLt27aJBgwaMGjWKUqVK0b9//0yX/eabb3jjjTdc96Ojo/M6XcmWlUA3oIS3ExERkSLKfDFeeukl2717d6bzLF682IYOHZqr9TgcDjMzczgcXn/OhTOKGwQUgDwUCoVCUZgiq9/fPrFrLD1ly5blxIkTF5zvgQce4NixY2zevJn33nuPiy66KNP5g4KCcDgcbiF5KQ5I9HYSPqIY0AHn7kSdiFJExFO8XrVlN2rWrGmnTp2yRx99NNP5+vbta23btrUGDRpYjx49bP/+/TZ16tRMlxk8eLClRz1C+RF6jdOPSw3eNNhvYMlxwNSTplAoFBlHNvboeC/J999/P92iI7U6deq4LRMcHGw7d+60UaNGZXt9t9xyi5mZ1ahRI8N5goKCzOFwuCI4OFiFUJ5HY4OdBlsKQC4FJYoZ3GUw2yDRcBVARw1OJt/uUgDyVCgUioIZWS2E/JJveEXFihWpUKFCpvP8888/JCQkAHDJJZewZMkSfv/9d3r37o1Z9lIvWbIkZ8+e5fbbb2fBggVZWsbhcBAZGUmZMmWIiorK1vokqy4GInAexFgVOOTddLzqUuCR5Eh9SoFfgW+A6cDrwGvJ027L7wRFRHxCVr+/vXrUWEREBBEREVmaNzg4mMWLF7Nu3Tr69OmT7SIIoHHjxgAcPnw428tKXjoJrAWuxzn25TvvpuNVLwH9km8fA74FRgE7U80zEugETMvXzERECiuvd19dKIKDg23Hjh22cOFCCw4OtsqVK7si9Txbt2616667zgCrUaOGvfbaa9akSRMLCQmxDh062K5du2zJkiV50rWmyG28a2AG3xWAXPIrqhoMNmiaalp9g18NuhsEFYAcFQqFwjfDJ8YIZTV69eqV4RiilHlCQkLMzKxVq1YG2KWXXmpLliyxiIgIi4mJsR07dtiHH36Y7YJGhVB+xS0GZnCoAOSSXzEy+Tn/UAByUSgUisIVPjFGyBdojFB+KQ6cAEoCDYAt3k3H46riHPczC9iQPK0J8AkwAvgxB21eBNyHc9fijFxnKCJSmGT1+9tnzyMkhU0csCz5dmE5R44/cAcwE9gLvAU8nerx9cAt5KwIAngUGJvcroiI5IQKISlAFib/bePVLHLvEpxHdoUBc4COOE+GuASY58H1fA/8BfyAj1wtR0SkwNGnpxQgi5L/tgICgQQv5pJTd+M86i3ljOTHgXE4D33f7uF1nQIaerhNEZGiRT1CUoBsAo4CpYFmXs4lu/yA/8N5nh8HsAZ4AOfYoBfxfBEkIiKeoEJIChADfkm+7UvjhMoCs3HuDgP4DGgB/A/n2Ke8Fohz0HSPfFiXiEjhokJICpiU3WO+UgjVBf4A7gRigAeB58nfC8l2BSYAH+AciyQiIlmlQkgKmJRCqDLOno6CrjRQDdgH3IBz4HJ+m4bzLNSXAXd5Yf0iIr5LhZAUMPuAGkAtfGOw9FqgM3ANzsPhvSEOGJN8+ykv5SAi4ptUCEkBFJbq9q1AKW8lko6ywGScJ0NMMQ/nRWO96WvgHNAWuMLLuYiI+A4VQlKAVcU5CHkX7ldi96Z3gW44B0IXpLfPXpznLAJ40puJiIj4lIL0SS5ynmDgELAD2O/lXFK8ivPEjz1w9sAUJF8m/+2D81IlIiJyISqEpABbA9QH7k81rSzOI6SuzKcc/HCOAUpxGufuJ2+NB8rMfGA3UA7310xERDKiQkgKuAScvUIpBuE8Z85GYCTOo8vyShmc1wmbBjyTh+vxFAO+Sr79dGYziohIMhVC4mNGAVNxni/nMWAnzt1VF3l4PSnnB+qA8/xAJz3cfl4JxZnv1UBTL+ciIlLwqRASH7Mb5wkEb8RZqDiAd3BewuJBnLuycqsTsBqow7/nBxrvgXbzwwlgYvJt9QqJiFyICiHxUctxXo/sfpxHTF2G82Kna3BetDUn/IC3gBk4d4stxrvnB8qplEHT9wIVvZmIiEiBp0JIfJjh7P2oAwzAOZD5GmAJzmKmdjbaShkP9Eby/c9wDor29vmBcmItzt6yROBaL+ciIlKwqRCSQiAO+Ajn2ahH4CwAOgF/8e+FUDNz/nggb1wvzNN64zwP0zwv5yEiUrCpEJJCJALn0V0NcZ6IMRA4cIFlOpJ2PJA3rhfmaVtx9pCJiEhmVAhJIbQNZ4FzAzAu1fSOQPdU91/EuTusDM7dadfie+OBskKX3BARyYgKISnEVvDv2Z9LAMNxjinqkzxtA5AEfA60wXkF98IkCPgd55m5a3g5FxGRgkmFkBQho4AtOM9MDfAL0AD4L749Higj8TgPp49D5xQSEUmfH85DbyQDDoeDyMhIypQpQ1RUlLfTkVzzp+BdIywv1QJO4ZtHv4mI5FxWv78D8jEnkQKgKBVBALu8nYCISIGmXWMiRYYGTYuInE+FkEih5wcswDloWidYFBFJTYWQSKFnwJHk2095MxERkQJHhZBIkTAi+e99QHlvJiIiUqCoEBIpElbjPFnkRfx7HiUREVEhJFJkpFyV/kmc44ZERESFkEiR8T+c5xSqCbT1bioiIgWECiGRIiMGCE2+/bQ3ExERKTBUCIkUKV8l/70TCPFmIiIiBYIKIZEiZSfOcwr5A497ORcREe9TISRS5KQMmn4UKO7NREREvE6FkEiR8xOwD/gP0NXLuYiIeJcKIZEiJwkYmXxbg6ZFpGjzmUIoLCwMM3OLAQMGZLpM8eLFGT58OBEREURFRfHjjz9SqVKlfMpYpCAbDXyDCiERKep8phACeP3116lSpYorhg0blun8Q4cOpUOHDnTr1o1WrVoRHBzMtGnT8ilbkYLsKM7B0n96OxEREa8K8HYC2REVFUV4eHiW5i1TpgyPPPIIPXr0YPHixQD06dOHbdu20bRpU1avXp2XqYqIiIgP8KkeoYEDBxIREcH69et56aWXKFasWIbzXnPNNQQFBbFo0SLXtO3bt7N3716aN2+e4XJBQUE4HA63ECm8GgJjgCe8nYiIiFf4TI/QF198wfr16zlx4gQtWrTg/fff55JLLuHFF19Md/4qVaoQFxfH6dOn3aaHh4dTpUqVDNczaNAg3nzzTU+mLlKANQceBm7AOYDavJuOiIgXmLfi/ffftwupU6dOusv26dPH4uPjLSgoKN3H77//fouNjU0zffXq1fbBBx9kmFNQUJA5HA5XBAcHm5mZw+Hw2uukUORdlDIYY9CsAOSiUCgUnguHw5Gl72+v9gh98sknfPvtt5nO888//6Q7ffXq1QQGBnL55ZezY8eONI8fOXKE4sWLU7ZsWbdeocqVK3PkyJEM1xcfH098fHzWnoCIzzsLPOLtJEREvMarhVBERAQRERE5WrZx48YkJSVx9OjRdB9ft24d8fHx3Hbbba4jxWrXrk1ISAirVq3Kcc4iIiJSuHi9++pC0axZM+vXr581atTIqlevbj169LDw8HD79ttvXfMEBwfb1q1b7brrrnNN+/LLL23Pnj128803W5MmTWzFihW2YsWKPOlaUyh8O2oZDDcYWAByUSgUitxHNr6/vZ/sheLqq6+2VatW2cmTJy06Otq2bNliAwcOdBsfFBISYmZmrVq1ck0rXry4DR8+3I4fP25nzpyxqVOnWuXKlfPqhVQofDjuMTCDIwaBBSAfhUKhyF1k9fvbL/mGZMDhcBAZGUmZMmWIiorydjoieSQA2ANUBe4HJno1GxGR3Mrq97dPnUdIRPJKIs5LbgA85c1ERETylc+cR0hE8too4DXgRuAzIAKIAs6c93c7zkt0AKhTWUR8mwohEUl2GJgGdAf6ZTLfI8DY5NutgXnA70DLVPN8D5Qj/UJqE7DAg3mLiOScCiERSeU5nIVKeaA04EiO0qn+pj5lhQPnHvak89q5Dbgkk/W8AAz1TMoiIrmgQkhEUjkKvJeN+WcDlUk73PAp3IuplL+XAp2Aj4EwYEbu0hURySUVQiKSCwm49xClmJHJMsOBp4HxQCtgrefTEhHJIh01JiL5rB/wM1ASZ49SNe+mIyJFmgohEclnSTgHZG8EqgCTvZuOiBRpKoRExAvOAHfi3C32tJdzEZGiTGOERMRLDgLXeTsJESni1CMkIgXEteis1iKS39QjJCIFQHXgN5wDqMOAud5NR0SKDBVCIlIAhOG8xEctYJmXcxGRokSFkIgUEC/gvHbZ+WepFhHJOxojJCIFxDnci6C+OK9XJiKSd1QIiUgB9DbwDTAVCPRyLiJSmKkQEpECaDLOK9XfCoz0ci4iUpipEBKRAmgz0A1IBPoAr3o3HREptFQIiUgBNR94Nvn2O8D9XsxFRAorFUIiUoB9DXycfDsUaOnFXESkMFIhJCIF3MvANKA4MAPnuYZERDxDhZCIFHAG9AT+ACoCc4DyXs1IRAoPFUIi4gNigI7AXqA2MB0I8mpGIlI4qBASER8RDtwJnAZuAsZ4Nx0RKRRUCImID9kCdMV5WH13oEk+rbcc0B/ngO278mmdIpIfVAiJiI9ZBDwKtAfW50H7AUBT4IZU0wz4AOgNzAY+AorlwbpFJL+pEBIRHzQO+MVDbQUCF6W6/yDwO/Beqmmngc+Bb5Pv9wcWApU8lIOIeIsKIRHxcbVxHlFWO4vzBwItgFeABcBJnD1MKX4DjgOHzlvuBZxnue6K8/Ift+DskWqe08RFpAAI8HYCIiK58ylwHTAcaJvO40HA9UAr4GacRVDJ8+a5PtXtf4D/4Nwdlp6pwF84z21UH2fh9DwwIkfZi4h3qRASER/XB+duq37J94vjLGxuTo7muO/6AjiGs4BZkhx/n/d4RkVQiu3J6xiDc9D2cKAZ8DgQnd0nICJepEJIRHzcMaBHqvvv4+yhSe0o/xY9v5G28MmJs8B9OMcTDcF50sergC7ALg+0LyL5QYWQiBQyS3FeoHUJ//b6bMvD9X0GrAUmAw2Tb98GrMvDdYqIp6gQEpFCZhbOa5Llp+U4z2k0GeduuL/yef3eFARcjPOElynaAgdw7kJM8kZSIlmmQkhECplzXlrvEeBWnEVBXPI0f6AsziPTChN/nEfN3Y9zV+Ai4N7kxwKAn3AenXcZzoIIoB1QDWdxtB3n6yXifSqEREQ8JhHnmKUUg3GehLErsMYbCXlYU5zFT3egSqrpjXEWR+dwXhD3T+BS4GCqeR4GuqW6fxrYgXO35fZUsROIzZPsRdKjQkhEJE+UwPnFXw3nOY58tRC6Eudg9PuAGqmmHwemABOAZfx7pN1RnAXT+X4HSgF1gMtx9pRdlxypncN5cd3twEScJ88UyTsqhERE8kQszoKgKzDey7lkV3Wchc/9OAeApziDc/zVBJxn1k7IRpufJgc4xxXVwlkU1U3+mxIXJ6+/Os6B5yn8knOakK1nIpIVVtCjVatWlpFrr702w+UWL16cZv6vvvoqW+t2OBxmZuZwOLz+OigUCl+PSgY/GdQoALlkFGUN4g0sOWINphvca3BRPqz/PwY3GDxi0CTV9FHJ+XxaAF4jhS9EVr+/faJHaOXKlVSpUsVt2ttvv81tt93G2rVrM1jK6ZtvvuGNN95w3Y+O1snORMRbhgF34jy7dU/gZ++mQymc433qAy8lTzsNzMe5a28CzjNon8rHnI4lx/Lzpq8EHsK5i03Ec3yiEEpISCA8/N9DMwMCAujUqRPDhg274LLR0dFuy4qIeM8LOI+kag7MAd4C/g/vHelWDhiFc6DzZ/x7hNfdFLzD3kNxXmh3n7cTkULGJy+62rFjRypUqEBoaOgF533ggQc4duwYmzdv5r333uOii84/1b67oKAgHA6HW4iIeMZBnNc8G558fzDOgqh8HqwrAKgKXIOzF+pR4AecA5xT5zMGGATEpJpe0IqgFKmLoKr824slkjte34+X3ZgzZ47NmTPngvP17dvX2rZtaw0aNLAePXrY/v37berUqZkuM3jw4HTHImmMkEKh8Gz0NDhrYAZh5j4eJrPwT3W7lsHzBh8afGewwGCTwdHkdtOLBIOKBeD55yZKGOxIfj7vF4B8FAUxsjHG13tJvv/++xkOgk5Rp04dt2WqVq1qiYmJ1qVLl2yv75ZbbjEzsxo1Mh6oGBQUZA6HwxXBwcEqhBQKRR5FQ4OdBmYQY/CMQSeDJwz6nzfvJHMOXO6ealqn5GUziniD/QZrDGYbfGLQtAA8b0/EU6me57sFIJ+M4maD1udN8/VC1DfCJwZLf/LJJ3z77beZzvPPP/+43e/Tpw/Hjx9n1qxZ2V7f6tWrAahVq1aadlPEx8cTHx+f7bZFRLJvM3At8B3QEedg6hRJwCf8O37oHFAc9xMZ7gD+h/MszYeT/6aO4zg/6wujL3GO7hgGvILz9Xoj0yXylx/OXY7/h3OweWOcY7DK4twluQXnbtIo76QnbrxetWUndu/ebUOGDMnRsi1atDAzs4YNG3q8olQoFIqch585e4D+MlhpMM3gS3M/XP2y5AgqAPkWpHjOcPUMDS4A+WBQweDnVHmNSfW/bG2QaLDlvGUeTX4ssADkXzjCJ3aNZTduvfXWdHeXARYcHGxbt2616667zgCrUaOGvfbaa9akSRMLCQmxDh062K5du2zJkiV59UIqFAqFwivxX8NVdLzh5VyaG+xLzuWsQe905qlgcHWq+yUMziQvc9Lgf+bcBVqmALy2vhuFshAaP368LV++PN3HQkJCzMysVatWBtill15qS5YssYiICIuJibEdO3bYhx9+mO2CRoWQQqFQ+EK8YLiKoVe9lMPz9u/JKLcZNMjicv8x5wkjj6R6DmYQZzDfnOOhLi0Ar7FvRaEshAr4C6lQKBQKr0Z/w1VEDMrH9ZY15+7MlHVPMCidg3b8zdmj9IHB1lTtpcRag9cNGhWA17rghwqh/H8hFQqFQuH1GGC4CoeX82F9TQx2J68v1uBJD7Zd2+Alg2UGSamelxlsNwgoAK93wY2sfn/75AkVRURE0vch8Gqq273zcF2P47z0Rw0gDGgJfOXB9ncAHwM34jxa8GFgJhCN8+SSianmHYXzBJ0VPLj+osEPZ0UkGXA4HERGRlKmTBmionSYo4iIb3gN6ArchvM0Ap52K85LfgDMAPqQf9dkuwioDOxJvl8OOJl8++JUeTyMs0hbnxwp8xcNWf3+9olrjYmIiGTPOzjPwxRzoRlz6FdgLM7zAX2aR+vISAzuRc054DngctyLsR44C8EUJ/m3KEqJnRT1/hD1CF2AeoRERAqDvkAJ3E9amV3dgQX82/tS0D0I3AA0ARriPCHn+aKADfxbGP0G7M2n/PJWVr+/VQhdgAohERFfdx3wR/LtG4HlOWhjMPAmMBvohO99dQYC9XEWRU1wXoz3KqDkefP1xzkuCZzjku4EVgN/5U+aHqRdYyIiIgCsAd4HgshZEQTOQcr9+beg8jUJwMbkCE2eVgyow7/FUROcRU+KVsBoYAlwS6rp03Hunjt4XhzAeamXhDx6DnlDhZCIiBQBr+Rgmcv5dyzOBpwDj496Jp0CIQn4Ozl+SOfxKGARsDXVtACc18XL7KDzcNIWSVOA7cmPF6ydUSqERESkiCmO84t5Fs4ej/MF4dw99BjOMTZrk6cXpiIoK35OjtT8gPuBqqni0uS/wThf28rJ0STVcuv5txDqAYwEpgK98ij3rFMhJCIiRUxPoENynMN59FeKEGAycH3y/dSFkDh3e03O5PGKpF8kbU81T1WgVF4lmG0qhEREpIgZAzQA/ovzRISGc9xMB2AcznPxHMd51NVc76TosyKSY2Mm83yOszcoKV8yuhAVQiIiUgQ9j3Ow8LM4d4/dBXRJfux34F5gv3dSK/TigN3eTsJFl9gQEZEi6jlgBM6vwpQiaChwEyqCig71CImISBH2LM5rd3UGBgDTvJuO5DsVQiIiUoQZ8HJySFGkXWMiIiJSZKkQEhERkSJLhZCIiIgUWSqEREREpMhSISQiIiJFlgohERERKbJUCImIiEiRpUJIREREiiwVQiIiIlJkqRASERGRIkuFkIiIiBRZKoRERESkyFIhJCIiIkWWCiEREREpsgK8nYCvcDgc3k5BREREsiir39sqhC4g5YU8ePCglzMRERGR7HI4HERFRWX4uB9g+ZeObwoODs70RcwJh8PBwYMHqVq1qsfbVvvea9vX2/fl3H29fV/O3dfb9+Xcfb39/Mj90KFDmc6jHqEsuNCLmBtRUVF58s9X+95t29fb9+Xcfb19X87d19v35dx9vf28ajsrbWqwtIiIiBRZKoRERESkyFIh5CVxcXG8+eabxMXFqf18bt+Xc8/r9n05d19v35dz9/X2fTl3X28/r3PPCg2WFhERkSJLPUIiIiJSZKkQEhERkSJLhZCIiIgUWSqEREREpMhSIZTPbrzxRmbNmsXBgwcxMzp16uTR9gcOHMgff/xBZGQk4eHhTJ8+ndq1a3uk7SeeeIKNGzdy+vRpTp8+zcqVK2nXrp1H2k7PgAEDMDOGDh3qkfYGDx6MmbnF1q1bPdJ2iuDgYL7//nsiIiKIjo5m06ZNXHPNNbluNywsLE3uZsbw4cM9kDX4+/vzf//3f/zzzz9ER0eza9cuXnvtNY+0naJ06dIMHTqUPXv2EB0dzYoVK7j22mtz1FZW3kdvvfUWhw4dIjo6moULF1KrVi2PtN25c2fmz59PREQEZsZVV13lsdwDAgL44IMP2LRpE2fOnOHgwYOMGzeOSy65xCPtg/N9sHXrVs6cOcOJEydYuHAh119/vcfaT+2rr77CzOjXr59H2g4NDU3zHpg7d65Hc69bty4zZ87k1KlTnDlzhj/++IPLLrvMI+2n9x42M1566aVct12qVCmGDRvG/v37iY6OZsuWLTz++ONZyjsr7VeqVInQ0FAOHjzI2bNnmTt3bpbfU1n5XipevDjDhw8nIiKCqKgofvzxRypVqpTl/HNDhVA+K1WqFBs3buTpp5/Ok/ZbtWrFiBEjaNasGW3atCEwMJAFCxZQsmTJXLd94MABBg4cyDXXXMO1117Lr7/+ysyZM6lfv74HMnd37bXX8vjjj7Nx40aPtvvXX39RpUoVV9xwww0ea7tcuXKsWLGChIQE2rdvT/369XnxxRc5efJkrtu+7rrr3PJu3bo1AFOmTMl12+AsOp988kmeeeYZ6tWrx4ABA3j55Zd59tlnPdI+wOjRo2nTpg0PPvggDRs2ZMGCBSxatIjg4OBst3Wh99HLL7/Mc889xxNPPEHTpk05e/Ys8+fPp3jx4rluu1SpUixfvpwBAwZkO+8LtV+yZEmaNGnC22+/TZMmTejSpQt16tRh1qxZHmkfYMeOHTzzzDM0bNiQG264gT179rBgwQIqVqzokfZT3H333TRr1ixb12nMSttz5851ey/cf//9Hmu/Ro0aLF++nG3btnHzzTfTqFEj3n77bWJjYz3Sfuq8q1SpQp8+fTh37hxTp07Ndduffvop7dq1o2fPntSrV4/PPvuM4cOH06FDB4/kPmPGDGrUqEGnTp24+uqr2bt3L4sWLcrSd0tWvpeGDh1Khw4d6NatG61atSI4OJhp06ZlKXdPMIV3wsysU6dOebqOihUrmpnZjTfemCftHz9+3B5++GGPtlmqVCnbvn273XbbbbZ48WIbOnSoR9odPHiw/fnnn3n2Wr///vu2dOnSfNl2hg4dajt37vRYe7Nnz7bRo0e7Tfvxxx/t+++/90j7JUqUsISEBLvjjjvcpq9du9befvvtXLWd3vvo0KFD9uKLL7rulylTxmJiYqx79+65bjslQkJCzMzsqquu8mju58e1115rZmaXXXZZnrTvcDjMzOzWW2/1WPvBwcG2f/9+q1+/voWFhVm/fv080nZoaKhNnz7dI9tkeu1PmDDBvvvuuzxr//yYPn26LVq0yCNtb9682V577TW3aTl9f53f/hVXXGFmZvXr13dN8/Pzs/DwcHvkkUey3f7530tlypSxuLg4u+eee1zz1KlTx8zMmjZt6pH/R2ahHqFCrmzZsgCcOHHCo+36+/vTvXt3SpUqxapVqzza9ogRI5gzZw6//PKLR9sFuOKKKzh48CC7d+/mhx9+yHKXd1Z07NiRtWvXMnnyZMLDw1m/fj2PPvqox9pPERgYSM+ePRk7dqzH2ly5ciW33XYbV1xxBQCNGjXihhtuyNZuh8wEBAQQEBCQ5pd1TEyMR3vlAKpXr84ll1zCokWLXNMiIyNZvXo1zZs39+i68kPZsmU5d+4cp06d8njbgYGBPPbYY5w6dcpjva9+fn58//33DBkyhL///tsjbaZ28803Ex4ezrZt2/jyyy8pX768R9r18/PjzjvvZMeOHcybN4/w8HB+//13jw9fSFGpUiXuvPNOxowZ45H2Vq5cSceOHV09rDfffDO1a9dmwYIFuW47pSc19fvXzIiLi8vR+/f876VrrrmGoKAgt/fs9u3b2bt3b769Z/O82lKkH3ndI+Tn52ezZ8+2ZcuWeazNBg0aWFRUlCUkJNjJkyetffv2Hs25e/futmnTJitevLgBHu0RateunXXt2tUaNmxobdu2tRUrVtiePXusdOnSHmk/JibGYmJi7N1337XGjRtb3759LTo62h566CGPvkbdunWzhIQEu+SSSzy6rbz//vuWlJRk8fHxlpSUZAMHDvRo3itWrLDFixfbJZdcYv7+/vbAAw9YYmKibdu2LVftnv8+at68uZmZValSxW2+SZMm2cSJE3PVdurIjx6h4sWL29q1a+2HH37waPt33nmnRUVFWVJSkh04cMCuvfZaj7U/cOBAmz9/vuu+J3uEunfvbh06dLAGDRpYp06dbMuWLbZ69Wrz9/fPdfuVK1c2M7MzZ87Yf//7X7vqqqtswIABlpSUZDfddJPH/7f9+/e348ePuz7rctt2UFCQffvtt2ZmFh8fb7Gxsfbggw965P8aEBBge/bssUmTJlm5cuUsMDDQXn75ZTMzmzdvXrbaTu976f7777fY2Ng0865evdo++OCDHD2H7ISuPl+IjRgxggYNGnj0F/f27dtp3LgxZcuWpWvXrowbN45WrVp5ZNDxpZdeyueff06bNm3y5HTr8+bNc93evHkzq1evZu/evdx7770e6V3x9/dn7dq1vPrqqwBs2LCBBg0a8MQTT/Ddd9/luv0UjzzyCHPnzuXw4cMea/Pee+/lgQceoEePHmzZsoXGjRvz2WefcejQIY/l/uCDDzJ27FgOHTpEYmIi69evZ8KECR4ZTF4YBQQEMHnyZPz8/HjyySc92vbixYtp3LgxFStWpG/fvkyePJmmTZty7NixXLXbpEkT+vXrR5MmTTyUqbtJkya5bv/1119s2rSJf/75h5tvvplff/01V237+zt3kMycOZPPPvsMgI0bN9KiRQueeOIJli5dmqv2z/fwww8zfvx4j33WPfvsszRr1owOHTqwd+9ebrrpJkaMGMGhQ4dy3buemJhIly5dGDNmDCdPniQxMZFFixbx888/4+fnl6228uJ7yRPyvNpSpB952SM0bNgw27dvn11++eV5+hwWLlxoX3/9tUfa6tSpk5mZJSQkuMLMLCkpyRISEnL0q+9C8ccff9h7773nkbb27Nljo0aNcpv2xBNP2IEDBzyWb7Vq1SwxMdE6duzo0ddh37599tRTT7lNe/XVV23r1q0ef81Llizp6q2ZOHGi/fTTT7lq7/z3UfXq1dPtqVmyZIl99tlnuWo7deRlj1BAQIBNmzbNNmzYYOXLl/d4++fHjh07ctQDeH77/fr1c71fU7+HExMTLSwsLE9yP3r0qD322GO5zj0wMNDi4+Pt1VdfdZvvgw8+sOXLl3v0tb/hhhvMzKxRo0Ye+b+WKFHC4uLi0ozBGzVqlM2dO9ejuZcpU8YqVqxogP3+++82fPjwLLeb0ffSLbfcYmZmZcuWdZu+Z88e++9//5uj1yg7oTFChdCwYcPo3Lkzt956K3v27MnTdfn7+2fpSJys+OWXX2jQoAGNGzd2xZo1axg/fjyNGzfm3LlzHllPilKlSlGzZk2P9aysWLGCOnXquE2rXbs2e/fu9Uj7AH369OHo0aPMmTPHY22C82il81/fpKQk169kT4qOjubIkSOUK1eO22+/nZkzZ3q0/bCwMA4fPsxtt93mmuZwOGjatKnHx7PlhZSeoCuuuILWrVt7fHxfejz1Pv7+++9p1KiR23v44MGDDBkyhNtvv90DmbqrWrUqFSpU8Mh7OCEhgTVr1uT5exicvbpr165l06ZNHmkvMDCQoKCgfHkPR0ZGEhERQa1atbj22muz/P7N7Htp3bp1xMfHu71na9euTUhISL68Z7VrLJ+VKlXK7dwL1atX56qrruLEiRPs378/1+2PGDGCHj160KlTJ6KioqhcuTIAp0+fzvIhoBl57733mDt3Lvv27cPhcNCjRw9uvvlmj33AnTlzhi1btrhNO3v2LMePH08zPSeGDBnC7Nmz2bt3L8HBwbz11lskJSUxYcKEXLcNzsM/V65cyaBBg5g8eTLXX389jz32GI899phH2vfz86NPnz6MGzeOpKQkj7SZYvbs2bz66qvs27ePLVu2cPXVV/PCCy94dEB227Zt8fPzY/v27dSqVYshQ4awbds2QkNDs93Whd5Hn332Ga+99ho7d+4kLCyMt99+m0OHDjFjxoxct33xxRdTrVo116DUlC/OI0eOEB4enqv2Dx8+zI8//kiTJk246667KFasmOs9fOLECRISEnLV/vHjx3n11VeZNWsWhw8fpmLFijz99NNUrVo1y6diuNDrc37hlpCQwJEjR9ixY0eu2j5x4gSDBw9m6tSpHDlyhJo1a/LRRx+xa9cu5s+f75HchwwZwqRJk1i6dCmLFy+mXbt2dOjQgZtvvtkj7YOzKO/WrRsvvvhiltrMattLlixhyJAhxMTEsHfvXlq1asVDDz3ECy+84JH2u3btyrFjx9i3bx8NGzbk888/Z8aMGSxcuPCCbV/oeykyMpIxY8bw6aefcuLECSIjIxk2bBgrV65k9erV2XqdcirPu50U/0arVq0sPaGhoR5pPyO9evXKddujR4+2sLAwi42NtfDwcFu4cKG1bt06T18vTw6WnjBhgh08eNBiY2Nt//79NmHCBKtRo4ZH873zzjtt06ZNFhMTY3///bc9+uijHmu7TZs2ZmZ2xRVXePx1Ll26tA0dOtT27Nlj0dHRtmvXLnv77bctMDDQY+vo1q2b7dq1y2JjY+3QoUM2bNgwK1OmTI7aysr76K233rLDhw9bTEyMLVy4MMuv24Xa7tWrV7qPDx48ONftp+xuS0+rVq1y3X7x4sVt6tSpduDAAYuNjbWDBw/ajBkzsjVYOrufYdkZLJ1Z2yVKlLB58+ZZeHi4xcXFWVhYmI0cOdIqVark0dz79OljO3bssOjoaPvzzz+ztRs6K+337dvXzp49m+1t/0JtV65c2caOHWsHDhyw6Oho27p1qz3//PMea//ZZ5+1ffv2WVxcnO3Zs8f+7//+L8ufDxlJ/b1UvHhxGz58uB0/ftzOnDljU6dOtcqVK+fo8yG74Zd8Q0RERKTI0RghERERKbJUCImIiEiRpUJIREREiiwVQiIiIlJkqRASERGRIkuFkIiIiBRZKoRERESkyFIhJCJpLF68mKFDh3o7DZ8QGhrK9OnTXfd95bUzMzp16uTtNES8ToWQiI86/wsY4J577iEmJibLp9UXz+vSpQuvv/66t9O4oCpVqjB37lxvpyHidbrWmEgh8cgjjzBixAieeOIJvv3223TnCQwMzNL1qiTnTp486e0UsiQr10UTKQrUIyRSCPTv359hw4Zx3333uRVBixcvZtiwYQwdOpRjx44xf/58xowZw+zZs92WDwgIIDw8nIcffjjd9suVK8e4ceM4ceIEZ8+e5eeff3ZdoNHhcBAdHU27du3clrn77ruJjIzkoosuSrfNe+65h02bNhEdHU1ERAQLFy6kZMmSwL+9XW+88QZHjx7l9OnTfPXVVwQGBrqWv/3221m2bBknT54kIiKC2bNnU6NGDbd1VK1alf/9738cP36cM2fOsGbNGq6//nrX4x07dmTdunXExMSwe/du3njjDYoVK5bh6+zv788nn3ziWueHH36In5+f2zzn7xoLCwvj1VdfZdy4cURFRbFnzx46dOhAxYoVmTFjBlFRUWzcuJFrrrnGrZ2WLVuydOlSoqOj2bdvH59//rnr9Ulpd9CgQYwZM4bIyEj27t1L3759XY8HBgYybNgwDh06RExMDHv27GHgwIGux8/fNdagQQN++eUX1/9j5MiRlCpVyvV4yv/kxRdf5NChQ0RERDB8+HACAvR7WnxfvlzUTKFQeDZCQ0Nt+vTp9sEHH1hkZKTdeuutaeZZvHixRUZG2ocffmi1a9e22rVrW/PmzS0hIcGqVKnimu/uu++2qKgoK1WqlGu51Be7nTFjhm3ZssVuuOEGa9Sokc2dO9d27NhhAQEBBtjkyZPtu+++c1v3lClT0kxLiSpVqlh8fLz997//tZCQEGvQoIE9+eSTrvWHhoZaZGSkTZgwwerXr2933HGHhYeH2zvvvONqo0uXLta5c2erWbOmXXXVVTZz5kzbuHGj+fn5GWClSpWyXbt22W+//WYtW7a0mjVrWrdu3axZs2YG2A033GCnTp2yhx56yKpXr26tW7e2f/75x954440MX/P+/fvb8ePHrXPnzla3bl0bNWqUnT592qZPn+72mqd+7cLCwiwiIsIee+wxq1Wrlo0YMcJOnTplP//8s3Xt2tWuuOIKmzZtmm3ZssW1TI0aNSwqKsr69etntWrVsubNm9u6dets7Nixadp98sknrWbNmjZgwABLTEy02rVrG2Avvvii7d2712644QarVq2atWzZ0u677z7X8mZmnTp1MsBKlixpBw8etB9//NGuvPJKu+WWW2z37t1uFwsNDQ21U6dO2Zdffml16tSxO++8086cOePRCwsrFF4KryegUChyEKGhoRYbG2tmZrfccku68yxevNjWrVuXZvpff/1l/fv3d92fOXOm25ds6i/zWrVqmZlZ8+bNXY+XL1/ezp49a127djXAOnXqZJGRkXbRRRcZYA6Hw6Kjo+32229PN6+rr77azMyqVauW4XOLiIhwtQfY448/bpGRka5C5/yoUKGCmZldeeWVBs6rfJ8+fdouvvjidOdfuHChDRw40G3aAw88YAcPHszwNT948KC99NJLrvvFihWzffv2XbAQSl0QVq5c2czM3nrrLde0pk2bmpm5rrY9atQo+/rrr93W3bJlS0tMTLTixYun2y5gR44csccff9wA+/zzz23RokUZPpfUhdCjjz5qx48ft5IlS7oeb9++vSUmJrqu7h4aGmphYWHm7+/vmmfSpEk2YcIEr78XFIrchHaNifiwTZs2ERYWxltvveW2GyO1devWpZk2evRo+vTpA0ClSpVo3749Y8eOTXf5evXqkZCQwOrVq13TTpw4wfbt26lXrx4AP//8MwkJCXTs2BFw7vaKjIxk0aJF6ba5ceNGFi1axObNm5k8eTKPPvoo5cqVSzNPTEyM6/6qVatwOBxcdtllANSqVYv//e9/7N69m9OnT7Nnzx4AqlWrBkDjxo35888/Mxyzc9VVV/HGG28QFRXlilGjRhEcHJzu7rwyZcoQHBzs9jokJSWxdu3adNtPbdOmTa7bKWNzNm/enGZapUqVXLn17t3bLbf58+dTrFgxqlevnm67AEeOHHG18e2339K4cWO2b9/O559/Tps2bTLMr169emzcuJHo6GjXtBUrVlCsWDHq1KnjmrZlyxbOnTvnun/48GHX+kR8lQohER928OBBbr75ZqpWrcq8efMoXbp0mnnOnj2bZtp3331HjRo1aNasGT179iQsLIzly5fnOI+EhAR+/PFHevToAUCPHj2YNGkSSUlJ6c5/7tw52rRpQ/v27fn777959tln2b59O5dffnmW1zl79mzKly9P3759adq0KU2bNgUgKCgIwK2ISk/p0qUZPHgwjRs3dkXDhg2pVasWsbGxWc4jK9IboJ56mpkBzjFIKbmNHDnSLberrrqKWrVqsXv37gzbNTNXG3/++SfVq1fn9ddf56KLLmLy5MlMmTLFo88j9fpEfJW2YBEft2/fPlq1akWVKlUyLIbOd+LECWbMmEGfPn3o3bs3oaGhGc67detWAgMDXYUGQPny5alTpw5///23a9r48eNp164d9evX59Zbb2X8+PEXzGPlypW8+eabXH311cTHx9O5c2fXY1dddRUlSpRw3W/WrBlRUVHs37+f8uXLU7duXd555x1+/fVXtm3bxsUXX+zW9qZNm2jcuHGa6SnWr19PnTp12L17d5pIKUxSi4yM5NChQ26vQ7FixdIMcvaE9evXU79+/XRzy85Rf1FRUUyePJnHHnuM7t2707Vr13Rfj61bt3LVVVe5DcZu2bIlSUlJbN++3SPPSaSgUiEkUggcOHCAm2++mUqVKjF//nwcDscFlxk9ejS9evWiXr16jBs3LsP5du3axYwZMxg1ahQtW7akUaNG/PDDDxw8eJCZM2e65lu6dClHjhxh/PjxhIWF8ccff2TY5vXXX8+gQYO45ppruOyyy+jSpQv/+c9/2Lp1q2ueoKAgxowZQ7169Wjfvj1vvfUWw4cPx8xcR2099thj1KxZk1tuuYVPP/3UbR0TJkzgyJEjzJgxgxYtWlC9enW6dOlCs2bNAPi///s/HnroId544w3q169P3bp16d69O2+//XaGeX/++ecMHDiQTp06UadOHb788ss0u/Q84cMPP6RFixYMGzbM1RPUsWNHhg0bluU2nn/+ee677z7q1KnDFVdcQbdu3Th8+DCnTp1KM+/48eOJjY1l3LhxXHnlldx8880MGzaM77//nqNHj3rwmYkUPCqERAqJlN1kFStWzFIxtGjRIg4fPsz8+fM5fPhwpvP26dOHdevW8dNPP7Fq1Sr8/Py44447SExMdJtvwoQJNG7c+IK9QZGRkdx00038/PPP7Nixg3feeYcXX3yRefPmueb55Zdf2LlzJ0uXLmXSpEnMmjWLN998E3Dukrnvvvu45ppr+Ouvvxg6dCj9+/d3W0dCQgJt27bl6NGj/Pzzz2zevJmBAwe6dtctWLCAu+66i7Zt27JmzRp+//13nn/+efbu3Zth3p988gnff/8948aNY9WqVURFRaU5qaUnbN68mVatWlG7dm2WLVvGn3/+yf/93/9x6NChLLcRFRXFyy+/zNq1a1mzZg2XX345d9xxR7q9XTExMdx+++2UL1+eNWvW8OOPP/LLL7/wzDPPePJpiRRIfjhHTYtIEVOqVCkOHjxInz598uTLPDdCQ0MpV66c264yEZG8oDNhiRQxfn5+VKxYkRdffJFTp04xa9Ysb6ckIuI1KoREiphq1aqxZ88e9u/fT+/evTM8sktEpCjQrjEREREpsjRYWkRERIosFUIiIiJSZKkQEhERkSJLhZCIiIgUWSqEREREpMhSISQiIiJFlgohERERKbJUCImIiEiRpUJIREREiqz/B05W/ifVBAqcAAAAAElFTkSuQmCC", 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nOH36NBEREbz77rsAOTrU+uDBg2mmnTx5kksvvdR1Pzg4ON1u6927d1+0/ZQv35IlS6Z57PHHH6d169bcf//96S6bkJCQJr/g4GAOHTqUprBK2b2Qk8OSz///nDx5EsD1XgQHB5OUlJTmvdixY0em2n///fc5c+YMa9asYefOnYwcOZLmzZtnOr+crgO1a9emQ4cObsVnREQECxcuBKBChQoXXBac5zw5f/l27dqlWTYmJsa1ay/FyZMnKVu2rFubZcqU4dixY2nadDgcadoMDQ1Nk1dW1s1JkyYRGxvrWt9KlSrF3XffzQ8//JDh606xbNkyqlSpQs2aNWnevDlmxqpVq9wKpFtuuYUVK1bg7LTInvPXQUj7eUxPZoqclMeOHj2a5bwuvfRSPvnkE44cOUJsbCwRERHs3bsXSH/du9hnyZOy8r2alRwef/xx4uPjmTNnDnXq1MlwvvS+pyD761twcDC7du1Ksx6d/x2XlJTElClT6Ny5M0WLFgWga9euFC1aNN8VQhoj5IOOHTtGkyZNaNeuHR06dKBDhw48/PDDjB8/nt69e2e73aSkpCxN9/PzA5y/YBYuXMj27dt5/vnnOXDgAPHx8dx55508//zz+Ptnv96+2HPnVGRkJIcOHaJhw4ZpHksZM5RR8RIXF5ftjUpGy13ovcrt92L79u3UrVuXu+++m/bt23Pvvffyv//9j9dff53XXnvtgst6Yh3w9/dn3rx5fPDBB+k+vnPnzgsuC86xHecf9Qe49XRCxu/l+W2Gh4dnWAinjI1KERMTc9E2L+TUqVP8+uuv3H///bz55pt069aN4sWLu/WIZiSll+bWW2+lRo0arF+/nujoaJYtW8YzzzxDUFAQ11xzDUOGDMlRjtldB7du3UqXLl1o1KgRy5YtS3eeRo0aAc6eNcj4M5K6JzrF5MmTad68OcOGDWPDhg2cOXMGf39/5s6dm+66l5PPUlbyutBz5fTzvHXrVu68804WLlzI/PnzadGiRboFT0bfUzlZ3zJr4sSJPPHEE3To0IHp06dz3333sW3bNjZt2uSx5/AEFUI+KiEhgV9//ZVff/0VPz8/Pv/8c5544gnefPNN9uzZk6NffVnVsWNHihcvTqdOndx+5aS3OyI38tq3bx8NGjRIM71WrVqZWn7WrFk8+uij3HDDDaxZsybHubRu3ZqSJUu69QrVq1fP9Tj8+wu0TJkybsvnpMdo3759FClShJo1a7oVDXXr1s10G9HR0UyePJnJkycTGBjIL7/8wpAhQ3j33XcvWPh5Yh3Ys2cPJUuWdPUAZUVKr8vRo0eztXxGbbZu3ZoVK1Zk+zD4rK6b3377LTNmzOD666/n/vvvZ/369RcchJziwIED7Nu3j1tuuYUaNWq4io2lS5cyfPhwunfvTkBAAEuXLr1gO7n1vTFz5kyGDBnCgw8+mG4h5O/vT8+ePTly5Igrx8x+RsqUKUPr1q159dVX3Q7gyOznPyMZvRcnT55Mk1N6eeWFNWvWcM899zBr1izmz5/PLbfckqan80Kys77t27ePRo0a4efn5/Yenf8dB87179ChQ/To0YPly5dzxx13uA6SyE+0a8wHpe6+B+cHNqXCLlasGABnz54F0n6J5IaUXzapf8mUKlWKPn36pJn37NmzHs9p7ty5XH755XTq1Mk1rVixYjz66KOZWv6DDz7g7NmzjBs3Lt3dL1npcfntt98ICAjg6aefdpv+3HPPce7cOWbPng04dxUcO3YszbiXp556KtPPdb6Utp955hm36c8++2ymlj9/vUpISGDr1q34+fkRGBgIZLxeeWIdSPlV37Zt2zSPlS5dOsNf3OBcB06fPs1LL71EQEDa33fly5fPcNmMTJ48mYCAAF555ZU0j52/a/hCeWVl3Zw9ezbHjh1j4MCBtGzZMku/zpctW8Ydd9zBjTfe6Co2NmzYQGRkJIMGDSI6Ovqi5yfLre+N1atXM3fuXPr06cNdd92V5vG3336bunXr8sEHH7jWpX379pGYmHjRz0h66x5kfr3PSEbr6Z49eyhTpozb2eYrVapEly5dcvR82bVo0SL+85//UKtWLebMmZOlcU7ZWd9+++03Kleu7Db2p0iRIvTt25eoqCi38UVmxs8//0zHjh154IEHCAwMzHe7xUA9QvlShw4dXNV1aitXriQ0NJQxY8ZQtmxZFi1axMGDBwkODqZv37789ddfrv20GzZsIDExkYEDB1K6dGni4uJcg9c8bd68ecTFxTFz5ky++uorSpYs6ToctUqVKm7zrlu3jieffJIhQ4awe/dujh49muPr2Hz11Vc8/fTTTJgwgU8//ZTDhw9z//33u37FX+xX7u7du+nZsycTJkxgx44d/PDDD2zcuBE/Pz+qV69Oz549SUpKSrfb+XwzZ85k0aJFvP3221x55ZVs3LiRtm3bcs899zB8+HBXtz84D3UfPHgwo0ePZu3atdx6660X3Nd/MRs3buTHH3/kf//7H6VLl2blypW0atUq07+M582bx5EjR1ixYgXh4eHUr1+fp59+mlmzZrl6t1I2pG+//TYTJ04kISGBmTNnemQdGDZsGJ06deLXX391HZIdFBTE1VdfTbdu3bjyyis5fvx4urlHRUXx5JNP8t1337F+/XomTpzIsWPHqFatGnfddRcrVqygb9++WXo/ly5dypdffslLL71EkyZNmDdvHgkJCdSuXZvu3bvTr18/pkyZcsE2srpuJiYmMnHiRPr27UtiYqLbgNSLWbZsGb169eLcuXOuXWXnzp1j5cqVtG/fnsWLF1/0ZKq5+b3x4IMPsmjRIqZPn86PP/7IsmXLKFasGF27duX222/nu+++Y/jw4a75IyMj+emnn+jbty9mxp49e7j77rvT/FhJ2fi++OKLBAYGEhYWRtu2balevXqO8l23bh2tW7fmueee49ChQ4SGhvLnn38yceJE3n//faZOncpnn33mOk3Dzp0701z2Iq9MmzaNRx99lJCQEGbMmEH79u0zdYLa7KxvX3/9NY8//jjffPMN1113HXv37qVbt27cfPPN9OvXL834yEmTJvHMM8/w+uuvs2nTJrZv357t15mbvH7omsIZFzp8PvXhol27drU5c+bYkSNHLDY21vbu3WtffPGFVaxY0a29//73v7Z7925LSEhwOyQyo8Pn77333nTzOf8EjymHiaa+5Mfdd99tGzZssOjoaPvnn39swIAB1rt37zSHg1aoUMFmzpxpp0+fNrPMnVDx/PcpvcNXr7zySps5c6adPXvWwsPDbdiwYdalSxczy/yJEmvUqGGjRo2ynTt3WnR0tJ09e9a2bt1qn3/+uTVq1ChNDlFRUem2ExQUZB999JEdPHjQ4uLibMeOHWlOqAjOQ35Hjx5tJ0+etNOnT9vEiROtfPnyZpb+4fPnX2Il5f+T+v0tVqyYffLJJ3bs2DGLiorK0gkVH330UVuyZIkdO3bMYmJibNeuXfb++++bw+Fwm2/IkCF24MABS0xMdHv+nK4DKe/d22+/bTt37rTY2Fg7evSoLV++3J5//nm3UztkFC1btrTZs2fbyZMnLTo62nbt2mXjxo2za6+99qL/u/QOfwbskUcesTVr1tjZs2ft9OnTtnHjRnvvvfesUqVKrnkudPmJrK6b119/vZmZzZkzJ0vfH/Xr1zczsy1btrhNf+mll8zM7PXXX0+zzPmHz1/oeyOj15iVSzAEBQXZK6+8Yps3b7bo6GjXd1t6uQFWrlw5++mnn+zMmTN2/Phx++KLL6xBgwZu34eAValSxaZMmWInTpywkydP2qRJk6xSpUo5+izVqVPHlixZYmfPnjUzc3ufWrdubZs2bbLY2Fjbtm2b9ezZ84InVEw9LeXw//O/EzL6Hj4/LnTi3eeff97MzGbMmGFFihS54PdUZte3jE6oOHbsWDt69KjFxsbaxo0b0z0VSErs27fPzNKeViQfhdcTUChyJfr162dmZlWqVPF6LgpF6rjQuplyPqjU588qqFGlShXbu3evHTx40K644gqv51MYozCtbxcIryegUOQ4zj+hWspJ63bs2OH13BSFO7K6bo4YMcIiIyOtRIkSXs89L6JevXoWERFhf//9d5pLlyhyPwrb+pZeaIyQFAi//PIL+/fvZ8OGDZQuXZpevXpRv359evbs6e3UpJDL7Lp5991306BBAx577DFGjhxZaC6MuX379mwNZpecKazrW0a8Xo0pFDmNfv362ebNmy0qKsqio6Nt7dq1dt9993k9L4Uis+tmaGioRUdH29SpU90uvaBQ5EZoffs3/JJviIiIiBQ6Oo+QiIiIFFoqhERERKTQ0mDpTKhSpcoFr5osIiIi+Y/D4eDQoUMXnEeF0EVUqVKFsLAwb6chIiIi2VC1atULFkMqhC4ipSeoatWq6hUSERHxEQ6Hg7CwsItuu1UIZVJUVJQKIRERkQJGg6VFRESk0FIhJCIiIoWWCiEREREptDRGSEREBAgICKBy5cr4+6uPIL8zMyIiIjxyjTQVQiIiUuhVqFCBt956i+LFi3s7FcmCJUuWEBISgln2rxamQkhERAo1Pz8/HnnkEc6cOcOHH35IXFyct1OSiwgICKBevXrcd999AIwbNy77bXkqKREREV9UpkwZ6tWrx+eff87OnTu9nY5k0p49ewDo0aMHEydOzPZuMu0IFRGRQs3hcABw9OhRL2ciWbV9+3YAypcvn+02VAiJiEih5ufnB0BSUpKXM5GsSkxMBP79H2aHCiEREREptFQIiYiICAAhISFMnTrV22nkKRVCIiIihUxwcDBmRuPGjd2m9+vXj969e+f68+engktHjYmIiAgAkZGR3k4hz6lHyKuqAtkf6S4iIoWbn58fgwYN4p9//iE6OpoNGzZw7733As7TAnz//fccPXqU6Ohodu7c6ert2bt3LwAbNmzAzFi8eDGQtqdm8eLFfPbZZwwfPpwTJ05w5MgRHnnkEUqUKMG4ceOIjIxk165dtG/f3rWMv78/Y8aMceW0fft2nnnmGdfjQ4cOpXfv3txzzz2YGWZGy5YtAbj88suZNGkSJ0+e5Pjx40ybNo3g4ODcfAvVI+Q9Y4GHgUHA+17ORURE0iqRjWXigJSjz4oAxYBzQGwm2s36eXAGDx5Mr169eOKJJ9i1axe33nor33//PceOHaN79+40aNCADh06EBERQa1atbjkkksAuOGGG1izZg2tWrViy5YtxMfHZ/gcDz30EB988AE33ngjPXr04IsvvqBLly5MnTqVd955h+eee47vvvuOatWqERMTg7+/PwcPHqR79+4cP36c5s2b8/XXX3P48GF++uknPvzwQ+rXr0+pUqXo06cPACdOnCAgIIC5c+eyatUqbrnlFhITE3n55ZeZM2cOjRo1IiEhIcvvT2aZIuNwOBxmZuZwODzc9hADMxjv9deoUCgUhTmCg4Pt22+/teDg4PMes2xEt1TLd0uetvi8do9msGzW8i5atKidOXPGmjZt6jZ99OjR9sMPP9j06dNt7NixGb5mM7PGjRu7TQ8JCbGpU6e67i9evNiWLl3quu/v729RUVE2fvy/266KFSuamdlNN92UYa4jRoywn376KcPnAez++++3bdu2uU0LDAy0s2fPWps2bbL4v8v89ls9Ql6zNflvfa9mISIivqlWrVoEBQUxf/58t+lFixblr7/+4rXXXmPKlClce+21zJs3j2nTprFq1aosP8+mTZtct8+dO8fx48fZvHmza1p4eDjgvF5biqeeeoqHH36YatWqcckll1C0aFE2bNhwwedp3LgxtWrVIioqym168eLFqVmzZprX6SkqhLxmW/Lfel7NQkREMhKUjWVSX6dsanIb586b58rsJuSmZMmSANx1112EhYW5ZxEXx8GDBwkODubOO++kTZs2LFy4kFGjRjFgwIAsPc/5u6TMLN3dVP7+zmHHPXr04MMPP6R///6sWrWKqKgoBgwYwE033XTR17Nu3Truv//+NI8dO3YsSzlnhQohr9kNJAAO4HLgoHfTERGR82Tv2lX/SsqgjZy267R161ZiY2OpVq0aS5cuTXeeiIgIvv32W7799luWLVvGsGHDGDBggGtMUJEiRTySS2otWrRg5cqVfPHFF65pNWvWdJsnPj4+zXOvX7+eHj16cPTo0TS9QrlJhZDXJOIshuoDDVAhJCIiWXHmzBk+/PBDhg8fjr+/P8uXL6d06dK0aNGCyMhIatasybp169iyZQvFihXj7rvvZts2596IlCPJ2rdvz8GDB4mNjfXYofO7du3iwQcfpG3btoSGhvLAAw9www03EBoa6ppn7969tGvXjjp16nD8+HFOnz7NDz/8wIABA5g+fTqvvvqqq0era9eufPDBB2l6vTxFh897lcYJiYhI9r3yyiu8+eabDB48mG3btjFnzhzuuusuQkNDiY+P591332XTpk0sXbqUpKQk/u///g9wXlftmWee4fHHH+fQoUNMnz7dYzl99dVX/PLLL0yaNInVq1dTrlw5Pv/8c7d5Ro8ezY4dO1i7di0RERG0aNGCmJgYbr31Vvbv388vv/zCtm3bGDt2LMWLF8/18xt5fcR+fo7cO2oMgzcNzOBLr79OhUKhKKxxoSOPFPk7PHHUmHqEvCplwLR6hERERLxBhZBXpRRCDbyahYiISGGlQsirtuM8rLI8utSGiIhI3lMh5FUxwL7k29o9JiIiktdUCHldyu6x2l7NQkSksDIzIHfOqSO5KyDAeRaglP9hdqgQ8rqncO4WG+ftRERECqWUk/elvkSE+IZ69ZxXZ4iIiMh2Gzqhotftu/gsIiKSa06dOsX27du57777OHHiBHFxcRdfSLwqICCAevXqcd9997FkyRKio7N/tm4/nMfRSwYcDgeRkZGUKlUqT0/5LSIieeeyyy7j7bffpnjx4t5ORbJgyZIlhISEpLtrLLPbbxVCF5H7hZA/8AHOwdL/B6jYEhHxhoCAACpVqqSxQj7AzIiIiLhgT1Bmt9/aNeZ154CeQGWcV6Jf4910REQKqcTERA4e1HUfCxsVQvnC2zivRL/f24mIiIgUKiqE8oVR3k5ARESkUNLh8yIiIlJoqRDKFwKBpsB93k5ERESkUNGusXyhHLAKSAKmAzqHhYiISF5Qj1C+cAQ4CRRBl9oQERHJOyqE8o2Ua47p4qsiIiJ5xWcKodDQUMwsTYwcOTLd+R966KE088bExORx1lmhQkhERCSv+cwYoRtuuMHtbJ8NGzZkwYIF/PTTTxkuc/r0aerWreu6n5Or0+a+lEKogVezEBERKUx8phA6/8qygwYNYvfu3fz+++8ZLmNmhIeH53ZqHrI1+a96hERERPKKz+waSy0wMJBevXoxbty4C85XsmRJ9u7dy/79+5k2bRoNGly8t6Vo0aI4HA63yBspPUJ18NF/i4iIiM/xyS3uPffcQ5kyZfjmm28ynGfHjh08/PDDdO7cmV69euHv78/KlSupWrXqBdsePHgwkZGRrggLC/Nw9hnZB0QDxYHqefScIiIihZtPXn1+zpw5xMfH06lTp0wvExAQwLZt25gwYQKvvvpqhvMVLVqUYsWKue47HA7CwsJy8erzqa0HrgE6ATNz+blEREQKrgJ79flq1arRunVrunbtmqXlEhMT+euvv6hVq9YF54uPjyc+Pj4nKebANpyFUH1UCImIiOQ+n9s11qdPH44ePcqsWbOytJy/vz9XX301hw8fzqXMPEEDpkVERPKSTxVCfn5+9OnTh/Hjx5OUlOT22Pjx43nnnXdc91955RXatGlD9erVueaaa/j+++8JDg5mzJgxeZ12FuhcQiIiInnJp3aNtW7dmuDg4HSPFqtWrRrnzp1z3b/00ksZPXo0lSpV4uTJk6xbt47mzZuzbdu2NMvmH9uAszgHTYuIiEhu88nB0nkps4OtPEf/EhERkZzK7Pbbp3aNFQ4qgkRERPKKCiEREREptFQI5Tv/B2wGPvFyHiIiIgWfTw2WLhyKAA2B495OREREpMBTIZTvLATuBP72diIiIiIFngqhfOcIMNvbSYiIiBQKGiMkIiIihZYKoXzpFuA1oJWX8xARESnYVAjlS/cAQ4G7vJyHiIhIwaZCKF/SxVdFRETyggqhfEkXXxUREckLKoTypZRCKBgI8mYiIiIiBZoKoXzpJBCefLueNxMREREp0FQI5VsaJyQiIpLbVAjlWxonJCIikttUCOVbKYVQA69mISIiUpCpEMq31CMkIiKS21QI5VspY4RqAoHeTERERKTAUiGUbx0GTuO8Lm5tL+ciIiJSMKkQytc0TkhERCQ3BXg7AbmQBTh7ho57OxEREZECSYVQvvaKtxMQEREp0LRrTERERAotFUI+oTLg5+0kREREChwVQvneYeAQUN3biYiIiBQ4KoTyvXAgEbjSy3mIiIgUPBosne/dBRwD4r2diIiISIGjQijfC/N2AiIiIgWWdo2JiIhIoaVCKN+7FBgDzPd2IiIiIgWOdo3le2eBh3D+qyrjPIpMREREPEE9QvlePLAn+XZ9byYiIiJS4KgQ8gkpF19VISQiIuJJKoR8gq5CLyIikhtUCPmErcl/1SMkIiLiSSqEfIJ2jYmIiOQGFUI+YXvy30o4D6cXERERT/CZQmjo0KGYmVts27btgst069aNbdu2ERMTw6ZNm+jQoUMeZetpZ4H9ybfVKyQiIuIpPlMIAfz9999UqlTJFTfffHOG8zZr1owJEyYwduxYrrnmGqZNm8a0adO46qqr8jBjT9I4IREREU/zqUIoMTGR8PBwVxw/fjzDefv168ecOXP48MMP2b59O6+++irr16/n6aefzsOMPUnjhERERDzNpwqh2rVrExYWxp49e/j++++54oorMpy3WbNmLFiwwG3a3Llzadas2QWfo2jRojgcDrfIH1QIiYiIeJrPFEKrV6+md+/etG/fnieffJLq1auzbNkySpYsme78lSpVIjw83G1aeHg4lSpVuuDzDB48mMjISFeEheWXq7/rXEIiIiKe5jPXGpszZ47r9ubNm1m9ejX79u3jvvvuY9y4cR57nnfffZePP/7Ydd/hcOSTYmgL8FnyXxEREfEEnymEznf69Gl27txJrVq10n38yJEjVKxY0W1axYoVOXLkyAXbjY+PJz4+3mN5es5JoJ+3kxARESlQfGbX2PmCgoKoWbMmhw+nfzX2VatW0apVK7dpbdq0YdWqVXmRnoiIiPgI84UYNmyY3XrrrRYcHGzNmjWzefPm2dGjR618+fIG2Pjx4+2dd95xzd+sWTOLj4+3559/3urWrWtDhw61uLg4u+qqq7L0vA6Hw8zMHA6H198DKGlwk8E1+SAXhUKhUCjyb2R2++0zPUKXX345EyZMYMeOHUyePJnjx4/TtGlTIiIiAKhWrRqVK1d2zb9q1Sp69uzJY489xsaNG+nWrRv33HMPW7b48hibPsAfwMveTkRERKRA8MNZEUkGHA4HkZGRlCpViqioKC9n0wYIAeYAj3g5FxERkfwrs9tvnx0sXTjNBy73dhIiIiIFhs/sGhMRERHxNBVCPsvP2wmIiIj4PBVCPmcAcBB4yduJiIiI+DwVQj7HD6iKLrUhIiKScyqEfI4uvioiIuIpKoR8TkohVA/9+0RERHJGW1KfEwrEAZcAwV7ORURExLepEPI5ScCO5NvaPSYiIpITKoR8ksYJiYiIeIIKIZ+kQkhERMQTVAj5JBVCIiIinqBCyCdtTf6rcwmJiIjkhAohn7QT56DpMkAl76YiIiLiw1QI+aR44J/k29o9JiIikl0qhHyWxgmJiIjkVIC3E5Ds+hD4Cljr7URERER8lgohn7XM2wmIiIj4PO0aExERkUJLhZBP6wa8ApTydiIiIiI+SbvGfNrHwBXAfOAPL+ciIiLie1QI+bQpOHuDzng7EREREZ+kQsinPeftBERERHyaxgiJiIhIoaVCyOcFAnW8nYSIiIhP0q4xn3YpcBRnPVsSiPFuOiIiIj5GPUI+7SRwCue/sa53UxEREfFBKoR8Xso1xxp4NQsRERFfpELI5+niqyIiItmlQsjnbU3+q0JIREQkq1QI+Tz1CImIiGSXCiGfl1II1UYHAYqIiGSNCiGfdwDnJTYCgVpezkVERMS3qBAqELR7TEREJDtUCBUIKoRERESyQ4VQgaBzCYmIiGSHCqECQT1CIiIi2eEzhdCgQYP4888/iYyMJDw8nKlTp1KnzoUvNvrQQw9hZm4RE1MQr8eVci4hDZYWERHJCp8phFq2bMmoUaNo2rQpbdq0ITAwkHnz5lGiRIkLLnf69GkqVarkiuDg4DzKOC/tAa4GKng7EREREZ/iMyee6dChg9v93r17c+zYMa677jqWLVuW4XJmRnh4eG6n52XngL+9nYSIiIjP8ZkeofOVLl0agBMnTlxwvpIlS7J3717279/PtGnTaNDgwgOKixYtisPhcAsREREpmHyyEPLz8+OTTz5h+fLlbNmyJcP5duzYwcMPP0znzp3p1asX/v7+rFy5kqpVq2a4zODBg4mMjHRFWFhYbryEXNAMGA0M8HYiIiIiPsV8LT7//HMLDQ21qlWrZmm5gIAA27Vrl73xxhsZzlO0aFFzOByuqFKlipmZORwOr7/uC0cPAzNYng9yUSgUCoXCu+FwODK1/faZMUIpRowYwd13382tt96a5d6axMRE/vrrL2rVyvjoqvj4eOLj43OaphesBl4H1ns7EREREZ/hU7vGRowYQZcuXbjjjjvYu3dvlpf39/fn6quv5vDhw55Pzuv2Aq8BM7ybhoiIiA/xmR6hUaNG0bNnTzp37kxUVBQVK1YEnIfHx8bGAjB+/HjCwsJ46aWXAHjllVf4448/2L17N2XKlGHAgAEEBwczZswYr70OERERyT98phB66qmnAPj999/dpvfu3Zvx48cDUK1aNc6dO+d67NJLL2X06NFUqlSJkydPsm7dOpo3b862bdsomCoBTYBDwCbvpiIiIuID/HAOFpIMOBwOIiMjKVWqFFFRUd5O5yLeB14ERgDPeDkXERER78ns9tunxgjJxeiaYyIiIlmhQqhA0VXoRUREskKFUIGSUghVAUp5MxERERGfoEKoQIkEUs6tpN1jIiIiF6NCqMDROCEREZHMUiFU4GickIiISGapECpwtib/VY+QiIjIxagQKnC0a0xERCSzVAgVOCmFUHWguDcTERERyfdUCBU4R4ETOP+1db2ci4iISP6mQqhAys1xQsWAa4GuOM9XJCIi4rtUCBVI24DDwCXZXD4AqAXcBTwH3JLqsWuBdcBHQJcc5CgiIuJ9PnP1ecmKJ4HHMjFfRaAOzl1oqf/WBAJTzfcxsCz59g6cu98GAxM9lK+IiIh3qBAqkJJS3S4OxKa6/wrQEWfBU/oCbUQDO3EWPutTTT+Bs4ASERHxfdkqhEqUKEF0dLSncxGP8gPeAfoDQUBC8vSawA3Jt88Be3EWOzvP+xsG2EWeIwBohHuhJCIi4juyVQiFh4czefJkxo0bx4oVKzydk3jEF8CdOHdxVcdZ4AB8BUzHWezsAeKy2X6Z5OVL4+whOp6DXEVERLwjW4Ole/XqRdmyZVm0aBE7duxg4MCBVK5c2dO5SY68AnQDyvFvEQSwCpiK88iy7BZBAKeAfUAR4O4ctCMiIuI92SqEpk+fTpcuXahatSpffvklPXv2ZN++fcycOZMuXbpQpEgRT+cpWXYM+BPnmJ7cMj35b+dcfA4REZHcZZ6Ip59+2mJiYiwpKcnCw8Pt9ddft0suucQjbXszHA6HmZk5HA6v55L/oomBGZw18P3/tUKhUCgKTmR2+52j8whVqFCBAQMGsGXLFt577z1+/vlnWrVqRf/+/enatSvTpk3LSfOS723AuXusBNDau6mIiIhkU5arrC5dutiMGTMsLi7O/vrrL/vf//5npUuXdpunRo0aFhcX5/WKMKehHqGLxacGZjAmH+SiUCgUCoUzMrv9ztZRYyEhIUycOJEWLVqwdu3adOc5dOgQb7/9dnaaF58yHXgG57mJ/HEeki8iIuIb/HBWRFlyySWXEBMTkwvp5D8Oh4PIyEhKlSpFVFSUt9PJhwJwnmn6UuBmQKdTEBER78vs9jtbPUIBAQE4HI40082MuLg4EhIS0llKCqZEYBbQC+fRYyqERETEd2RrsPSpU6c4efJkmjh16hQxMTHs3buX1157DT8/P0/nK/mSDqMXERHflK0eod69e/P222/zzTff8OeffwJw44038tBDD/HWW29x2WWX8cILLxAXF8e7777r0YQlP5qD8+SMdYB6wHbvpiMiIpIFWR6JvWDBAuvevXua6d27d7cFCxYYYL169bJt27Z5fdR4TkNHjWU2ZhmYwcB8kItCoVAoCnvk6nmEmjdvzl9//ZVm+l9//UWzZs0AWL58OdWqVctO8+KTpgIrgQPeTkRERCTTslUIHThwgP/+979ppv/3v//lwAHnhrBcuXKcPHkyZ9mJDxkDtAB+9HYiIiIimZatMUIvvPACP/30Ex06dGDNmjUAXH/99dSrV49u3boBcMMNNzBp0iTPZSoiIiLiYdk6jxBAcHAwjz/+OHXr1gVgx44dfPXVV+zbt8+T+XmdziOUVWWAa4DFXs5DREQKs1w7j1BAQABz5szhiSee4KWXXspRklLQVAP24Dy30GXAGe+mIyIichFZHiOUmJhIo0aNciMX8Xn7gVBgF86iSEREJH/L1mDp77//Pt3B0iJwPdAI2OrtRERERC4q25fYePjhh2ndujXr1q3j7Nmzbo/379/fI8mJL4r0dgIiIiKZlq1CqGHDhqxfvx6AOnXquD1mlq2x11LgXAKUAI57OxEREZEMZasQuuOOOzydhxQoTwPvA6OBZ72bioiIyAVka4xQipo1a9K2bVuKFy/uqXwu6qmnniI0NJSYmBj++OMPbrjhhgvO361bN7Zt20ZMTAybNm2iQ4cOeZRpYbYfZ29QZ28nIiIiclFZvn5H2bJlbcGCBZaUlGSJiYlWvXp1A2zs2LH24Ycf5tp1Q+677z6LjY213r17W/369e2rr76yEydO2GWXXZbu/M2aNbOEhAR74YUXrF69evbGG29YXFycXXXVVR6/VokidVxicNbADBrlg3wUCoVCUdgiC9vvrDc+fvx4mz17tlWtWtUiIyNdhVDbtm3t77//zrUX9ccff9iIESNc9/38/OzgwYM2cGD6F/qcOHGizZw5023aqlWr7IsvvsiNN1LhFlMNzOCVfJCLQqFQKApb5OpFV9u2bcvAgQMJCwtzm75r1y6Cg4Oz0+RFBQYGct1117FgwQLXNDNjwYIFrgu9nq9Zs2Zu8wPMnTs3w/nFk6Yn/73Hm0mIiIhcULYGSwcFBREdHZ1metmyZYmLi8txUukpX748AQEBhIeHu00PDw+nXr166S5TqVKldOevVKlShs9TtGhRihUr5rrvcDhykHVh9iuQBFwLXIGuSi8iIvlRtnqEli1bxoMPPui6b2b4+fnx4osvsnjxYo8l5w2DBw8mMjLSFef3eklmRQArk2938mYiIiIiGcpWj9CLL77IwoULuf766ylatCgffPABV111FWXLlqVFixaezhGAiIgIEhMTqVixotv0ihUrcuTIkXSXOXLkSJbmB3j33Xf5+OOPXfcdDoeKoWybDtyCc/fYKO+mIiIiko5s9Qht2bKFOnXqsHz5cqZPn05QUBC//PIL11xzDf/884+ncwQgISGBdevW0apVK9c0Pz8/WrVqxapVq9JdZtWqVW7zA7Rp0ybD+QHi4+OJiopyC8mulHFCLYHS3kxEREQkQ14f2Z3ZuO+++ywmJsYefPBBq1evnn355Zd24sQJq1ChgoHzaLZ33nnHNX+zZs0sPj7enn/+eatbt64NHTpUh8/nefxtYAb/yQe5KBQKhaKwRGa339naNQZQunRpbrzxRipUqIC/v3vH0nfffZfdZi9o8uTJXHbZZbzxxhtUqlSJDRs20L59e44ePQpAtWrVOHfunGv+VatW0bNnT9566y3eeecddu3axT333MOWLVtyJT9Jz3TgKpy7xyZ4NxUREZHz+OGsiLLk7rvv5ocffqBkyZJERka6XV/MzChXrpwnc/Qqh8NBZGQkpUqV0m6ybLkRWA1EAeWBeO+mIyIihUJmt9/ZGiP00UcfMW7cOEqWLMmll15K2bJlXVGQiiDxhDXAXpxHkF3m3VRERETOk61dY1WrVuWzzz4jJibG0/lIgWNAbSDR24mIiIikka0eoblz53L99dd7OhcpsFQEiYhI/pStHqFZs2YxbNgwGjRowObNm0lISHB7fObMmR5JTgqaKjjPNh1+sRlFRETyRLYGSyclJWX4mJkREJDtg9HyHQ2W9pR3gMHA28DLXs5FREQKusxuv7NVsRQpUiTbiUlh9TdwDud1x0RERPKHLI0RmjVrFqVKlXLdHzhwIKVLl3bdL1u2rM7RIxmYhnPX2ENezkNERORfWSqE2rVr53Zl9pdeeomyZcu67gcEBFC3bl3PZScFSDQaGyQiIvlNlgohPz+/C94XyZwgbycgIiICZPPweZHsKQbMByIAnXhTRES8L0uFkJm5XU4jZZpI5sThLICKA3d7ORcREZEsHjXm5+fHN998Q1xcHADFixfnyy+/5OzZswBu44dE0jcNuAboDIz3bioiIlLoZek8QuPGjcvUfA8//HB288l3dB4hT2sMbMA5eLo8oMu0iIiI52V2+52tEyoWJiqEckMocCXQCdBZyEVExPNy9erzIjkzI/lvZ69mISIiokJIvGBa8t+OaBUUERFv0lZIvGAZcBKoADTzci4iIlKYqRASL0gEZiXf1u4xERHxHhVC4iXTk//e480kRESkkFMhJF4yB+cJFmsD9b2ci4iIFFYqhMRLzgALk29r95iIiHiHCiHxouk4C6KS3k5EREQKqSxdYkPEs77DeZmNOG8nIiIihZQKIfEiXV5DRES8S7vGJJ+o5O0ERESkEFIhJF5WFtgK7EVjhUREJK+pEBIvO4FzD60/cJ2XcxERkcJGY4QkH+iO84r0kd5OREREChkVQpIPbPR2AiIiUkhp15jkM37eTkBERAoRFUKST9wJrAY+9nYiIiJSiKgQknwiALgR6OLtREREpBBRIST5xHwgGggGGns5FxERKSxUCEk+EQPMS76ti7CKiEjeUCEk+cj05L8qhEREJG+oEJJ85FcgCbgWqOblXEREpDBQIST5SASwMvl2J28mIiIihYRPFELBwcGMGTOGf/75h+joaHbv3s1rr71GYGDgBZdbvHgxZuYWX3zxRR5lLdkzLfmvdo+JiEju84kzS9erVw9/f38ef/xxdu/eTcOGDRk9ejRBQUEMGDDggst+/fXXvPrqq6770dHRuZ2u5Mh04COgJVAGOOXNZEREpBAwX4wXXnjB9uzZc8F5Fi9ebMOHD8/R8zgcDjMzczgcXn/NhSf+NjCDB/JBLgqFQqHwxcjs9tsndo2lp3Tp0pw4ceKi891///0cO3aMzZs3884773DJJZfkQXaSMz8n//0YqO3NREREpIDziV1j56tZsyZ9+/blhRdeuOB8P/74I/v27ePQoUM0atSI999/n7p163LvvfdmuEzRokUpVqyY677D4fBY3pJZH+C85MYNOI8kawgkeDUjEREpuLzWbfXuu+/axdStW9dtmSpVqtiuXbts9OjRWX6+22+/3czMatSokeE8Q4cOTTcP7RrL67jMYKPB3fkgF4VCoVD4WmR215hf8g2vKF++POXKlbvgPP/88w8JCc7egMqVK7NkyRL++OMPevfujVnWUi9RogRnz56lXbt2zJs3L9150usRCgsLo1SpUkRFRWXp+SSn/IFz3k5CRER8kMPhIDIy8qLbb6/uGouIiCAiIiJT81apUoXFixezbt06+vTpk+UiCKBJkyYAHD58OMN54uPjiY+Pz3LbkhtSF0FXAg8Br3snFRERKZB8YrB0lSpVWLJkCfv37+eFF17gsssuo2LFilSsWNFtnm3btnHDDTcAUKNGDV5++WWuvfZagoOD6dixI99++y2///47mzdv9tZLkWwpASwHXgOe824qIiJSoPjEYOk2bdpQu3ZtateuTVhYmNtjfn5+AAQGBlKvXj1KlCgBOHt2WrduzbPPPktQUBAHDhxgypQpvPXWW3mev+RUNPAG8CQw0cu5iIhIQeLVMUK+ILP7GCUvBKKjx0REJDMyu/32iV1jIk6pi6AewHXeSkRERAoIFULig+7FuYtsFlDdy7mIiIgvUyEkPmgusB6oCMwByns3HRER8VkqhMQHnQHuAvYCdYCZgC6dIiIiWadCSHzUEaA9cBxoCkwAing1I6e7gc3AEqCod1MREZGLUiEkPmwH0AmIAToDI7yYSy2c10WbifPaaC2B/l7MR0REMkOFkPi4lcD9OM9C/SQwOI+fvwTwNvA3zt118cC05MdeBoLzOB8REckKFUJSAEwF+iXffgd4II+e9z5gO/ASUAyYjbM3qAvOXWMlgOF5lIuIiGSHCiEpIEYCHyTfHgu0yeXnC8R5tusrgH9w7qK7E9iV/Pj/cJ73qAvQIZdzERGR7FIhJAXIIOBHnEXKFKCJh9svxb9XpUkAngZeAa7COTYota3AJ8nz1fNwHiIi4ikqhKQAMaAPsAhwALd7sO3uwE6gb6ppC4C3gNgMlnkDaIx2j4mI5F8qhKSAice5O+o+PFuAOHCewLFHFpY5A2zzYA4iIuJpKoSkAIoEfkp1/xKgeBbbKAfckOp+CNAbuCWbOTUG3szmsiIikltUCEkBVx7nrrIfyNzqXgR4CudusCk4j/wC52638bhf+DWzygGrcB5Of3c2lhcRkdwScPFZRHxZHeAaoDZQA9h9gXlb4Dz6rEny/f1AZWBPDnM4DnyK8wKxf+WwLRER8SQVQlLAreTf8/1kVARVxnnofa/k+yeBIcDXQJKH8ngJZ6+SiIjkJyqEpBCYcd79IOAszsPsnwGG4hwMfQ4Yg7MIivBwDucXQUVxDuwWERFv0hghKWRaAaHA88BG4EOcRdAfwI3A43i+CEqtEs5zHf2Si88hIiKZpR4hKWR6A5cBHyXfDwcGAt+SN7uuSgH34uwR6kTa3ioREclL6hGSQuYRnCdCTMR55ue6OI8Gy6vxOzuBYcm3P8V5aL+IiHiLCiEpZOKAtkAZ4DngtBdyeAfYB1yJcxC1iIh4iwohKYQM52Bpb4kGnk2+PQDnof0iIuINKoREvGIaMBsoBozwbioiIoWYCiERr3kG5666djivjyYiInlNhZCI1+zGeSJHcA7cLpHxrCIikitUCIl41bs4z2tUDee1yEREJC+pEBLxqhigX/Lt/jgP5xcRkbyiQkjE62YCv+I8yaIGTouI5CUVQiL5Qj8gFmcPUZCXcxERKTx0iQ2RfOEfoCGwx9uJiIgUKuoREsk3VASJiOQ1FUIi+c5lwBiggbcTEREp8LRrTCTf+RjohfNaZK29m4qISAGnQkgk33kZZxE0xMt5iIgUfCqERPKdfcAt3k5CRKRQ0BghkXyvtLcTEBEpsFQIieRbfsBrwEHgKu+mIiJSQPlMIRQaGoqZucXAgQMvuEyxYsUYOXIkERERREVF8fPPP1OhQoU8ylgkpwznuYVKAqO8nIuISMHkM4UQwCuvvEKlSpVcMWLEhS9HMHz4cDp27Ej37t1p2bIlVapU4ZdffsmjbEU84TkgGmgJ3O/lXERECibzhQgNDbV+/fplev5SpUpZXFyc3Xvvva5pdevWNTOzm266KdPtOBwOMzNzOBxefw8UhTUGGZjBYYNS+SAfhUKhyP+R2e23T/UIDRo0iIiICNavX88LL7xAkSJFMpz3uuuuo2jRoixYsMA1bceOHezbt49mzZrlRboiHvIxsAOoBLzu5VxERAoWnzl8/rPPPmP9+vWcOHGC5s2b8+6771K5cmX69++f7vyVKlUiLi6O06dPu00PDw+nUqVKGT5P0aJFKVasmOu+w+HwzAsQybZ44GlgPtAXCAE2eTUjEZGCxGvdVu+++65dTN26ddNdtk+fPhYfH29FixZN9/H//Oc/Fhsbm2b66tWr7b333sswp6FDh6abh3aNKbwfkwzMYFk+yEWhUCjyd2R215hf8g2vKF++POXKlbvgPP/88w8JCQlppjdo0IAtW7ZQt25ddu7cmebx22+/nUWLFlGmTBm3XqG9e/fyySef8Mknn6T7fOn1CIWFhVGqVCmioqIy+cpEckNVYDvOo8gextkzJCIi6XE4HERGRl50++3VXWMRERFERERka9kmTZqQlJTE0aNH03183bp1xMfH06pVK9eRYnXq1CE4OJhVq1Zl2G58fDzx8fHZykkkd4XhHCM0DPgSOAlM82ZCIiIFgte7ry4WTZs2tX79+lmjRo2sevXq1rNnTwsPD7dvvvnGNU+VKlVs27ZtdsMNN7imff7557Z371677bbb7Nprr7UVK1bYihUrcqVrTaHImyhiMMHADBIM/pMPclIoFIr8F1nYfns/2YvFNddcY6tWrbKTJ09adHS0bdmyxQYNGuQ2Pig4ONjMzFq2bOmaVqxYMRs5cqQdP37czpw5Y1OmTLGKFSvm1hupUORR+BuEGJjBIYOgfJCTQqFQ5K/wiTFCviCz+xhF8pYf8B7wPbDZy7mIiOQ/PjFGSESyy4DzLzFzBXDAC7mIiPgunzqhoohk5GZgG/CytxMREfEpKoRECoSbgCCgOZDxGddFRMSddo2JFAgfAfuBmUCSl3MREfEd6hESKTB+AmJT3e+Oc1C1iIhkRIWQSIH0FjAZ+AbtKhMRyZgKIZECaTOQCDwITAACvZuOiEg+pUJIpECaBNwLxOHcRTYFKHbBJURECiMVQiIF1gygMxADdMQ5kLqEVzMSEclvVAiJFGhzgTuBM0AbYDbOq9eLiAioEBIpBJYAbYHTwK3AfKCMF/MREck/VAiJFAqrgDuA40BTYBFQ3qsZiYjkByqERAqN9cBtQDhwDc6eokpezEdExPtUCIkUKn/j3D12ELgKWIBOMC8ihZkKIZFCZyfOYmg38BrO8w2JiBRO+ikoUiiF4uwRivd2IiIiXqUeIZFCK3URdDnOAdUNc9BeUaB4qvtXAC8C/c6bbwjwDtAcfQWJiLf5AebtJPIzh8NBZGQkpUqVIioqytvpiOSSScB9OIuh5qmmlwIqAhUy8bcM8CzwafKyNwF/AHuB6snT/HCOT6qSfD8C57mNfsV5zqPTnn1ZIlJoZXb7rV1jIgI8jvM30Quppv2Nc/dZVlRIdXsfMB7Yn2qaf/Jz3A10wHkI/wPJkQgsw1kU/YpzLJOISO5Sj9BFqEdICq/lQAsgEuch90cz8fdUFtovgrP36e7kaHDe47v4tyhaBiRk72WISKGU2e23CqGLUCEkhVc54CwQm0fPVwO4C2dRdBvOMUcpqgEHkm8XAZLyKCcR8VWZ3X5rpKKIZOA4eVcEAfwDjADa4SzCugBjgXn8WwQBTMU5lqlZHuYmIgWVxgiJSD50BpiWHKkVA1oBJXDusktxI3AZsJC8Ld5ExNepR0hEfEgcUBt4ENiSavqzOMcSHcdZPN0POPI4NxHxRSqERMTHHAK+O29aKM6j1EoAnYHvgWPAdKAXztMAiIikpUJIRAqAIcCVQGPgDWAbzt1onXAWTUdRUSQi6VEhJCIFyCZgKM5D8RsCrwNbSVsUzcC5i01ECjsVQiJSQG3BeVHZq5IjdVF0J+7nPKoDlM7b9EQkX1AhJCKFwFbci6JHcI4hSvE1zp6iLnmemYh4lw6fF5FCZmtypCgKXJr8d22q6XfgvBjtdHQNNJGCSz1CIlLIxeMcZF0D9xM3Po/zWmlHgZk4D9nX7jORgkY9QiIigPMQ/NSWA8E4B12nXA8tHmdv0rZUsRXnddF0LTQRX6RrjV2ErjUmUtjVB7onR8MM5kkE9gD9gVnJ0y7BeV20M7mdoIikQ9caExHxiG04z010NVAd6Ai8CIQAf+AcPxQA1MV55usUXYEo4Kfz2msKVMjdlEUk07RrTEQk0/Ymx6/nTa+Ms+co9WDr4OS/EammlQBW4PwNegL3XWzbgM3AQQ/nLCIXol1jF6FdYyKSfWVwnrcoPPl+DWA+zrNgZ9Qhv4V/Lzi7Dn1Fi2RPZrff6hESEck1p867/w9QE+f4oTo4e5FSRz3+PdfRECAM5+H7LwMn8yRjkcJGhZCISJ6LATYmR2plgA7APcl/qwI9gX6p5mmMs6BSD7WIJ/jEYOmWLVtiZunG9ddfn+FyixcvTjP/F198kYeZi4hkxSlgAtADKI+zGOqP86i0FFNxjjtqkdfJpaMSzhNP/g8YAbwJBHo1I5Gs8okeoZUrV1KpUiW3aW+++SatWrVi7dq1GSzl9PXXX/Pqq6+67kdHR+dKjiIinhUPzDlvWvnk6UnAX6mmP4zzSLRpwPZcyOVynBeyPT8uPW++w8Arqe4PTP77I+4nqxTJP3yiEEpISCA8PNx1PyAggM6dOzNixIiLLhsdHe22rIiI74rAOY6oCpD6R10/oBHwLrAD57iiaTgP78/sYGs/nOc9Sul9agW8jbPgcWSwTBLO8ydtxVmAHTrv8Wdx9hot5d9CqAXQBFiDc9dgHCLeZr4WXbt2tcTERKtateoF51u8eLEdPXrUjh07Zps3b7Z33nnHLrnkkgsuU7RoUXM4HK6oUqWKmZk5HA6vv26FQqFIPx41mGUQa2Cp4rDBVwZ3GhRLnreIQY3zlv/S4KxBr1TTbk/VTrzB3waTDV4zuM+gYao204siBv0NJhqk/t4dkardOIM/DUYZPGTQwMA/H7yfioIQDocjs9tv7yeb1Zg1a5bNmjXrovM9+uij1rZtW2vYsKH17NnTDhw4YFOmTLngMkOHDrX0qBBSKBT5P0oadDP43uCk4VYURRlstn+LpaBUy41MnvZOqmmlDboa1DMI8GCODxv8anD0vPxSItJgkcH7BvcaXJEP3leFL4ZPFELvvvtuukVHanXr1nVbpmrVqpaYmGhdu3bN8vPdfvvtZmZWo8b5v4b+DfUIKRSKghGBBq3NWeQcMNyKjTPm7H1JmfdKg1rm7MXJyxyDDbobDDNYkpxXesXRqFTLOAx6GtySD95jRX6OzBZCXj2hYvny5SlXrtwF5/nnn39ISPj3YoYvv/wyffv2pWrVqiQmJl5gybRKlCjB2bNnadeuHfPmzcvUMjqhoogUDNfiHFC9DdiPF7/6L6AIzvMp3QDcmPy3Ec6xRp8nz3MdzjN4H8J5eoEUY3GOnTqI8/xLYefdPp7r2Uv+4hMnVIyIiCAiIuLiM6bSp08fvv322ywXQQBNmjQB4PDhw1leVkTEt633dgKZkAT8nRwhydOK4yyQUpwDFuK8RElqtwK1LtB2LP8WRSlF0kxgWY6zFt/n9e6rzMYdd9yR7u4ywKpUqWLbtm2zG264wQCrUaOGvfzyy3bttddacHCwdezY0Xbv3m1LlizJla41hUKhUHgzbjfobTDE4AuDGQbrDMKNdHe3mcFzqZavaRBqMDofvBaFJyKz22+fOHw+xX//+19WrFjBjh070jwWGBhIvXr1KFGiBADx8fG0bt2aZ599lqCgIA4cOMCUKVN466238jptERHJdYsv8FhRnBfGrYrznEhVk+OPVPPcivMacPXOW/ZDnIf+L8V5uP85z6Qr+YYuunoRGiMkIlIYBAHNkm8vSP5bGucuuJSLMEQCK3EWRctwngvJG+dBKo7zbN41gKf5dzNeHOcuQIHMb79VCF2ECiERkcKqDPA4cAtwM87CKLVY4E+cRdFSnEXSmRw+ZxEgGKidHHWS/24GXkw1TwzOy5lcgXO8E8DXOK9F9xEwBeeYq8JLhZCHqBASERFnr9DVOHeh3ZIclc6bJwnYANwFXOiKBn44j3BLKXJS/62Bc1fe+f7g3x4rgOE4e6g+T36uS3AOAk+57Mle4BOcR9PltDjzTSqEPESFkIiIpK8W7oVRTZwXzi3Hv2OJ3sR52oKByY8BvMe/12FLTyywKzl2Jv/dAqy+SD7lgadw7jarkDztFM6eos9wFkqFhwohD1EhJCIimVMFZ3G0NNW0f4DqOHetrUie9hgwEgjl30In9d+D5GzTXBx4AHiefwd/JwATce4225iDtn2HCiEPUSEkIiLZdzfO3qJf+LdHpxjO3WhZPx9e1vgBdwIvALelmr4AZ0E0J5ef37tUCHmICiEREfF91+HsIbqPf8+lPB7o7a2Ecl1mt9/+GT4iIiIiBcQ64H6cg7E/wjnQelqqxx1A2bxPKx9QISQiIlJoHMC5q+wKYEaq6X2TH+vvjaS8SoWQiIhIoROJ+1mymwMlgCOpphWOEsGnLrEhIiIiueFunKcCWJVqWl/gP8CnwD7+vTzXOdJesitlWjj/FlOBOI+iS8J5NFyKyjjPe5Sy7GG8c4ZuJxVCIiIigvth/wBP4Dz8/scstPEeMDj5djVgKxAFlEo1TwjQLtX91KcWyHsqhERERCQdLXGeoPFenIf8++HcXeaXKvzPux2ZavlzwHHSntk6BmdxlLKsdy8FosPnL0KHz4uIiPgeHT4vIiIichEqhERERKTQUiEkIiIihZYKIRERESm0VAiJiIhIoaVCSERERAotFUIiIiJSaKkQEhERkUJLhZCIiIgUWiqEREREpNBSISQiIiKFlgohERERKbRUCImIiEihpUJIRERECq0AbyfgKxwOh7dTEBERkUzK7HZbhdBFpLyRYWFhXs5EREREssrhcBAVFZXh436A5V06vqlKlSoXfBOzw+FwEBYWRtWqVT3ettr3Xtu+3r4v5+7r7fty7r7evi/n7uvt50Xuhw4duuA86hHKhIu9iTkRFRWVK/98te/dtn29fV/O3dfb9+Xcfb19X87d19vPrbYz06YGS4uIiEihpUJIRERECi0VQl4SFxfHa6+9RlxcnNrP4/Z9Offcbt+Xc/f19n05d19v35dz9/X2czv3zNBgaRERESm01CMkIiIihZYKIRERESm0VAiJiIhIoaVCSERERAotFUJ57JZbbmHGjBmEhYVhZnTu3Nmj7Q8aNIg///yTyMhIwsPDmTp1KnXq1PFI20888QQbN27k9OnTnD59mpUrV9K+fXuPtJ2egQMHYmYMHz7cI+0NHToUM3OLbdu2eaTtFFWqVOG7774jIiKC6OhoNm3axHXXXZfjdkNDQ9PkbmaMHDnSA1mDv78/b7zxBv/88w/R0dHs3r2bl19+2SNtpyhZsiTDhw9n7969REdHs2LFCq6//vpstZWZz9Hrr7/OoUOHiI6OZv78+dSqVcsjbXfp0oW5c+cSERGBmdG4cWOP5R4QEMB7773Hpk2bOHPmDGFhYYwfP57KlSt7pH1wfg62bdvGmTNnOHHiBPPnz+fGG2/0WPupffHFF5gZ/fr180jbISEhaT4Ds2fP9mju9erVY/r06Zw6dYozZ87w559/csUVV3ik/fQ+w2bGCy+8kOO2g4KCGDFiBAcOHCA6OpotW7bw+OOPZyrvzLRfoUIFQkJCCAsL4+zZs8yePTvTn6nMbJeKFSvGyJEjiYiIICoqip9//pkKFSpkOv+cUCGUx4KCgti4cSP/+9//cqX9li1bMmrUKJo2bUqbNm0IDAxk3rx5lChRIsdtHzx4kEGDBnHddddx/fXXs2jRIqZPn06DBg08kLm766+/nscff5yNGzd6tN2///6bSpUqueLmm2/2WNtlypRhxYoVJCQk0KFDBxo0aED//v05efJkjtu+4YYb3PJu3bo1AD/99FOO2wZn0fnkk0/y9NNPU79+fQYOHMiLL75I3759PdI+wJgxY2jTpg0PPPAAV199NfPmzWPBggVUqVIly21d7HP04osv8swzz/DEE09w0003cfbsWebOnUuxYsVy3HZQUBDLly9n4MCBWc77Yu2XKFGCa6+9ljfffJNrr72Wrl27UrduXWbMmOGR9gF27tzJ008/zdVXX83NN9/M3r17mTdvHuXLl/dI+ynuuecemjZtmqXrNGam7dmzZ7t9Fv7zn/94rP0aNWqwfPlytm/fzm233UajRo148803iY2N9Uj7qfOuVKkSffr04dy5c0yZMiXHbX/88ce0b9+eXr16Ub9+fT755BNGjhxJx44dPZL7tGnTqFGjBp07d+aaa65h3759LFiwIFPblsxsl4YPH07Hjh3p3r07LVu2pEqVKvzyyy+Zyt0TTOGdMDPr3Llzrj5H+fLlzczslltuyZX2jx8/bg8//LBH2wwKCrIdO3ZYq1atbPHixTZ8+HCPtDt06FD766+/cu29fvfdd23p0qV5su4MHz7cdu3a5bH2Zs6caWPGjHGb9vPPP9t3333nkfaLFy9uCQkJduedd7pNX7t2rb355ps5aju9z9GhQ4esf//+rvulSpWymJgY69GjR47bTong4GAzM2vcuLFHcz8/rr/+ejMzu+KKK3KlfYfDYWZmd9xxh8far1Klih04cMAaNGhgoaGh1q9fP4+0HRISYlOnTvXIOple+xMmTLBvv/0219o/P6ZOnWoLFizwSNubN2+2l19+2W1adj9f57dfu3ZtMzNr0KCBa5qfn5+Fh4fbf//73yy3f/52qVSpUhYXF2f33nuva566deuamdlNN93kkf/HhUI9QgVc6dKlAThx4oRH2/X396dHjx4EBQWxatUqj7Y9atQoZs2axcKFCz3aLkDt2rUJCwtjz549fP/995nu8s6MTp06sXbtWiZPnkx4eDjr16/nkUce8Vj7KQIDA+nVqxfjxo3zWJsrV66kVatW1K5dG4BGjRpx8803Z2m3w4UEBAQQEBCQ5pd1TEyMR3vlAKpXr07lypVZsGCBa1pkZCSrV6+mWbNmHn2uvFC6dGnOnTvHqVOnPN52YGAgjz32GKdOnfJY76ufnx/fffcdw4YNY+vWrR5pM7XbbruN8PBwtm/fzueff07ZsmU90q6fnx933XUXO3fuZM6cOYSHh/PHH394fPhCigoVKnDXXXcxduxYj7S3cuVKOnXq5Ophve2226hTpw7z5s3LcdspPampP79mRlxcXLY+v+dvl6677jqKFi3q9pndsWMH+/bty7PPbK5XW4r0I7d7hPz8/GzmzJm2bNkyj7XZsGFDi4qKsoSEBDt58qR16NDBozn36NHDNm3aZMWKFTPAoz1C7du3t27dutnVV19tbdu2tRUrVtjevXutZMmSHmk/JibGYmJi7O2337YmTZrYo48+atHR0fbggw969D3q3r27JSQkWOXKlT26rrz77ruWlJRk8fHxlpSUZIMGDfJo3itWrLDFixdb5cqVzd/f3+6//35LTEy07du356jd8z9HzZo1MzOzSpUquc03adIkmzhxYo7aTh150SNUrFgxW7t2rX3//fcebf+uu+6yqKgoS0pKsoMHD9r111/vsfYHDRpkc+fOdd33ZI9Qjx49rGPHjtawYUPr3LmzbdmyxVavXm3+/v45br9ixYpmZnbmzBl79tlnrXHjxjZw4EBLSkqyW2+91eP/2wEDBtjx48dd33U5bbto0aL2zTffmJlZfHy8xcbG2gMPPOCR/2tAQIDt3bvXJk2aZGXKlLHAwEB78cUXzcxszpw5WWo7ve3Sf/7zH4uNjU0z7+rVq+29997L1mvISujq8wXYqFGjaNiwoUd/ce/YsYMmTZpQunRpunXrxvjx42nZsqVHBh1ffvnlfPrpp7Rp0yZXTrc+Z84c1+3NmzezevVq9u3bx3333eeR3hV/f3/Wrl3LkCFDANiwYQMNGzbkiSee4Ntvv81x+yn++9//Mnv2bA4fPuyxNu+77z7uv/9+evbsyZYtW2jSpAmffPIJhw4d8ljuDzzwAOPGjePQoUMkJiayfv16JkyY4JHB5AVRQEAAkydPxs/PjyeffNKjbS9evJgmTZpQvnx5Hn30USZPnsxNN93EsWPHctTutddeS79+/bj22ms9lKm7SZMmuW7//fffbNq0iX/++YfbbruNRYsW5ahtf3/nDpLp06fzySefALBx40aaN2/OE088wdKlS3PU/vkefvhhfvjhB4991/Xt25emTZvSsWNH9u3bx6233sqoUaM4dOhQjnvXExMT6dq1K2PHjuXkyZMkJiayYMECfvvtN/z8/LLUVm5slzwh16stRfqRmz1CI0aMsP3799uVV16Zq69h/vz59uWXX3qkrc6dO5uZWUJCgivMzJKSkiwhISFbv/ouFn/++ae98847Hmlr7969Nnr0aLdpTzzxhB08eNBj+VarVs0SExOtU6dOHn0f9u/fb0899ZTbtCFDhti2bds8/p6XKFHC1VszceJE+/XXX3PU3vmfo+rVq6fbU7NkyRL75JNPctR26sjNHqGAgAD75ZdfbMOGDVa2bFmPt39+7Ny5M1s9gOe3369fP9fnNfVnODEx0UJDQ3Ml96NHj9pjjz2W49wDAwMtPj7ehgwZ4jbfe++9Z8uXL/foe3/zzTebmVmjRo088n8tXry4xcXFpRmDN3r0aJs9e7ZHcy9VqpSVL1/eAPvjjz9s5MiRmW43o+3S7bffbmZmpUuXdpu+d+9ee/bZZ7P1HmUlNEaoABoxYgRdunThjjvuYO/evbn6XP7+/pk6EiczFi5cSMOGDWnSpIkr1qxZww8//ECTJk04d+6cR54nRVBQEDVr1vRYz8qKFSuoW7eu27Q6deqwb98+j7QP0KdPH44ePcqsWbM81iY4j1Y6//1NSkpy/Ur2pOjoaI4cOUKZMmVo164d06dP92j7oaGhHD58mFatWrmmORwObrrpJo+PZ8sNKT1BtWvXpnXr1h4f35ceT32Ov/vuOxo1auT2GQ4LC2PYsGG0a9fOA5m6q1q1KuXKlfPIZzghIYE1a9bk+mcYnL26a9euZdOmTR5pLzAwkKJFi+bJZzgyMpKIiAhq1arF9ddfn+nP74W2S+vWrSM+Pt7tM1unTh2Cg4Pz5DOrXWN5LCgoyO3cC9WrV6dx48acOHGCAwcO5Lj9UaNG0bNnTzp37kxUVBQVK1YE4PTp05k+BDQj77zzDrNnz2b//v04HA569uzJbbfd5rEvuDNnzrBlyxa3aWfPnuX48eNppmfHsGHDmDlzJvv27aNKlSq8/vrrJCUlMWHChBy3Dc7DP1euXMngwYOZPHkyN954I4899hiPPfaYR9r38/OjT58+jB8/nqSkJI+0mWLmzJkMGTKE/fv3s2XLFq655hqef/55jw7Ibtu2LX5+fuzYsYNatWoxbNgwtm/fTkhISJbbutjn6JNPPuHll19m165dhIaG8uabb3Lo0CGmTZuW47YvvfRSqlWr5hqUmrLhPHLkCOHh4Tlq//Dhw/z8889ce+213H333RQpUsT1GT5x4gQJCQk5av/48eMMGTKEGTNmcPjwYcqXL8///vc/qlatmulTMVzs/Tm/cEtISODIkSPs3LkzR22fOHGCoUOHMmXKFI4cOULNmjX54IMP2L17N3PnzvVI7sOGDWPSpEksXbqUxYsX0759ezp27Mhtt93mkfbBWZR3796d/v37Z6rNzLa9ZMkShg0bRkxMDPv27aNly5Y8+OCDPP/88x5pv1u3bhw7doz9+/dz9dVX8+mnnzJt2jTmz59/0bYvtl2KjIxk7NixfPzxx5w4cYLIyEhGjBjBypUrWb16dZbep+zK9W4nxb/RsmVLS09ISIhH2s/IQw89lOO2x4wZY6GhoRYbG2vh4eE2f/58a926da6+X54cLD1hwgQLCwuz2NhYO3DggE2YMMFq1Kjh0Xzvuusu27Rpk8XExNjWrVvtkUce8Vjbbdq0MTOz2rVre/x9LlmypA0fPtz27t1r0dHRtnv3bnvzzTctMDDQY8/RvXt32717t8XGxtqhQ4dsxIgRVqpUqWy1lZnP0euvv26HDx+2mJgYmz9/fqbft4u1/dBDD6X7+NChQ3PcfsrutvS0bNkyx+0XK1bMpkyZYgcPHrTY2FgLCwuzadOmZWmwdFa/w7IyWPpCbRcvXtzmzJlj4eHhFhcXZ6GhofbVV19ZhQoVPJp7nz59bOfOnRYdHW1//fVXlnZDZ6b9Rx991M6ePZvldf9ibVesWNHGjRtnBw8etOjoaNu2bZs999xzHmu/b9++tn//fouLi7O9e/faG2+8kenvh4yk3i4VK1bMRo4cacePH7czZ87YlClTrGLFitn6fshq+CXfEBERESl0NEZIRERECi0VQiIiIlJoqRASERGRQkuFkIiIiBRaKoRERESk0FIhJCIiIoWWCiEREREptFQIiUgaixcvZvjw4d5OwyeEhIQwdepU131fee/MjM6dO3s7DRGvUyEk4qPO3wAD3HvvvcTExGT6tPrieV27duWVV17xdhoXValSJWbPnu3tNES8TtcaEykg/vvf/zJq1CieeOIJvvnmm3TnCQwMzNT1qiT7Tp486e0UMiUz10UTKQzUIyRSAAwYMIARI0bwf//3f25F0OLFixkxYgTDhw/n2LFjzJ07l7FjxzJz5ky35QMCAggPD+fhhx9Ot/0yZcowfvx4Tpw4wdmzZ/ntt99cF2h0OBxER0fTvn17t2XuueceIiMjueSSS9Jt895772XTpk1ER0cTERHB/PnzKVGiBPBvb9err77K0aNHOX36NF988QWBgYGu5du1a8eyZcs4efIkERERzJw5kxo1arg9R9WqVfnxxx85fvw4Z86cYc2aNdx4442uxzt16sS6deuIiYlhz549vPrqqxQpUiTD99nf35+PPvrI9Zzvv/8+fn5+bvOcv2ssNDSUIUOGMH78eKKioti7dy8dO3akfPnyTJs2jaioKDZu3Mh1113n1k6LFi1YunQp0dHR7N+/n08//dT1/qS0O3jwYMaOHUtkZCT79u3j0UcfdT0eGBjIiBEjOHToEDExMezdu5dBgwa5Hj9/11jDhg1ZuHCh6//x1VdfERQU5Ho85X/Sv39/Dh06REREBCNHjiQgQL+nxfflyUXNFAqFZyMkJMSmTp1q7733nkVGRtodd9yRZp7FixdbZGSkvf/++1anTh2rU6eONWvWzBISEqxSpUqu+e655x6LioqyoKAg13KpL3Y7bdo027Jli918883WqFEjmz17tu3cudMCAgIMsMmTJ9u3337r9tw//fRTmmkpUalSJYuPj7dnn33WgoODrWHDhvbkk0+6nj8kJMQiIyNtwoQJ1qBBA7vzzjstPDzc3nrrLVcbXbt2tS5duljNmjWtcePGNn36dNu4caP5+fkZYEFBQbZ79277/fffrUWLFlazZk3r3r27NW3a1AC7+eab7dSpU/bggw9a9erVrXXr1vbPP//Yq6++muF7PmDAADt+/Lh16dLF6tWrZ6NHj7bTp0/b1KlT3d7z1O9daGioRURE2GOPPWa1atWyUaNG2alTp+y3336zbt26We3ate2XX36xLVu2uJapUaOGRUVFWb9+/axWrVrWrFkzW7dunY0bNy5Nu08++aTVrFnTBg4caImJiVanTh0DrH///rZv3z67+eabrVq1ataiRQv7v//7P9fyZmadO3c2wEqUKGFhYWH2888/21VXXWW333677dmzx+1ioSEhIXbq1Cn7/PPPrW7dunbXXXfZmTNnPHphYYXCS+H1BBQKRTYiJCTEYmNjzczs9ttvT3eexYsX27p169JM//vvv23AgAGu+9OnT3fbyKbemNeqVcvMzJo1a+Z6vGzZsnb27Fnr1q2bAda5c2eLjIy0Sy65xABzOBwWHR1t7dq1Szeva665xszMqlWrluFri4iIcLUH2OOPP26RkZGuQuf8KFeunJmZXXXVVQbOq3yfPn3aLr300nTnnz9/vg0aNMht2v33329hYWEZvudhYWH2wgsvuO4XKVLE9u/ff9FCKHVBWLFiRTMze/31113TbrrpJjMz19W2R48ebV9++aXbc7do0cISExOtWLFi6bYL2JEjR+zxxx83wD799FNbsGBBhq8ldSH0yCOP2PHjx61EiRKuxzt06GCJiYmuq7uHhIRYaGio+fv7u+aZNGmSTZgwweufBYUiJ6FdYyI+bNOmTYSGhvL666+77cZIbd26dWmmjRkzhj59+gBQoUIFOnTowLhx49Jdvn79+iQkJLB69WrXtBMnTrBjxw7q168PwG+//UZCQgKdOnUCnLu9IiMjWbBgQbptbty4kQULFrB582YmT57MI488QpkyZdLMExMT47q/atUqHA4HV1xxBQC1atXixx9/ZM+ePZw+fZq9e/cCUK1aNQCaNGnCX3/9leGYncaNG/Pqq68SFRXlitGjR1OlSpV0d+eVKlWKKlWquL0PSUlJrF27Nt32U9u0aZPrdsrYnM2bN6eZVqFCBVduvXv3dstt7ty5FClShOrVq6fbLsCRI0dcbXzzzTc0adKEHTt28Omnn9KmTZsM86tfvz4bN24kOjraNW3FihUUKVKEunXruqZt2bKFc+fOue4fPnzY9XwivkqFkIgPCwsL47bbbqNq1arMmTOHkiVLppnn7NmzaaZ9++231KhRg6ZNm9KrVy9CQ0NZvnx5tvNISEjg559/pmfPngD07NmTSZMmkZSUlO78586do02bNnTo0IGtW7fSt29fduzYwZVXXpnp55w5cyZly5bl0Ucf5aabbuKmm24CoGjRogBuRVR6SpYsydChQ2nSpIkrrr76amrVqkVsbGym88iM9Aaop55mZoBzDFJKbl999ZVbbo0bN6ZWrVrs2bMnw3bNzNXGX3/9RfXq1XnllVe45JJLmDx5Mj/99JNHX0fq5xPxVVqDRXzc/v37admyJZUqVcqwGDrfiRMnmDZtGn369KF3796EhIRkOO+2bdsIDAx0FRoAZcuWpW7dumzdutU17YcffqB9+/Y0aNCAO+64gx9++OGieaxcuZLXXnuNa665hvj4eLp06eJ6rHHjxhQvXtx1v2nTpkRFRXHgwAHKli1LvXr1eOutt1i0aBHbt2/n0ksvdWt706ZNNGnSJM30FOvXr6du3brs2bMnTaQUJqlFRkZy6NAht/ehSJEiaQY5e8L69etp0KBBurll5ai/qKgoJk+ezGOPPUaPHj3o1q1buu/Htm3baNy4sdtg7BYtWpCUlMSOHTs88ppE8isVQiIFwMGDB7ntttuoUKECc+fOxeFwXHSZMWPG8NBDD1G/fn3Gjx+f4Xy7d+9m2rRpjB49mhYtWtCoUSO+//57wsLCmD59umu+pUuXcuTIEX744QdCQ0P5888/M2zzxhtvZPDgwVx33XVcccUVdO3alcsuu4xt27a55ilatChjx46lfv36dOjQgddff52RI0diZq6jth577DFq1qzJ7bffzscff+z2HBMmTODIkSNMmzaN5s2bU716dbp27UrTpk0BeOONN3jwwQd59dVXadCgAfXq1aNHjx68+eabGeb96aefMmjQIDp37kzdunX5/PPP0+zS84T333+f5s2bM2LECFdPUKdOnRgxYkSm23juuef4v//7P+rWrUvt2rXp3r07hw8f5tSpU2nm/eGHH4iNjWX8+PFcddVV3HbbbYwYMYLvvvuOo0ePevCVieQ/KoRECoiU3WTly5fPVDG0YMECDh8+zNy5czl8+PAF5+3Tpw/r1q3j119/ZdWqVfj5+XHnnXeSmJjoNt+ECRNo0qTJRXuDIiMjufXWW/ntt9/YuXMnb731Fv3792fOnDmueRYuXMiuXbtYunQpkyZNYsaMGbz22muAc5fM//3f/3Hdddfx999/M3z4cAYMGOD2HAkJCbRt25ajR4/y22+/sXnzZgYNGuTaXTdv3jzuvvtu2rZty5o1a/jjjz947rnn2LdvX4Z5f/TRR3z33XeMHz+eVatWERUVleaklp6wefNmWrZsSZ06dVi2bBl//fUXb7zxBocOHcp0G1FRUbz44ousXbuWNWvWcOWVV3LnnXem29sVExNDu3btKFu2LGvWrOHnn39m4cKFPP300558WSL5kh/OUdMiUsgEBQURFhZGnz59cmVjnhMhISGUKVPGbVeZiEhu0JmwRAoZPz8/ypcvT//+/Tl16hQzZszwdkoiIl6jQkikkKlWrRp79+7lwIED9O7dO8Mju0RECgPtGhMREZFCS4OlRUREpNBSISQiIiKFlgohERERKbRUCImIiEihpUJIRERECi0VQiIiIlJoqRASERGRQkuFkIiIiBRaKoRERESk0Pp/YMAZCsjx39sAAAAASUVORK5CYII=", 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" ] @@ -1031,7 +1029,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.8.17" + "version": "3.12.1" } }, "nbformat": 4, From 7dfd267646c5335c946ba71fd695cd4b2171f38f Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 19 Feb 2024 11:24:35 -0700 Subject: [PATCH 15/22] remove redundant notebook --- ...h the quantum krylov subspace method.ipynb | 1039 ----------------- 1 file changed, 1039 deletions(-) delete mode 100644 docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb diff --git a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb deleted file mode 100644 index 16a24fb..0000000 --- a/docs/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ /dev/null @@ -1,1039 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Calculating ground states on large scale systems: Quantum Krylov Subspaces" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 1: Map problem to quantum native format\n", - "\n", - "Given a matrix H that we are interested in, subspace methods use a set of states as a basis for the construction of a smaller representation of H, which captures its properties of interest (e.g. lowest eigenvalue).\n", - "\n", - "\n", - "What is the Krylov subspace? \n", - "\n", - "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", - "\n", - "Is the Krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", - "\n", - "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", - "\n", - "$$ \\vert \\psi \\rangle = c_1 \\vert \\lambda_1 \\rangle + c_2 \\vert \\lambda_2 \\rangle + ... + c_n \\vert \\lambda_n \\rangle $$\n", - "\n", - "Applying $j^{th}$ power of the matrix $H$ gives:\n", - "\n", - "$$ H^n \\vert \\psi \\rangle = c_1 \\lambda_1^n \\vert \\lambda_1 \\rangle + c_2 \\lambda_2^n \\vert \\lambda_2 \\rangle + ... + c_n \\lambda_n^n \\vert \\lambda_n \\rangle $$\n", - "\n", - "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $H^{-1}$.\n", - "\n", - "Why is it useful for ground state energy problems?\n", - "\n", - "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", - "\n", - "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}$ which can be shown to give similar convergence guarantess as the power method. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", - "\n", - "\n", - "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", - "\n", - "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", - "\n", - "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", - "\n", - "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", - "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi \\rangle$. \n", - "\n", - "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", - "\n", - "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi \\rangle$$" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Imports and definitions\n", - "\n" - ] - }, - { - "cell_type": "code", - "execution_count": 1, - "metadata": {}, - "outputs": [], - "source": [ - "import math\n", - "import numpy as np\n", - "import scipy as sp\n", - "import matplotlib.pylab as plt\n", - "import warnings\n", - "warnings.filterwarnings('ignore')\n", - "\n", - "from qiskit.quantum_info import SparsePauliOp, Operator\n", - "from qiskit.circuit import Parameter\n", - "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", - "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", - "from qiskit.providers.fake_provider import FakePrague\n", - "from qiskit.primitives import Estimator\n", - "\n", - "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", - " s_vals, s_vecs = sp.linalg.eigh(s)\n", - " s_vecs = s_vecs.T\n", - " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", - " h_reg = good_vecs.conj() @ h @ good_vecs.T\n", - " s_reg = good_vecs.conj() @ s @ good_vecs.T\n", - " if k==1:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][0]\n", - " else:\n", - " if return_dimn:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k], len(good_vecs)\n", - " else:\n", - " return sp.linalg.eigh(h_reg, s_reg)[0][:k]" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Define Hamiltonian\n", - "Let's consider the Heisenberg Hamiltonian for $N$ qubits on a linear chain: $H=-J \\sum_{i,j}^N Z_i Z_j + J \\sum_{i,j}^N X_i X_j + Y_i Y_j$" - ] - }, - { - "cell_type": "code", - "execution_count": 2, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "SparsePauliOp(['ZZIIIIIIII', 'IZZIIIIIII', 'IIZZIIIIII', 'IIIZZIIIII', 'IIIIZZIIII', 'IIIIIZZIII', 'IIIIIIZZII', 'IIIIIIIZZI', 'IIIIIIIIZZ', 'XXIIIIIIII', 'IXXIIIIIII', 'IIXXIIIIII', 'IIIXXIIIII', 'IIIIXXIIII', 'IIIIIXXIII', 'IIIIIIXXII', 'IIIIIIIXXI', 'IIIIIIIIXX', 'YYIIIIIIII', 'IYYIIIIIII', 'IIYYIIIIII', 'IIIYYIIIII', 'IIIIYYIIII', 'IIIIIYYIII', 'IIIIIIYYII', 'IIIIIIIYYI', 'IIIIIIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j])" - ] - }, - "execution_count": 2, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Define problem Hamiltonian. Kicked Ising in this case\n", - "n_qubits = 10\n", - "J = 1 # coupling strength for ZZ interaction\n", - "\n", - "# Define interacting part of the Hamiltonian: sum_ij Z_i Z_j\n", - "H_int = [['I']*n_qubits for _ in range(3*(n_qubits-1))]\n", - "for i in range(n_qubits-1):\n", - " H_int[i][i] = 'Z'\n", - " H_int[i][i+1] = 'Z'\n", - "for i in range(n_qubits-1):\n", - " H_int[n_qubits-1+i][i] = 'X'\n", - " H_int[n_qubits-1+i][i+1] = 'X'\n", - "for i in range(n_qubits-1):\n", - " H_int[2*(n_qubits-1)+i][i] = 'Y'\n", - " H_int[2*(n_qubits-1)+i][i+1] = 'Y'\n", - "H_int = [''.join(term) for term in H_int]\n", - "H_tot = [(term, -J) if term.count('Z') == 2 else (term, 1) for term in H_int]\n", - "\n", - "# Get operator\n", - "H_op = SparsePauliOp.from_list(H_tot)\n", - "H_op" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Set parameters for the algorithm" - ] - }, - { - "cell_type": "code", - "execution_count": 3, - "metadata": {}, - "outputs": [], - "source": [ - "# Set parameters for quantum Krylov algorithm\n", - "krylov_dim = 20 # size of krylov subspace\n", - "dt = 0.1 # time step\n", - "num_trotter_steps = 4\n", - "dt_circ = dt/num_trotter_steps" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### State preparation\n", - "Pick a reference state $\\vert \\psi \\rangle$ that has some overlap with the ground state. For this Hamiltonian, We use the \"checkerboard\" state $\\vert 0101...01 \\rangle$ as our reference." - ] - }, - { - "cell_type": "code", - "execution_count": 4, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 4, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "qc_state_prep = QuantumCircuit(n_qubits)\n", - "for i in range(n_qubits):\n", - " if i%2 != 0:\n", - " qc_state_prep.x(i)\n", - "qc_state_prep.draw('mpl')" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Time evolution\n", - "\n", - "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 5, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - " ## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1) )\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "qc_evol = QuantumCircuit(qr)\n", - "qc_evol.append(evol_gate, qargs=qr)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" - ] - }, - { - "attachments": { - "H_test.PNG": { - "image/png": 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" - } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Hadamard test\n", - "\n", - "![H_test.PNG](attachment:H_test.PNG)\n", - "\n", - "\n", - "\\begin{equation}\n", - " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", - "\\begin{equation}\n", - " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", - "\\end{equation}\n", - "... then measure:\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\Rightarrow\\quad\\langle X\\rangle_a &= \\frac{1}{4}\\Bigg(\\Big\\||\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2-\\Big\\||\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big\\|^2\\Bigg) \\\\\n", - " &= \\text{Re}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{split}\n", - "\\end{equation}\n", - "Similarly, measuring $Y$ yields\n", - "\\begin{equation}\n", - " \\langle Y\\rangle_a = \\text{Im}\\Big[\\langle\\psi_0|U_j^\\dagger PU_k|\\psi_0\\rangle\\Big].\n", - "\\end{equation}" - ] - }, - { - "cell_type": "code", - "execution_count": 6, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Circuit for calculating the real part of the overlap in S via Hadamard test\n" - ] - }, - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 6, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "## Create the time-evo op circuit\n", - "evol_gate = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) ) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "## Create the time-evo op dagger circuit\n", - "evol_gate_d = PauliEvolutionGate(H_op, time=dt, synthesis= SuzukiTrotter(order=1) )\n", - "evol_gate_d = evol_gate_d.inverse()\n", - "\n", - "# Put pieces together\n", - "qc_temp = QuantumCircuit(n_qubits)\n", - "qc_temp.compose(qc_state_prep, inplace=True)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate, qargs=qc_temp.data[0].qubits[0].register)\n", - "for _ in range(num_trotter_steps):\n", - " qc_temp.append(evol_gate_d, qargs=qc_temp.data[0].qubits[0].register)\n", - "qc_temp.compose(qc_state_prep.inverse(), inplace=True)\n", - "\n", - "# Create controlled version of the circuit\n", - "controlled_U = qc_temp.to_gate().control(1)\n", - "\n", - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.append(controlled_U, list(range(n_qubits+1)))\n", - "qc_real.h(0)\n", - "\n", - "print('Circuit for calculating the real part of the overlap in S via Hadamard test')\n", - "qc_real.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "The Hadamard test circuit can be a deep circuit once we transpile to native gates and topology of a device. For example the 5 qubits case considered here " - ] - }, - { - "cell_type": "code", - "execution_count": 7, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 8047\n" - ] - } - ], - "source": [ - "circuit_trans = transpile(qc_real.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits ==2))\n" - ] - }, - { - "attachments": { - "optimized_H_test.png": { - "image/png": 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- } - }, - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 2: Optimize circuits and operators\n", - "\n", - "We can optimize the deep circuits for the Hadamard test that we have obtained by introducing some approximations and relying on some assumption about the model Hamiltonian. For example, consider the following circuit for the Hadamard test:\n", - "\n", - "\n", - "![optimized_H_test.png](attachment:optimized_H_test.png)\n", - "\n", - "Assume we can classically calculate $E_0$, the eigenvalue of $|0\\rangle^N$ under the Hamiltonian $H$.\n", - "This is satisfied when the Hamiltonian preserves the U(1) symmetry.\n", - "Assume that the gate $\\psi_0-prep$ prepares our desired reference state $\\ket{\\psi_0}$, e.g., to prepare the HF state for chemistry $\\psi_0-prep$ would be a product of single-qubit NOTs, so controlled-$\\psi_0-prep$ is just a product of CNOTs.\n", - "Then the circuit above implements the following state prior to measurement:\n", - "\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\ket{0} \\ket{0}^N\\xrightarrow{H}&\\frac{1}{\\sqrt{2}}\n", - " \\left(\n", - " \\ket{0}\\ket{0}^N+ \\ket{1} \\ket{0}^N\n", - " \\right)\\\\\n", - " \\xrightarrow{\\text{1-ctrl-init}}&\\frac{1}{\\sqrt{2}}\\left(|0\\rangle|0\\rangle^N+|1\\rangle|\\psi_0\\rangle\\right)\\\\\n", - " \\xrightarrow{U}&\\frac{1}{\\sqrt{2}}\\left(e^{i\\phi}\\ket{0}\\ket{0}^N+\\ket{1} U\\ket{\\psi_0}\\right)\\\\\n", - " \\xrightarrow{\\text{0-ctrl-init}}&\\frac{1}{\\sqrt{2}}\n", - " \\left(\n", - " e^{i\\phi}\\ket{0} \\ket{\\psi_0}\n", - " +\\ket{1} U\\ket{\\psi_0}\n", - " \\right)\\\\\n", - " =&\\frac{1}{2}\n", - " \\left(\n", - " \\ket{+}\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", - " +\\ket{-}\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", - " \\right)\\\\\n", - " =&\\frac{1}{2}\n", - " \\left(\n", - " \\ket{+i}\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", - " +\\ket{-i}\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", - " \\right)\n", - "\\end{split}\n", - "\\end{equation}\n", - "\n", - "where we have used the classical simulable phase shift $ U\\ket{0}^N = e^{i\\phi}\\ket{0}$ in the third line. Therefore the expectation values are obtained as\n", - "\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\langle X\\otimes P\\rangle&=\\frac{1}{4}\n", - " \\Big(\n", - " \\left(e^{-i\\phi}\\bra{\\psi_0}+\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+U\\ket{\\psi_0}\\right)\n", - " \\\\\n", - " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-U\\ket{\\psi_0}\\right)\n", - " \\Big)\\\\\n", - " &=\\text{Re}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right],\n", - "\\end{split}\n", - "\\end{equation}\n", - "\n", - "\\begin{equation}\n", - "\\begin{split}\n", - " \\langle Y\\otimes P\\rangle&=\\frac{1}{4}\n", - " \\Big(\n", - " \\left(e^{-i\\phi}\\bra{\\psi_0}+i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}-iU\\ket{\\psi_0}\\right)\n", - " \\\\\n", - " &\\qquad-\\left(e^{-i\\phi}\\bra{\\psi_0}-i\\bra{\\psi_0}U^\\dagger\\right)P\\left(e^{i\\phi}\\ket{\\psi_0}+iU\\ket{\\psi_0}\\right)\n", - " \\Big)\\\\\n", - " &=\\text{Im}\\left[e^{-i\\phi}\\bra{\\psi_0}PU\\ket{\\psi_0}\\right].\n", - "\\end{split}\n", - "\\end{equation}\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", - "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." - ] - }, - { - "cell_type": "code", - "execution_count": 8, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "execution_count": 8, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "t = Parameter('t')\n", - "\n", - "# ## Create the time-evo op circuit\n", - "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", - "# Create instruction for rotation about XX+YY-ZZ:\n", - "Rxyz_circ = QuantumCircuit(2)\n", - "Rxyz_circ.rxx(t,0,1)\n", - "Rxyz_circ.ryy(t,0,1)\n", - "Rxyz_circ.rzz(-t,0,1)\n", - "Rxyz_instr = Rxyz_circ.to_instruction(label='RXX+YY-ZZ')\n", - "\n", - "interaction_list = [[[i, i+1] for i in range(0, n_qubits-1, 2)], [[i, i+1] for i in range(1, n_qubits-1, 2)]] # linear chain\n", - "\n", - "qr = QuantumRegister(n_qubits)\n", - "trotter_step_circ = QuantumCircuit(qr)\n", - "for i, color in enumerate(interaction_list):\n", - " for interaction in color:\n", - " trotter_step_circ.append(Rxyz_instr, interaction)\n", - "\n", - "\n", - "qc_evol = QuantumCircuit(qr)\n", - "for _ in range(num_trotter_steps):\n", - " qc_evol.compose(trotter_step_circ, inplace=True)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale = 0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Use an optimized circuit for state preparation" - ] - }, - { - "cell_type": "code", - "execution_count": 9, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 9, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "controlled_state_prep = QuantumCircuit(n_qubits + 1)\n", - "for idx in range(n_qubits):\n", - " if idx % 2 == 0:\n", - " controlled_state_prep.swap(idx, idx+1)\n", - " else:\n", - " controlled_state_prep.cx(idx+1, idx)\n", - " controlled_state_prep.cx(idx, idx+1)\n", - "\n", - "\n", - "controlled_state_prep.draw('mpl', fold=-1, scale=0.5)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{S}$ via Hadamard test" - ] - }, - { - "cell_type": "code", - "execution_count": 10, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", 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" - ] - }, - "execution_count": 10, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "# Create hadamard test circuit for real part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real = QuantumCircuit(qr)\n", - "qc_real.h(0)\n", - "qc_real.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(n_qubits)\n", - "qc_real.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_real.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real.x(0)\n", - "qc_real.h(0)\n", - "\n", - "S_real_circ = qc_real.decompose().copy()\n", - "\n", - "# # Create hadamard test circuit for imaginary part\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag = QuantumCircuit(qr)\n", - "qc_imag.h(0)\n", - "qc_imag.sdg(0)\n", - "qc_imag.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(n_qubits)\n", - "qc_imag.compose(qc_evol, list(range(n_qubits)), inplace=True)\n", - "qc_imag.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag.x(0)\n", - "qc_imag.h(0)\n", - "\n", - "\n", - "S_imag_circ = qc_imag.decompose().copy()\n", - "\n", - "S_real_circ.draw('mpl', fold=-1, scale = 0.2)" - ] - }, - { - "cell_type": "code", - "execution_count": 11, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The circuit has 2Q gates depth: 96\n" - ] - } - ], - "source": [ - "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), FakePrague())\n", - "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "We have considerably reduced the depth of the Hadamard test with a combination of Trotter approximation and uncontrolled unitaries" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "### Template circuits for calculating matrix elements of $\\tilde{H}$ via Hadamard test\n", - "The only difference between the circuits used in the Hadamard test will be the phase in the time-evolution operator and the observables measured. Therefore we can prepare a template circuit which represent the generic circuit for the Hadamard test, with placeholders for the gates that depend on the time-evolution operator.\n" - ] - }, - { - "cell_type": "code", - "execution_count": 12, - "metadata": {}, - "outputs": [], - "source": [ - "# Hamiltonian terms to measure\n", - "observable_list = []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " # print(pauli)\n", - " observable = pauli[::-1].to_label() + 'Z'\n", - " observable_list.append(observable)\n", - "\n", - "\n", - "\n", - "# Real part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_1 = QuantumCircuit(qr)\n", - "qc_real_1.h(0)\n", - "qc_real_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_real_1.x(n_qubits)\n", - "qc_real_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_real_circ_1 = qc_real_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_real_2 = QuantumCircuit(qr)\n", - "qc_real_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_real_2.x(0)\n", - "qc_real_2.h(0)\n", - "H_real_circ_2 = qc_real_2.decompose().copy()\n", - "\n", - "# Imaginary part\n", - "# First half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_1 = QuantumCircuit(qr)\n", - "qc_imag_1.h(0)\n", - "qc_imag_1.compose(controlled_state_prep, list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_1.x(n_qubits)\n", - "qc_imag_1.compose(qc_evol, list(range(n_qubits)), inplace=True) \n", - "H_imag_circ_1 = qc_imag_1.decompose().copy()\n", - "\n", - "# Second half hadamard test\n", - "qr = QuantumRegister(n_qubits+1)\n", - "qc_imag_2 = QuantumCircuit(qr)\n", - "qc_imag_2.compose(controlled_state_prep.inverse(), list(range(n_qubits+1)), inplace=True)\n", - "qc_imag_2.x(0)\n", - "qc_imag_2.sdg(0)\n", - "qc_imag_2.h(0)\n", - "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 3: Execute using a quantum primitive" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Generate circuits to calculate all matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 13, - "metadata": {}, - "outputs": [], - "source": [ - "S_real_circuits, S_imag_circuits = [], []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " \n", - "\n", - " circuit_real = S_real_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - " circuit_imag = S_imag_circ.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " S_real_circuits.append(circuit_real)\n", - " S_imag_circuits.append(circuit_imag)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 14, - "metadata": {}, - "outputs": [], - "source": [ - "count = 0\n", - "H_real_circuits, H_imag_circuits = [], [] \n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " circuit_real = H_real_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " circuit_imag = H_imag_circ_1#.compose(hamiltonian_circuits[count], list(range(n_qubits)))\n", - " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.bind_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " H_real_circuits.append(circuit_real)\n", - " H_imag_circuits.append(circuit_imag)\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Execute circuits for $\\tilde{S}$ with the Estimator" - ] - }, - { - "cell_type": "code", - "execution_count": 15, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "210 circuits to run\n" - ] - } - ], - "source": [ - "estimator = Estimator()\n", - "\n", - "jobs = {'S': {'real':[], 'imag':[]},\n", - " 'H': {'real':[], 'imag':[]}\n", - " } # store executed jobs\n", - "\n", - "\n", - "shots = 100000\n", - "observable = 'I'*(n_qubits) + 'Z'\n", - "\n", - "job_size_S = 20\n", - "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", - "\n", - "\n", - "\n", - "print(len(S_real_circuits), 'circuits to run')\n", - "\n", - "S_real_results_list, S_imag_results_list = [], []\n", - "for i in range(len(job_idxs_S)-1):\n", - "\n", - " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['real'].append(job.job_id())\n", - " S_real_results = job.result()\n", - "\n", - " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['imag'].append(job.job_id())\n", - " S_imag_results = job.result()\n", - "\n", - "\n", - " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n", - "# np.save(f'S_real_results_{i}', S_real_results); np.save(f'S_imag_results_{i}', S_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And for $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 16, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "5670 circuits to run\n" - ] - } - ], - "source": [ - "estimator = Estimator()\n", - "\n", - "jobs['H']['real'], jobs['H']['imag'] = [], []\n", - "shots = 100000\n", - "\n", - "\n", - "job_size = 50\n", - "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", - "\n", - "print(len(H_imag_circuits), 'circuits to run')\n", - "\n", - "H_real_results_list, H_imag_results_list = [], []\n", - "for i in range(len(job_idxs)-1):\n", - " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", - "\n", - "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_real.job_id()}\")\n", - " jobs['H']['real'].append(job_real.job_id())\n", - " H_real_results = job_real.result()\n", - "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_imag.job_id()}\")\n", - " jobs['H']['imag'].append(job_imag.job_id())\n", - " H_imag_results = job_imag.result()\n", - "\n", - "\n", - " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n", - " # np.save(f'H_real_results_{i}', H_real_results); np.save(f'H_imag_results_{i}', H_imag_results)\n" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "## Step 4: Post-process and analyze results" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Once we have the results of the circuit executions we can post-process the data to calculate the matrix elements of $\\tilde{S}$" - ] - }, - { - "cell_type": "code", - "execution_count": 17, - "metadata": {}, - "outputs": [], - "source": [ - "S_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - "\n", - " eff_count = count % (job_size_S)\n", - " res_idx = count // (job_size_S)\n", - "\n", - " S_real_results = S_real_results_list[res_idx]\n", - " S_imag_results = S_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = S_real_results.values[eff_count]\n", - " expval_imag = S_imag_results.values[eff_count]\n", - "\n", - " # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - " # Fill-in matrix elements\n", - " S_circ[idx_bra, idx_ket] = expval\n", - " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", - "\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And the matrix elements of $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 18, - "metadata": {}, - "outputs": [], - "source": [ - "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " eff_count = count % (job_size)\n", - " res_idx = count // (job_size)\n", - "\n", - " H_real_results = H_real_results_list[res_idx]\n", - " H_imag_results = H_imag_results_list[res_idx]\n", - "\n", - " # Get expectation values from experiment\n", - " expval_real = H_real_results.values[eff_count]\n", - " expval_imag = H_imag_results.values[eff_count]\n", - "\n", - " # # Get expectation values\n", - " expval = expval_real + 1j*expval_imag\n", - "\n", - "\n", - " # Fill-in matrix elements\n", - " H_eff_circ[idx_bra, idx_ket] += coeff*expval\n", - " if idx_bra != idx_ket: # don't duplicate terms on diagonal\n", - " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", - "\n", - "\n", - "\n", - " count+=1" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Finally, we can solve the generalized eigenvalue problem for $\\tilde{H}$:\n", - "\n", - "$$\\tilde{H} \\vec{c} = c \\tilde{S} \\vec{c}$$\n", - "\n", - "and get an estimate of the ground state energy $c_{min}$" - ] - }, - { - "cell_type": "code", - "execution_count": 19, - "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "The estimated ground state energy is: 8.975147310913348\n", - "The estimated ground state energy is: 0.6699145941880671\n", - "The estimated ground state energy is: 1.3257378975608196\n", - "The estimated ground state energy is: -3.3030639423840706\n", - "The estimated ground state energy is: -3.9934796043575798\n", - "The estimated ground state energy is: -3.003872747466045\n", - "The estimated ground state energy is: -2.5086442931004727\n", - "The estimated ground state energy is: -5.48481710169914\n", - "The estimated ground state energy is: -5.545506988684572\n", - "The estimated ground state energy is: -6.98377741561271\n", - "The estimated ground state energy is: -6.676634627880108\n", - "The estimated ground state energy is: -7.6408885159105715\n", - "The estimated ground state energy is: -7.524234968608674\n", - "The estimated ground state energy is: -7.093259720004493\n", - "The estimated ground state energy is: -7.282617495801976\n", - "The estimated ground state energy is: -8.530915996980566\n", - "The estimated ground state energy is: -7.592245638927923\n", - "The estimated ground state energy is: -7.973568152294788\n", - "The estimated ground state energy is: -8.215496239766923\n", - "The estimated ground state energy is: -8.346530278432619\n" - ] - } - ], - "source": [ - "gnd_en_circ_est_list = []\n", - "for d in range(1, krylov_dim+1):\n", - " # Solve generalized eigenvalue problem\n", - " gnd_en_circ_est = solve_regularized_gen_eig(H_eff_circ[:d, :d], S_circ[:d, :d], threshold=1e-2)\n", - " gnd_en_circ_est_list.append(gnd_en_circ_est)\n", - " print('The estimated ground state energy is: ', gnd_en_circ_est)" - ] - }, - { - "cell_type": "code", - "execution_count": 20, - "metadata": {}, - "outputs": [ - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": {}, - "output_type": "display_data" - } - ], - "source": [ - "plt.plot(range(1, krylov_dim+1), gnd_en_circ_est_list, color = 'blue', linestyle='-.' , label = 'estimate')\n", - "plt.xticks(range(1, krylov_dim+1), range(1, krylov_dim+1))\n", - "plt.legend()\n", - "plt.xlabel('Krylov space dimension')\n", - "plt.ylabel('Energy')\n", - "plt.title('Estimating Ground state energy with Quantum Krylov')\n", - "plt.show()" - ] - } - ], - "metadata": { - "kernelspec": { - "display_name": "Python 3", - "language": "python", - "name": "python3" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.17" - } - }, - "nbformat": 4, - "nbformat_minor": 2 -} From 9ab64ab2ec992ff1b62891fa1fce1466f022f913 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 26 Feb 2024 12:43:18 -0700 Subject: [PATCH 16/22] revise introduction --- ...h the quantum krylov subspace method.ipynb | 32 +++++++++++-------- 1 file changed, 19 insertions(+), 13 deletions(-) diff --git a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index 43a7eb0..6e0d6cb 100644 --- a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -13,16 +13,17 @@ "source": [ "## Step 1: Map problem to quantum native format\n", "\n", - "Given a matrix H that we are interested in, subspace methods use a set of states as a basis for the construction of a smaller representation of H, which captures its properties of interest (e.g. lowest eigenvalue).\n", + "Across disciplines, we're interested in learning ground state properties of quantum systems. Examples include understanding the fundamental nature of particles and forces, predicting and undestanding the behavior of complex materials and understanding bio-chemical interactions and reactions. Because of the exponential growth of the Hilbert space and the correlation that arise in entangled systems, classical algorithm struggle to solve this problem for quantum systems of increasing size. At one end of the spectrum, existing approach that take advantage of the quantum hardware focus on variational quantum methods (e. g. variational quantum eigen-solver). These techniques face challenges with current devices because of the high number of function calls required in the optimization process, which is incompatible with advanced error mitigation techniques, thus limiting their efficacy to small systems. At the other end of the spectrum, there are fault-tolerant quantum methods with performance guarantees (e.g. [quantum phase estimation](https://arxiv.org/pdf/quant-ph/0604193.pdf)) which require require deep circuits that can be executed only on a fault-tolerant device. For these reasons, we introduce here a quantum algorithm based on subspace methods (as reviewed [here](https://arxiv.org/pdf/2312.00178.pdf)), the quantum Krylov algorithm. This algorithm performs well at large scale on existing quantum hardware, shares similar [performance guarantees](https://arxiv.org/pdf/2110.07492.pdf) as phase estimation, are compatible with advanced error mitigation techniques and could provide results that are classically inaccessible.\n", "\n", + "Let us now go into more details of how subspace methods, and the quantum Krylov algorithm in particular, work. Given a matrix $H$ for which we want to know its lowest eigenvalue, subspace methods construct of a smaller representation $\\tilde{H}$ of $H$, which captures its properties of interest. In the case of the quantum Krylov algorithm, the Krylov subspace is used to construct the effective representation.\n", "\n", - "What is the Krylov subspace? \n", + "### What is the Krylov subspace? \n", "\n", - "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", + "By definition, the Krylov subspace $K^r$ of order $r$ is the subspace spanned by vectors obtained by multiplying higher powers of $H$, up to $r-1$, with a reference vector $\\vert \\psi \\rangle$.\n", "\n", - "Is the Krylov subspace for a given matrix $H$ and vector $\\vert \\psi \\rangle$ of order $r$ where $\\vert \\psi \\rangle$ is an aribitrary state called \"reference state\".\n", + "$$K^r = \\left\\{ \\vert \\psi \\rangle, H \\vert \\psi \\rangle, H^2 \\vert \\psi \\rangle, ..., H^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", "\n", - "The reference state can be expanded in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", + "We can gain some insight on why this subspace is interesting by expanding the reference state in terms of the eigenvectors $\\vert \\lambda_i \\rangle$ of the matrix $H$:\n", "\n", "$$ \\vert \\psi \\rangle = c_1 \\vert \\lambda_1 \\rangle + c_2 \\vert \\lambda_2 \\rangle + ... + c_n \\vert \\lambda_n \\rangle $$\n", "\n", @@ -32,30 +33,35 @@ "\n", "Which means that the component $k$ with the largest eigenvalue $\\lambda_k$ is amplified by the power iteration (This can also be a problem as the basis vector become too similar to each other). The same is true for the smallest eigenvalue, if we consider power iteration of the matrix $H^{-1}$.\n", "\n", - "Why is it useful for ground state energy problems?\n", + "### Why is it useful for ground state energy problems?\n", "\n", "The Krylov subspace is constructed using the power iteration method. Therefore, states in the Krylov subspace corresponding to the multiplication with higher power of the matrix with the reference states will have the contribution of the ground state $\\vert \\lambda_k \\rangle$ enhanced.\n", "\n", "\n", - "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}$ which can be shown to give similar convergence guarantess as the power method. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", + "The Krylov subspace that we use classically cannot be accessed on a quantum computer as $H$ is not a unitary matrix. Instead, we can use the time-evolution operator $U = e^{-iHt}$ which can be shown to give similar [convergence guarantees](https://arxiv.org/pdf/2110.07492.pdf) as the power method. Powers of $U$ then become different time steps $U^k = e^{-iH(kt)}$.\n", "\n", "\n", "$$K_U^r = \\left\\{ \\vert \\psi \\rangle, U \\vert \\psi \\rangle, U^2 \\vert \\psi \\rangle, ..., U^{r-1} \\vert \\psi \\rangle \\right\\}$$\n", "\n", + "The subspace $K_U^r$ obtained in this way is called \"Unitary\" Krylov subspace.\n", + "\n", + "\n", + "### How does the algorithm work in summary?\n", + "\n", "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", "\n", "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", "\n", - "Where $\\tilde{H}=\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", + "Where $\\tilde{H}=\\langle \\psi_m \\vert H \\vert \\psi_n \\rangle$ is the Hamiltonian matrix in the Krylov subspace $K_D = \\left\\{ \\vert \\psi_0 \\rangle, \\vert \\psi_1 \\rangle, ..., \\vert \\psi_D \\rangle \\right\\}$ with dimension $D$, $\\vec{c}$ is a vector of variational coefficients that are optimized to get the lowest value of the energy $c_{min}=E_{GS}$ and $\\tilde{S}=\\langle \\psi_m \\vert \\psi_n \\rangle$ is a matrix of overlaps between states of the Krylov subspace.\n", "\n", - "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi \\rangle$ under the Hamiltonian $\\hat{H}$ for a certain time: $\\vert \\psi_l \\rangle = \\hat{U} \\vert \\psi \\rangle = e^{-i \\hat{H} t_l}\\vert \\psi \\rangle$. \n", + "Each of the Krylov subspace's vectors are obtained by time-evolving the reference state $\\vert \\psi \\rangle$ under the Hamiltonian $H$ for a certain time: $\\vert \\psi_l \\rangle = U \\vert \\psi \\rangle = e^{-i H t_l}\\vert \\psi \\rangle$. \n", "\n", "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", "\n", - "$$\\langle \\psi_m \\vert \\hat{H} \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i \\hat{H} t_m} \\hat{H} e^{-i \\hat{H} t_n} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i \\hat{H} m \\delta t} \\hat{H} e^{-i \\hat{H} n \\delta t} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert \\hat{H} e^{-i \\hat{H} (n-m) \\delta t} \\vert \\psi \\rangle$$" + "$$\\langle \\psi_m \\vert H \\vert \\psi_n \\rangle$$\n", + "$$\\langle \\psi \\vert e^{i H t_m} H e^{-i H t_n} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert e^{i H m \\delta t} H e^{-i H n \\delta t} \\vert \\psi \\rangle$$\n", + "$$\\langle \\psi \\vert H e^{-i H (n-m) \\delta t} \\vert \\psi \\rangle$$" ] }, { From 6ceab7de22b6ecc7850595ab7f4e4546f80f7f0d Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 26 Feb 2024 15:16:33 -0700 Subject: [PATCH 17/22] review more comments --- ...h the quantum krylov subspace method.ipynb | 116 ++++++++++-------- 1 file changed, 63 insertions(+), 53 deletions(-) diff --git a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb index 6e0d6cb..09ac02b 100644 --- a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb @@ -48,7 +48,7 @@ "\n", "### How does the algorithm work in summary?\n", "\n", - "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure theyr overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", + "First, we want to find a compact represention of the Hamiltonian in the Krylov subspace $\\tilde{H}$. Given that the Krylov subspace has dimension $r$, the Hamiltonian projected into the Krylov subspace will have dimensions $r \\times r$. We can then easily diagonalize the projected Hamiltonian $\\tilde{H}$. However, we cannot directly diagonalize $\\tilde{H}$ because of the non-orthogonality of the Krylov subpace vectors. We'll have to measure their overlaps and construct a matrix $\\tilde{S}$ collecting them to do so. We can then solve the generalized eigenvalue problem\n", "\n", "$$ \\tilde{H} \\ \\vec{c} = c \\ \\tilde{S} \\ \\vec{c} $$\n", "\n", @@ -74,7 +74,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": {}, "outputs": [], "source": [ @@ -82,6 +82,7 @@ "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pylab as plt\n", + "from typing import Union, List\n", "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", @@ -93,7 +94,27 @@ "from qiskit.providers.fake_provider import Fake20QV1\n", "from qiskit.primitives import Estimator\n", "\n", - "def solve_regularized_gen_eig(h, s, threshold, k=1, return_dimn=False):\n", + "def solve_regularized_gen_eig(h: np.ndarray, s:np.ndarray, threshold: float, k: int =1, return_dimn: bool = False) -> Union[float, List[float]]:\n", + " \"\"\"\n", + " Method for solving the generalized eigenvalue problem with regularization\n", + "\n", + " Args:\n", + " h (numpy.ndarray):\n", + " The effective representation of the matrix in the Krylov subspace\n", + " s (numpy.ndarray):\n", + " The matrix of overlaps between vectors of the Krylov subspace\n", + " threshold (float):\n", + " Cut-off value for the eigenvalue of s\n", + " k (int):\n", + " Number of eigenvalues to return\n", + " return_dimn (bool):\n", + " Whether to return the size of the regularized subspace\n", + "\n", + " Returns:\n", + " lowest k-eigenvalue(s) that are the solution of the regularized generalized eigenvalue problem\n", + "\n", + " \n", + " \"\"\"\n", " s_vals, s_vecs = sp.linalg.eigh(s)\n", " s_vecs = s_vecs.T\n", " good_vecs = np.array([vec for val, vec in zip(s_vals, s_vecs) if val > threshold])\n", @@ -121,22 +142,15 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 5, "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "SparsePauliOp(['ZZIIIIIIII', 'IZZIIIIIII', 'IIZZIIIIII', 'IIIZZIIIII', 'IIIIZZIIII', 'IIIIIZZIII', 'IIIIIIZZII', 'IIIIIIIZZI', 'IIIIIIIIZZ', 'XXIIIIIIII', 'IXXIIIIIII', 'IIXXIIIIII', 'IIIXXIIIII', 'IIIIXXIIII', 'IIIIIXXIII', 'IIIIIIXXII', 'IIIIIIIXXI', 'IIIIIIIIXX', 'YYIIIIIIII', 'IYYIIIIIII', 'IIYYIIIIII', 'IIIYYIIIII', 'IIIIYYIIII', 'IIIIIYYIII', 'IIIIIIYYII', 'IIIIIIIYYI', 'IIIIIIIIYY'],\n", - " coeffs=[-1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j, -1.+0.j,\n", - " -1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j, 1.+0.j,\n", - " 1.+0.j, 1.+0.j, 1.+0.j])" - ] - }, - "execution_count": 3, - "metadata": {}, - "output_type": "execute_result" + "name": "stdout", + "output_type": "stream", + "text": [ + "[('ZZIIIIIIII', -1), ('IZZIIIIIII', -1), ('IIZZIIIIII', -1), ('IIIZZIIIII', -1), ('IIIIZZIIII', -1), ('IIIIIZZIII', -1), ('IIIIIIZZII', -1), ('IIIIIIIZZI', -1), ('IIIIIIIIZZ', -1), ('XXIIIIIIII', 1), ('IXXIIIIIII', 1), ('IIXXIIIIII', 1), ('IIIXXIIIII', 1), ('IIIIXXIIII', 1), ('IIIIIXXIII', 1), ('IIIIIIXXII', 1), ('IIIIIIIXXI', 1), ('IIIIIIIIXX', 1), ('YYIIIIIIII', 1), ('IYYIIIIIII', 1), ('IIYYIIIIII', 1), ('IIIYYIIIII', 1), ('IIIIYYIIII', 1), ('IIIIIYYIII', 1), ('IIIIIIYYII', 1), ('IIIIIIIYYI', 1), ('IIIIIIIIYY', 1)]\n" + ] } ], "source": [ @@ -160,7 +174,7 @@ "\n", "# Get operator\n", "H_op = SparsePauliOp.from_list(H_tot)\n", - "H_op" + "print(H_tot)" ] }, { @@ -172,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [ @@ -193,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -203,7 +217,7 @@ "
" ] }, - "execution_count": 5, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -222,22 +236,21 @@ "source": [ "### Time evolution\n", "\n", - "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$" + "We can realize the time-evolution operator generated by a given Hamiltonian: $U=e^{-iHt}$ via the [Suzuki-Trotter approximation]((https://docs.quantum.ibm.com/api/qiskit/qiskit.synthesis.SuzukiTrotter))." ] }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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" + "" ] }, - "execution_count": 16, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -250,9 +263,7 @@ "\n", "qr = QuantumRegister(n_qubits)\n", "qc_evol = QuantumCircuit(qr)\n", - "qc_evol.append(evol_gate, qargs=qr)\n", - "\n", - "qc_evol.decompose().draw('mpl', fold=-1, scale=0.2)" + "qc_evol.append(evol_gate, qargs=qr)\n" ] }, { @@ -272,7 +283,7 @@ "\\begin{equation}\n", " |0\\rangle_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle+|1\\rangle\\Big)_a|\\psi_0\\rangle\\quad\\longrightarrow\\quad\\frac{1}{\\sqrt{2}}\\Big(|0\\rangle_a|\\psi_0\\rangle+|1\\rangle_aU_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", "\\end{equation}\n", - "To measure $X$, first apply $H$...\n", + "Where $P$ is one of the terms in the decomposition of the Hamiltonian $H=\\sum P$. To measure $X$, first apply $H$...\n", "\\begin{equation}\n", " \\longrightarrow\\quad\\frac{1}{2}|0\\rangle_a\\Big(|\\psi_0\\rangle+U_j^\\dagger PU_k|\\psi_0\\rangle\\Big) + \\frac{1}{2}|1\\rangle_a\\Big(|\\psi_0\\rangle-U_j^\\dagger PU_k|\\psi_0\\rangle\\Big)\n", "\\end{equation}\n", @@ -291,7 +302,7 @@ }, { "cell_type": "code", - "execution_count": 17, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -303,12 +314,12 @@ }, { "data": { - "image/png": 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", + "image/png": 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", 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" + "
" ] }, - "execution_count": 17, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -354,21 +365,21 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 79349\n" + "The circuit has 2Q gates depth: 78772\n" ] } ], "source": [ - "circuit_trans = transpile(circuits=qc_real.decompose().decompose(), backend=Fake20QV1())\n", + "circuit_trans_unopt = transpile(circuits=qc_real.decompose().decompose(), backend=Fake20QV1())\n", "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans.depth(lambda x: x[0].num_qubits == 2))\n" + "print('The circuit has 2Q gates depth: ', circuit_trans_unopt.depth(lambda x: x[0].num_qubits == 2))\n" ] }, { @@ -450,22 +461,22 @@ "metadata": {}, "source": [ "### Decompose time-evolution operator with Suzuki-Trotter decomposition\n", - "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation." + "Instead of implementing the time-evolution operator exactly we can use the Suzuki-Trotter decomposition to implement an approximation of it. Repeating several times a certain order Trotter decomposition gives us further reduction of the error introduced from the approximation. In the following, we directly build the Trotter implementation in the most efficient way for the interaction graph of the Hamiltonian we are considering (nearest neighbor interactions only). In practice we insert Pauli rotations $R_{xx}$, $R_{yy}$, $R_{zz}$ with a parametrized angle $t$ which correspond to the approximate implementation of $e^{-i (XX + YY -ZZ) t}$. This gives a much shallower circuit than what is obtained using the generic `PauliEvolutionGate()` functionality. " ] }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 12, "metadata": {}, "outputs": [ { "data": { - "image/png": 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qx6Hq+kJEGzliJcQSenWlz3fG8PG/XsPw+qKufmvg83rBZ8En5Ow27A6HugznqS9aRvU4VF0/0lnWA6DRcSg9ILKpHoOq67cG0gdES6keh6rrR7qo6QHnqS+aRhZWQqz80CmlDUx1/Ujn83pZc9UduE6Xhb1WXJcOTN23LKCRWZWhsfqi5VSPQ9X1I5mVPQCCj0PpAZFP9RhUXT/SSR8QoaB6HKquH8miqQc0Vl80nRwfFmJln5xgwMyJyg69U10/4vkMy5qo63RZ8FVoizI0Wl+0mOpxqLp+RLOwB0Aj41B6QMRTPQZV14940gdECKgeh6rrR7Qo6gGN1hdNJkeshFjR2u1RXV8IoX4cqq4vRLRTPQZV1xdCqB+HqusLEW1kCVMIIYQQQgghhBCimWRhRQghhBBCCCGEEKKZZGFFCCGEEEIIIYQQopm0Xlh55JFH6NevH3a7nXXr1vldN2bMGHr37k1GRgYZGRnk5uaGvP7YfzzILfufZvDPvh3y+46kDOF0sBReOGz+XOpWGqVRaVPHMPGFx5iw/lE6D+odtRnCwWvA9pOw/EPYeARcHtWJAukwBnXIEC6VHth20vx53+d6njtNh/GnQ4ZwKa6CfxTBMx/BB2dVpwmkw/jTIUM4fXC2bi7webXaLI3RYQzqkCEcfAbsOAVPf2juB5UyF9A2Q7i4PPDGKfPnt0+b80Pd6DD+dMgQLqddsLoIVnwEB86oTtM8Wp+8duzYsdx6663MmDEj6PULFy4kOzs7bPV33PckKaMGE5/SJWw1IiFDOHgNeDAfXj9Z1zx/thvmZ8L4y9Rmq8+Z2I4Bt09k06RfEt+tM6OW3MWWyfOiLkM4lLrh9jfgVBW4feC0wx/3w19HQt9E1enq6DAGdcgQDu+Xwp1vQs2X3wT5p4Pwn0Ow7BpoH6s0Wi0dxp8OGcLlhcPwm3fNv/J4DVj6AYxNgYczwW5Tnc6kw/jTIUM4GAbkvgMvHaubC9y3Bx4YDNm9lEbzo8MY1CFDOJTXwB074EiF+V7gtMMf9sNfRsIVHVWnq6PDGNQhQzgUlsEPd0C119z+8/vw70Pw9FehYxu12c7RYfzpkCFcth6Dh/fWzQWW2WBUV/j1MHBoMhe4GMqPWCktLWX69OkMHDiQIUOGcPfddzNz5kwAsrKySE1NbdL9lZSUMGTIEOLi4lqcrfLE5y2+j9aQIRw2HDaPVHD76iZTHgNy3oHPXEqj+UnKTOPU7vfx1XgoP1JMbLu22J3WrkfqkCEcfvsuHK2AKq+5D1R54YsamJ1nTrZ1ocMY1CFDqPkMuHc3lHug+suFlWofHKowF9h0ocP40yFDOJyoNBdVanzma+8xzPeE/54wJ1m60GH86ZAhHLYeh5ePB84FfvseHK9Um60+HcagDhnCYdEB+LQcXPXmAhUeuG+3Xkct6DAGdcgQaoYBc/aY87/6c4FjFeb7gy50GH86ZAiH0y5zUaXhXGBHcd2RjJFC+asxZcoUJk2axMqVKykpKSEtLY0FCxZc1G0feOAB5s2bR3p6Oo899hjp6ekkJibyyiuvcNNNN13w9pWVlRQUFNRuGx5vsx9Hc+3duxdbjENJhoa1rbTqVDouX7vAK3w+Vuw+xnXtS6wPReDz36ZTe9ylFbXb7rIK2nRMoKq4NCT1gr0GVmZQtQ94DPjv8Ux8+C9DG0BJpY/1uz+gp7PK8lxgfR9Q2QOC1bfKx9XtKHOnAf61a3yw5YiPG3zvYFPwVwqrewBceB9ojT0A4MWyrhi+S2n4Nx6XF57Z/wWXFH+kJJfMBayzsrgvLm/7gMsNn48Ve04wocMpBamkD1jFMGDTsQxqgvydt8zt5fldhfRtUxHkluGn+r1YdX2rHHW35VRlOkaDfcBjwP9OGOzJf4cYm/UrbNHWA4LVt8r/ypOw+brTcD7o8sKqg5X0Ol0Q/IYW6N+/P/Hx8Rf9+0oXVrZt20ZxcTH33nsvAMnJyaSkpDB8+PAL3nbVqlX07NkTwzBYsWIF48aNo6ioCKfTSefOnS+qfkFBAUOHDq3ddmBjebcLL8iE0ogRI/BS1zCszNCwtpUGPllAXPf0gMurazz8cclf+Pnzv1GQKvD5d5eW40ysG1DO9vFUl5aHrF6w18DKDKr2AZszjiH/Cr5w4qos53szf0j5wTcsTmWyug+o7AHB6lulfcZY+tz/PI74DgHX1RgwbPgwJYcuWd0D4ML7QGvsAQAp/5dLtym/xBZkHvfuB0UMnTA08AoLyFzAOgP+mE98nyEBl9f44MmnV/Lgc79SkEr6gJWG/MeLLcjx81UVFfww52eUvf2i9aFQ/16sur5V2vUfSd+cF3G0DVxg9Rpw9TWj8LmsX1yLth4QrL5Vun77flK+Ox97bOBk4KNDxxg6Uc1cACA/P58hQwLfoxqjdGElLy+PESNG1G6fPn2aY8eOMXjw4AvetmfPngDYbDZmzJjB3LlzOXToUJM+OtS/f3/y8/Nrtw2Pl/cm/7YJj6Dldu/eHbA6aVWGhrWt9HxpIv8t9+FtsELdJjaGP8+exuW/mKIkV8Pnv+Ttj8i8/7vYYhzEd+1ETaULnzt0Z1UL9hpYmUHlPvDIqUqO1ASuArdt146tK/9EG7uaSZ7VfUBlDwhW3ypVPjuzjycQuCcb9GlTybK33rI8E1jfA+DC+0Br7QEfVifwp8/A3WCox+Bj6uBkvlnv/dlKMhewzsaybmwp8wUcseC0w+9/MoX0e69Xkkv6gHUeL66g0J0ADY5gbROfwKa//oZ4+2NKcql+L1Zd3ypuw8Z9x+MD3gcAejirWLZjm+WZIPp6QLD6VjnkbsvjxbHUNLg8Bh839uvAKkVzATDXCppC6cJKcnIya9euxev14vV6ufPOO0lPT8fpdJ73di6Xi/LycpKSkgDYvHkzDoeDHj16NKl+fHy83yqUr8bDe/WuH/n7H5M8LB2HM4akq/rw6g8eb9L9X4zMzEzssXUvg5UZGta20uXVkP8alLnNv04DxDngq5fYuWl403biUGr4/LvPVlDwzEtMWJuLYRjseWhFSOsFew2szKByH3j4NPx0p/mXyS8/VkusHe4d6ODq3plKMoH1feBCPSDcGVTuA3cVwpMFdZ+rtgNOh42HRyQwsNPF/4UglKzuAXDhfaC19oBMA3buhrc+q9sHYmzQuY2dn301hY7OFCW5ZC5gnTQ37Hnd/CYg95f7QJwdhiTZuWVEPyUfBwTpA1Z6uNQ8eW2NF8598CHWDj/pb+eatAwlmUDmAlaa08U8YXH9uUCsHR7+SjyZXWQuYFUGVfvAEGDPW7D9lPnxHzDnAh1i7cwe2ZWkuK6WZ2oupQsrU6dOZc2aNaSnp9OrVy/69etHly51Z7rOyclh+fLllJSUsH//fmbNmsWuXbtwOp1MmDABt9uN3W6nU6dObNy4kdjY0H6NxJtzngrp/UVqhnDo3Ab+fi089zG8dhLaxcCUy+HGnqqTBSpc/SqFq1+N+gyhltEFVo6Gv30I73wOxS64byB8R7Nvj9NhDOqQIRxuTYNe7eHZQvPboQZ1hh/0hdTAI4KV0mH86ZAh1Gw2+MNXYN0h+HsRHK6ACZfBPVdAx/P/fcVSOow/HTKEQwcnPHct/L+P4b/HzT+wfKuX+Z+qRZXG6DAGdcgQagM6wnOj4emPIP8zcy5w9wD4bh/VyfzpMAZ1yBAON10O3dvByo/gWKX5bVAz+ur1DZGgx/jTIUM4PDrU/GKT5z42T2Y9NgV+NhC6tPy7aCyldGElLi6OjRs31m5Pnz6da6+9tnY7JyeHnJycoLfNb+SwIJ/Px7hx49i3bx/f+MY3+N3vfkdmprq/fovGdYmDewaa/4nolNbB/Cq1glK4bRsM6qQ6kbDaNV3N/0R0irHDlN5wZSezB9zcW5+v1xTW6OiEnw4w/xPR6fL28MiQurlAZuv6NmFxEUYkm/+J6OSwQXYv6J9o9oBb+0Teogpo8K1A9eXl5TF79uwW3YfdbueVV14JUSIhhBBCCCGEEEKIxmm1sHLw4EHVEYQQQgghhBBCCCEumlYLK0JEioTLkrnx5d9x5uAhHHFOPln3BgeXbYq6DEJEM9VjUHV9IaKdDmNQhwxCRDPVY1B1fVFHFlaEaKbT7xax9eZcbHY72a8v5MPnXsFTVR11GYSIZqrHoOr6QkQ7HcagDhmEiGaqx6Dq+sJkVx1AiEjnaOvE7ozB5lA3nHTIIEQ0Uz0GVdcXItrpMAZ1yCBENFM9BlXXj3ZyxIoQzdRlcCrXr51P5ysuZ9+if1NTXhWVGYSIZqrHoOr6QkQ7HcagDhmEiGaqx6Dq+sIky1n12W3EdelgWbm4Lh3AblOSIWht0SSn3y3ixZseZstND5EyehAAycPSueJHN9D2ko6MeHRGwLYVGYY9NI123ZPoclUfBv74mwHb4gIs7AMqe0Cj9UWTqO4D0gPCQOYCoglU94DGMkgfaCHV78Wq64smUd0HpAfoQY5YqcfucDB13zLwGRYVtGF3ONRkCFJbNM+Zg4eoPHmG7l/P5Nire0nK6EPWgjvYftdiPBUuv20rMux9fDUjHp2Bp8rNnnl/wxHn9NsW52dpH1DZAxqpL5pHdR+QHhA6MhcQzaG6BzTMIH2gZVS/F6uuL5pHdR+QHqCWLKw0YHc4QHFv0SGDaJoDSzeS9ZvbOfbqXtr36kr1mXJiE9riqXAFbFuRoXhPAWWfngTA63L7bYsLUz0GVdcXzaO6D0gPCB0dxqAOGUTTqO4BDTNIH2gZ1WNQdX3RPKr7gPQAdeSjQEI0Q/nRErbenFu7XVpwmBe/9RDp08dz5OV89sxbQebcmxkwc6LfdihPJtVYhtZkw4YNLFq0iMmTJ7N+/franzdv3lz7Oy6XiyVLlgS9/f79+8nOzqawsLD2sry8PObPn09OTg47d+5k6dKlHDhwgJycHDweD6tXr+b48eNhf2wi8qnuA9IDTNIDhCqqe8D5MrQm0geEzlT3AekBJh16gByxIkQIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIV06EPSA8wSQ8QKujQA0D6wDnSB4QKOvQB6QEmq3qALKwIIbRVUVHBE088wcKFC/1+rq+oqIjx48ezadMmVqxYUXv5888/f8H7HzNmDJmZmaSlpZGamsq0adOIiYnh7NmzIX8sQoimkx4ghJA+IER0i5QeIAsrQght3XfffSQlJbFkyRK2bNnCsGHDWLJkCVlZWWRlZQGQmprKkSNHmDRpEpMmTfK7/ZEjR9i6dSuFhYWMGjWKQYMGccMNN5Cbm4thGCQnJ5OcnAxA3759Wbx4MTNnziQxMdHyxyqECCQ9QAghfUCI6BYpPcBmGIZFp70XQn++Gg+ret5iWb1ph1djj/Vf37QyQ7D6KhSUwm3b4LnR0L9j027rcrlYvnw5s2bNCkmW1atXM3r0aFJSUkJyfyKyWN0DIHAcSg9o2m2lB4hQkz6ghvQBoYto6wHB6qsQ6T1AfRcVQogWiIuLC1kTBbjlFmvfSIUQLSM9QAghfUCI6KZDD5BvBRIixDJmTw3pGf8jrb4Q0U71GFRdXwihfhyqri9EtNNhDOqQIZrIESsN+Lxe8Fn06Si7zfyOehUZGqktWi6hV1f6fGcMH//rNQyvL+rqtwaW9QGVPeA89UXLqB6Dquu3BjIXEC2lehyqrt8aqH4vVl1ftIwOY1CHDNFEFlbq8Xm9rLnqDlynyyypF9elA1P3LfNrZlZlCFZbhEb5oVNKG5jq+pHOyj6gsgc0Vl+0nOoxqLp+pJO5gAgF1eNQdf1Ip/q9WHV90XI6jEEdMkQTOTaoPp9h2UQKMGs1XIm2KEPQ2iIkyj45wYCZE5Udeqe6fsSzsA+o7AGN1hctpnoMqq4f8WQuIEJA9ThUXT/iqX4vVl1ftJgOY1CHDNFEjlgRIsSK1m6P6vpCRDvVY1B1fSGE+nGour4Q0U6HMahDhmgiy1dCCCGEEEIIIYQQzSQLK0IIIYQQQgghhBDNJAsrQgghhBBCCCGEEM2k9cLKI488Qr9+/bDb7axbt87vujFjxtC7d28yMjLIyMggNzdXTUjRIuU1sOMU7D0NXjlvVlQ6WWm+/iJ6fXgW3jgFp6pUJxEqeHxQUGr+XOVRGkUoUuGBN4sh/zNzfxDRp7iqbi5gyHwwKhWWmXOBE5WqkwgVvAZ8cNb8uSJC5wJan7x27Nix3HrrrcyYMSPo9QsXLiQ7OzusGdKmjqHfbWMxDIPdDz7N5+99EtZ6umYIh+cK4ckCiLGbb6LxMfDHr8DATqqT1Rn7jwfpMqg3B5dv5t1F/47aDOFQ44OH34b/nTD3AYCH3oanvgqd26jNVp8O40+HDOFQ4oJ7dsGhcnMfqPbC+O4wL6Nun9CBDmNQhwzh8M5pmJsHlV9Oon6yC+4dCFN7q83VkA5jUIcM4fCvT2DRAXB8ORdo44DfD4eMLqqT1dFh/OmQIRw8Pnh0H7x4FGK/7Pu/ehueGgmXtFWbrT4dxp8OGcLhTDX8bDd8VGbuA24vjLkUcofU7RM60GEM6pAhHN4vhXt3wxc15vZPd8JPBsC0NKWxmkz57lpaWsr06dMZOHAgQ4YM4e6772bmzJkAZGVlkZqa2qT7e/nll8nKyuLqq6/mD3/4Q4uyORPbMeD2ibz47YfZPutPjHg0+AJPOOmQIRzeOAV/KQC3z5xQV3nhdDX8ZGfdBFsHO+57krdyn436DOHw5/fh9ZNQY5ivP8ChCpizR22u+nQYfzpkCJef7YKPv4Bqn/nXCY8BrxyH5R+qTuZPhzGoQ4ZQK3PDXbvgjNvcB8BccH3iAOSVqM1Wnw5jUIcM4ZD/GSw8YL7+5+YCpW6YtQvOulWnq6PD+NMhQzis+AhePmb2/3NzgaMVcM9utbnq02H86ZAhXObmmUcquL+cC9QYsO0k/Omg6mT+dBiDOmQItSoP3PkmfFZdNxfwGPDXAth+Um22plJ+xMqUKVOYNGkSK1eupKSkhLS0NBYsWHBRt33ggQeYN28e6enpPPbYY6SnpzNgwAC2b99OTEwMY8aM4Uc/+hEJCQlBb19ZWUlBQUHttuHx+l2flJnGqd3v46vxUH6kmNh2bbE7Y/C5Q/cv/71792KLcSjJ0LC2lZ4s7ku1r33A5TVeL0/vPMJX232uIFXg8195Irw5gr0GVmZQtQ/4DFhz/Crchn9trwEHz/jYsvt9usZWW54L/J//1t4DgtW3ytGaOIrK+uNtsL5f7YP/95GHr1S+a3kmCHz+wfo+YGUGle8D/ytPwuvtDvjXr/YZPLm3jLuSPlaSS+YC1vnzZ6m4fYmAze9yr9fLsl3H+XqCmhU2q+cCcOF9oDXOBQCePTaYasP/nyM+4NMyH+t3fUAPp5rPiMpcwBrFHif7P78CT5C5wL8/8TK6eh8OWyM3DqNomwsEq2+VNys6U+PtQeBcAJ585wvaXfKR5ZnO6d+/P/Hx8Rf9+0oXVrZt20ZxcTH33nsvAMnJyaSkpDB8+PAL3nbVqlX07NkTwzBYsWIF48aNo6ioiMsuu6z2d2JiYrDbGz8op6CggKFDh9ZuO7CxvNtNtdttOrXHXVpRu+0uq6BNxwSqikub8jDPa8SIEXip+zCplRka1rbSwKc+JO7SwIWV6hofv168nJP/ekxBqsDnP9yCvQZWZlC1D9jbxJO5piLoddWV5Uyd+RPKD2yzOJWp/vPf2ntAsPpW6ZA5ntS5/8TRLjHguiojhqHDh4PP+pMtWN0D4ML7gJW1rZRy26N0m/JLbAGTZhu7Cw7xzD1Dg90s7GQuYJ0Bi/YS3zsj4PIaHCxc/v+Y++wvrA+F9AErDV0fvK6r8gumzZpNWf4WixOZZC5gjYQrriFt3iYc8R0Crqv22ckadS2+qnLLc0VbDwhW3yrdpvyCS7+bgz3Ios7+w8UMnaBmLgCQn5/PkCFDLvr3lS6s5OXlMWLEiNrt06dPc+zYMQYPHnzB2/bs2RMAm83GjBkzmDt3LocOHar96NCLL75IWlraeVeZ+vfvT35+fu224fHy3uTf1m67S8txJtbd3tk+nurS0A7u3bt3B6xOWpWhYW0r/e10Z/ZUGfga/JWqTaydBfd8n0EPWNvMzmn4/IdbsNfAygyq9gHDgAdOujnjdQZc54xPYOOKP9HeEbhSb4X6z39r7wHB6lul1BvDL060J9irfEmMi/y8PMszgfU9AC68D1hZ20pvV3Xkb5/7Ao5cc+BjwsBLea7e+7OVZC5gnb+fSWF7hS/gyDWnzUvOD6cy9GfjlOSSPmCdeSddnPLEBVzujG/P2r/8lk6ORxWkkrmAVSp8DuYeTyDYcTedHDXs2f56kMX38Iu2HhCsvlUOuNrzl9MO3A3WdOwYjOrdkZWK5gJgrhU0hdKFleTkZNauXYvX68Xr9XLnnXeSnp6O0xn4j636XC4X5eXlJCUlAbB582YcDgc9evQA4PDhw/zud7/jhRdeOO/9xMfH+61C+Wo8vFfv+pK3PyLz/u9ii3EQ37UTNZWukB72B5CZmYk9tu5lsDJDw9pW6lwOt70Ornr/qoqxQa/2Dr43Mg27giYKgc9/uAV7DazMoHIfmHMU5r9jfqb2nDZ2yO5l59pBVynJBP7Pf2vvAcHqW2nSO/DS0brP1AI47fDzzDiGXHrxfyEIJat7AFx4H7CytpUG+2DLa3C8wvxMPZgfCHE67Nyblcxl7ZKV5JK5gHW6VcLu/5lzgXNzaocNusU7+MHIVGUnsZY+YJ37T8IDbwXOBcZ3t3Nd5iAlmUDmAlb6zn74zyH/fxM47TD7KidDe8hcQFV9q2QY8OLrUFRunmftHKfDxtysLvRur9GZzC9A6cLK1KlTWbNmDenp6fTq1Yt+/frRpUvdk5eTk8Py5cspKSlh//79zJo1i127duF0OpkwYQJutxu73U6nTp3YuHEjsbGxVFZWMn36dJYtW0a7du1alM99toKCZ15iwtpcDMNgz0MrWvqQIzJDOFyeAMu/Cr/fD/s+NydU13SFnEyULaoEM/L3PyZ5WDoOZwxJV/Xh1R88HpUZwmH8Zea3QCw5CEcrIdEJ0/rA9zQ6A7gO40+HDOHyq6sgJR6eLTRPWHdpW5h9pfltADrRYQzqkCHUYuzwt2tg4X7YetycUA1NgtkD4bKWvX2HlA5jUIcM4ZASDytGwR/2w1ufmXOBq5MhZ4he3wymw/jTIUM4jO4GC4aZJ60+VAEdYuG7qTCjn+pkdXQYfzpkCJd7B0JSG3im0PxWmEvizMvGdledzJ8OY1CHDKFmt8FfvwpPHITNR8xF1qs6m/PB3oFnjdCazTD0+bb46dOnc+211zb69coXY/HixSxYsIC+ffsCdediuRi+Gg+ret7S7NrNMe3w6oDVSasyNKytyvtn4Hvb4bnR0L+j2ixW7wPBXoNo3AcMAyWHegajeh9QXV+FglK4bVt09gCQ9wEwewDo0QdkH1AjmucCIPsAyFxA5gIyF4j2fUCnuUBzqO+i9eTl5TF79uwW3cddd93FXXfdFaJEwgqROnhE6Mg+IER0kx4gZB8Qsg8IEd0ivQdotbBy8KBmX1guhBBCCCGEEEIIcR5aLaxEioTLkrnx5d9x5uAhHHFOPln3BgeXbYq6DEJEMx3GoA4ZhIhmqseg6vpCRDsdxqAOGYQQsrDSbKffLWLrzbnY7HayX1/Ih8+9gqeqOuoyCBHNdBiDOmQQIpqpHoOq6wsR7XQYgzpkECLaaXTO9cjkaOvE7ozB5lD3VOqQQYhopsMY1CGDENFM9RhUXV+IaKfDGNQhgxDRSo5YaaYug1O5fu18Ol9xOfsW/Zua8qqozCBENNNhDOqQQYhopnoMqq4vRLTTYQzqkEGIaCfLmc10+t0iXrzpYbbc9BApowcBkDwsnSt+dANtL+nIiEdnBGxbkWHYQ9No1z2JLlf1YeCPvxmwLS7AbiOuSwdLSsV16WB+ebuiDI3WFxdN+kArZGEPgEbGofSAiKK6D0gPCAPpA6IJVPeAxjJIH2iBKOoBjdYXTSZHrLTQmYOHqDx5hu5fz+TYq3tJyuhD1oI72H7XYjwVLr9tKzLsfXw1Ix6dgafKzZ55f8MR5/TbFudndziYum8Z+AwLitmwOxzqMjRSXzSd9IHWw9IeAEHHofSAyKS6D0gPCB3pA6I5VPeAhhmkDzRfVPWARuqLppOFlRA4sHQjWb+5nWOv7qV9r65UnyknNqEtngpXwLYVGYr3FFD26UkAvC6337a4MLvDAYp7iw4ZRNNIH2g9dBh/OmQQTae6D0gPCB0dxqAOGUTTqO4BDTNIH2g+HcafDhnExZOPAjVD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8k1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLySR+whvQBoTPVfUB6gEl6gFBFdQ84X4bWRPqAiARyxEoIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIVkz4QWtIHRCTSoQ9IDzBJDxAq6NADQPrAOdIHhBVkYUVoq6KigieeeIKFCxf6/VxfUVER48ePZ9OmTaxYsaL28ueff/6C9z9mzBgyMzNJS0sjNTWVadOmERMTw9mzZ0P+WIQQzSN9QIjoJj1ACCF9QEQCWVgR2rrvvvtISkpiyZIlbNmyhWHDhrFkyRKysrLIysoCIDU1lSNHjjBp0iQmTZrkd/sjR46wdetWCgsLGTVqFIMGDeKGG24gNzcXwzBITk4mOTkZgL59+7J48WJmzpxJYmKi5Y9VCBGc9AEhopv0ACGE9AERCWyGYVh0umP9+Wo8rOp5i6U1px1ejT22bn3LygwNa6tSUAq3bYPnRkP/jk27rcvlYvny5cyaNSskWVavXs3o0aNJSUkJyf2JyGN1H1DZA4LVV6ElPQCkD4jQkrmAGjIXEDpR/V6sur4KMhcQkU79O6kQLRAXFxeyBgpwyy3WTqaFEC0nfUCI6CY9QAghfUCoJt8KFGIZs6eG9EzfkVZfCKF+HKquL0S0Uz0GVdcXQqgfh6rrCxFt5IiVEEvo1ZU+3xnDx/96DcPri7r6rYHP6wWfBZ+Qs9vM76dXleE89UXLqB6HqutHOst6ADQ6DqUHRDbVY1B1/dZA+oBoKdXjUHX9SBc1PeA89UXTyMJKiJUfOqW0gamuH+l8Xi9rrroD1+mysNeK69KBqfuWBTQyqzI0Vl+0nOpxqLp+JLOyB0DwcSg9IPKpHoOq60c66QMiFFSPQ9X1I1k09YDG6oumk+PDQqzskxMMmDlR2aF3qutHPJ9hWRN1nS4LvgptUYZG64sWUz0OVdePaBb2AGhkHEoPiHiqx6Dq+hFP+oAIAdXjUHX9iBZFPaDR+qLJ5IiVECtauz2q6wsh1I9D1fWFiHaqx6Dq+kII9eNQdX0hoo0sYQohhBBCCCGEEEI0kyysCCGEEEIIIYQQQjSTLKwIIYQQQgghhBBCNJPWCyuPPPII/fr1w263s27dOr/rxowZQ+/evcnIyCAjI4Pc3Fw1IUWLGAaUulWnECp5fFDiApdXdRKhSvWXr71XzpsWtb6ogdMu8z1BRB/DgLMyF4hqtXMBj+okQhX3l3MBj3yJUdQqr4HPInguoPXJa8eOHcutt97KjBkzgl6/cOFCsrOzw1f/Hw/SZVBvDi7fzLuL/h22OrpnCJddxfCbd+FElbn92/fg8eGQHKc2V0NpU8fQ77axGIbB7gef5vP3PonKDKFmGPD3Ilj2gbmoYrfBN3vCfQPBqdG3vekwBnXIEA4uL/zuPdh0xNz+yU746QCY2lttroZ0GH86ZAiHk5WQsxf2fm5ud4+HX14Fw5LU5qpPh/GnQ4Zwyf8MHtsHRyvM7cf2mXOBS+PV5mpIhzGoQ4ZweP4T+EsBVHjAZoMJl8HPB0GczAW0yxAONT5YuB/+c8jc/slO+FE6/F8fc3/QhQ7jT4cM4fCZC+bvhT2fmdtd4+AXV8HVl6jN1VTKF1ZKS0u55557eOutt2jTpg3XXHMNFRUVPP3002RlZTX5/j788EO+//3v43A46Nu3L08//TS2Zo7KHfc9ScqowcSndGnW7UNBhwzhUFAKs/dAdb1V6YNnYMZ2+M91EKPJsVTOxHYMuH0imyb9kvhunRm15C62TJ4XdRnC4flP4cn36+0DBmw4bP7l+rGhKpP502EM6pAhHB7MhzeLwfPlXyYqPPDEAXMy/c2earOdo8P40yFDOFR74QdvwOcuOHfA2uEKuGcXrBwNaR2Uxqulw/jTIUM4FH0Bd+/ynwt8cBZ+sB3WfUOff1jrMAZ1yBAOGw/DwgP+c4EXj0JpNfxxhNJofnQYgzpkCIdH3oH/HoeaL+cClV54sgAcdrglVWm0WjqMPx0yhIPHBzPfgJNVdUcuH68y/524/Bq4oqPSeE2i/J+vU6ZMISMjgwMHDvDSSy+xcuVKhg0bdlG3feCBBxg0aBBTpkzhgw8+ACA1NZUdO3awfft2bDYb77zzTrOzVZ74vNm3DRUdMoTD0x+Bu8Ghfl7MjwVtO6kkUlBJmWmc2v0+vhoP5UeKiW3XFrvT2vVIHTKEmmHA0g/8J9Ngbv/3uHk4sC50GIM6ZAi145XwxqnAPlDtg6cK1GQKRofxp0OGcPjvcfOw34afAvT4YGWhkkhB6TD+dMgQDqs+qltYPceHucj63+NKIgWlwxjUIUM4PBVkLuD2wc7iuqOYdKDDGNQhQ6h95oKXjwWfDy77EHyafCREh/GnQ4ZweOMUfF4d+HHwGh/87UM1mZpL6auxbds2iouLuffeewFITk4mJSWF4cOHX/C2q1atomfPnhiGwYoVKxg3bhxFRUXExNQ9pNjYWLp3797ofVRWVlJQUDeDNzzWn+Rh79692GLq/iRjZYaGta20v/gKDAI/81PtNdjx4Qk6nlSzutLw+W/TqT3u0rp3dndZBW06JlBVXBqSesFeAyszqNoHqn12zrgzgl4Xg5dX9n5Meptya0N9yeo+oLIHBKtvlf2uDsRwOZ4gb0PFLngr/23sCg4BtroHwIX3gdbYAwB2nk2hytsV8H+hvcC+k1W8/fb7SnLJXMA6e0/2x2sEfuanygtvfnSSS0vUrK5IH7CGYcDJqiFBr3Pg5ZV3PmFw2zKLU5lUvxerrm+Vj6rb4SCNGgJrn3Ub7MzfR1u79SddibYeEKy+Vd4o64rbeykNj/cwgP0l1bz99gHLM53Tv39/4uMv/nOpShdW8vLyGDGi7ji/06dPc+zYMQYPHnzB2/bsaR4nbrPZmDFjBnPnzuXQoUOkpqby4osvMmfOHPr160enTp0avY+CggKGDq37zIEDG8u73dSCR9R0I0aMwEvdEp2VGRrWtlLavI10GDIBm91/ENVUlbPwD3N4aNs/lORq+Py7S8txJtYNKGf7eKpLQ/cP/mCvgZUZlO0DNhtXPXeamITA8Vnp9vD9yWNxlxy2PhfW9wGVPSBYfau0SenLFX96D3ts4NtQTWkxwyer+TyY1T0ALrwPtMoeAHT5xgx63P4EjrYJfpcbXi/7d2xk6ONTleSSuYB1es/5Bx1HTsHu8O8D3qpyli6Zx69fXq4kl/QB6wx+5jixnS4NuLyyuoYf33wD1cc+UJBK/Xux6vpWiU26jCufKsQeG/gPem9FGdeMGAo+6xdWoq0HBKtvlU7XTKXXrOU42rb3u9zw+fj47f8xdP4EyzOdk5+fz5AhwRd/g1G6sJKcnMzatWvxer14vV7uvPNO0tPTcTqd572dy+WivLycpCTz7HabN2/G4XDQo0cPAK6//nquv/567rrrLl588UVuvPHGoPfTv39/8vPza7cNj5f3Jv82RI/u4uzevTtgddKqDA1rW+mj6nYsKoGaepfZ8NGxXRxP/XEusbY5SnI1fP5L3v6IzPu/iy3GQXzXTtRUuvC5Q3fK+mCvgZUZVO4Dm8sq2VzWAXe9v1I48HFlgovlL/5HSSawvg+o7AHB6lvp9yVuiqpj8dT7K0Wszct3elWzol5vtpLVPQAuvA+01h7g8tl54EQcVYaBUe+oFafDxu++NYjeN+uxD1ghWucCn7rjebzYTv292YZB+/g41v/6p8QtuFNJLukD1vnvFx7WnvVRU+99wIGPvgk1LH/h70oygfr3YtX1rbTksyoOuvznAk68jL+0gqfz8pRkirYeEKy+VWoMG784EccXPh9G/X3ADrnjU0n/ppq5AJhrBU2hdGFl6tSprFmzhvT0dHr16kW/fv3o0qXuhEw5OTksX76ckpIS9u/fz6xZs9i1axdOp5MJEybgdrux2+106tSJjRs3EhsbS3V1NW3atAGgQ4cOxMU1/hUz8fHxfqtQvhoP79W7fuTvf0zysHQczhiSrurDqz94POTPQWZmpt9fbK3M0LC2lYYAHY+a3wTk9pmfq7s8wc6CYXZ6JWQqyQSBz7/7bAUFz7zEhLW5GIbBnodWhLResNfAygwq94EMA9ofhH9+Yn4QoNoHmV3s/GFEIu1iLn51ONSs7gMX6gHhzqByH/hrDcx72/yGsFi7+Vnq29Ic/Di9BzZbDyWZrO4BcOF9oLX2AIBnvoAH3oLD5ea5NhJi4KEMO19PadpkJpRkLmCdIUDnE/DoPqjymId+d4+3sWBYDH06ZCjJBNIHrJRpQPsP4Nkvz6tU7YMrO9lZlNWe9rEyF6ivtfaBJR54eC9sP2nOBbwGTO3t4O4rUrDbUpRkirYeEKy+lVaWw/1vmSc09xjQLgYeGGRnQo9+SvI0l80w9Pmm6OnTp3Pttdc2+vXKF2Pr1q089thjAPTt25elS5dib/Bxk8b4ajys6nlLs2s3x7TDqwMGkVUZGtZWweODT76AtjFwWTulUQDr94Fgr0G07QPlNbDjFPzqbXhuNPTvqDSO8n1AdX0VPnPB6Wro0Q7iFZ+HTd4H1HjtBMzJg1Wj4IrGP8FrCdkHrOc1zLlAGzv0SLjw74eb7APWq/SY/7CWuYAe9VX4vNr88oLu8ZAQqzRK1PWAYPVV2HYC7suDZ66BKzsrjdIs6mdT9eTl5TF79uwW3ce4ceMYN25ciBKJcIuxQ99E1SmESgmx0EuDibRQJynO/E9Er25tzf+rOGGxUM9h0+frtYUa8TEyF4h2nduY/4nodcmXc4EY5d9b3DxaLawcPHhQdQQhhBBCCCGEEEKIixah60FCCCGEEEIIIYQQ6ml1xIoQkSLhsmRufPl3nDl4CEeck0/WvcHBZZuiLoMQ0Uz1GFRdX4hop8MY1CGDENFM9RhUXV/UkYUVIZrp9LtFbL05F5vdTvbrC/nwuVfwVFVHXQYhopnqMai6vhDRTocxqEMGIaKZ6jGour4wyUeBhGghR1sndmcMNoe64aRDBiGimeoxqLq+ENFOhzGoQwYhopnqMai6frSTI1bqs9uI69IB1+kyS8rFdekQ+BUIFmUIWls0SZfBqVy/dj6dr7icfYv+TU15VVRmaHUs7AMqe0Cj9UWTqB6Dquu3SjIXEE2gwxjUIUOro/q9WHV90SSqx6Dq+sIkCyv12B0Opu5bBj7DooI27A6HmgxBaoumOXfYXacrejHswds48NQLJA9LJ3loXz75zxsMvvsmitbt8Nve/eDfwp5h2EPTeP/pzcQlJdLt6oG0vaSj3/aBp14IaYbWxtI+oLIHNFJfNI3qPiA9IPRkLiCaQnUPaCyD9IGWUf1erLq+aBrVfUB6gB5kYaUBu8MBinuLDhnExTtz8BCVJ8/Q/euZHHt1L0kZfchacAfb71qMp8Llt21Fhr2Pr2bEozPwVLnZM+9vOOKcftviwlSPQdX1RdOp7gPSA0JLhzGoQwZx8VT3gIYZpA+0nOoxqLq+aDrVfUB6gFryASwhQuDA0o0MuutbALTv1ZXqM+XEJrQNuh3uDF6Xm+I9BXy64U2AgG0hRHio7gPSA4RQS3UPqJ9B+oAQaqjuA9ID1JGFFSGaofxoCVtvzq3dLi04zIvfeoj06eM58nI+e+atIHPuzQyYOdFvO5Qnk2osQ2uyYcMGFi1axOTJk1m/fn3tz5s3b679HZfLxZIlS4Lefv/+/WRnZ1NYWFh7WV5eHvPnzycnJ4edO3eydOlSDhw4QE5ODh6Ph9WrV3P8+PGwPzYR+VT3AekBJukBQhXVPeB8GVoT6QNCZ6r7gPQAkw49QD4KJEQIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIV06EPSA8wSQ8QKujQA0D6wDnSB4QKOvQB6QEmq3qALKwIIbRVUVHBE088wcKFC/1+rq+oqIjx48ezadMmVqxYUXv5888/f8H7HzNmDJmZmaSlpZGamsq0adOIiYnh7NmzIX8sQoimkx4ghJA+IER0i5QeIAsrQght3XfffSQlJbFkyRK2bNnCsGHDWLJkCVlZWWRlZQGQmprKkSNHmDRpEpMmTfK7/ZEjR9i6dSuFhYWMGjWKQYMGccMNN5Cbm4thGCQnJ5OcnAxA3759Wbx4MTNnziQxMdHyxyqECCQ9QAghfUCI6BYpPcBmGIZF3ycohP58NR5W9bzFsnrTDq/GHuu/vmllhmD1VSgohdu2wXOjoX/Hpt3W5XKxfPlyZs2aFZIsq1evZvTo0aSkpITk/kRksboHQOA4lB7QtNtKDxChJn1ADekDQhfR1gOC1Vch0nuAnLxWiBDLmD01pCemi7T6VouLiwtZEwW45ZZbZCIlWkT1GFRd32rSA4SOVI9D1fWtJn1A6EaHMahDBqvo0APUL09rxuf1gs+ig3jsNvM76lVkaKS2aLmEXl3p850xfPyv1zC8vqir3xpY1gdU9oDz1Bcto3oMqq7fGshcQLSU6nGoun5roPq9WHV90TI6jEEdMkQTWVipx+f1suaqO3CdLrOkXlyXDkzdt8yvmVmVIVhtERrlh04pbWCq60c6K/uAyh7QWH3RcqrHoOr6kU7mAiIUVI9D1fUjner3YtX1RcvpMAZ1yBBNouPYoIvlMyybSAFmrYYr0RZlCFpbhETZJycYMHOiskPvVNePeBb2AZU9oNH6osVUj0HV9SOezAVECKgeh6rrRzzV78Wq64sW02EM6pAhmsgRK0KEWNHa7VFdX4hop3oMqq4vhFA/DlXXFyLa6TAGdcgQTWT5SgghhBBCCCGEEKKZZGFFCCGEEEIIIYQQoplkYUUIIYQQQgghhBCimWRhRQghhBBCCCGEEKKZtF1YeeSRR+jXrx92u51169b5XTdmzBh69+5NRkYGGRkZ5Obmhi1H2tQxTHzhMSasf5TOg3qHrY7uGcLhSDk88BaM2QzXvwRPFUC1V3Uqf2P/8SC37H+awT/7dlRnCJe3PoMZ2+H2Heb2tpNgaHZieh3Gnw4ZwsEwYN0huOm/cO1muP0N2HtadapAOoxBHTKEQ5UHlhyEn+40t//8PhyrUJspGB3GoA4ZwuF4JTyYD1/bDONegsUHzf1CJzqMPx0yhMs7p+GOHeZ/AK8el7mArhnCwTBg0xGY8qo5F/jBdsgrUZ0qkA5jUIcM4VDthaUFMGuXuf3EQThcrjZTc2j7rUBjx47l1ltvZcaMGUGvX7hwIdnZ2WHN4Exsx4DbJ7Jp0i+J79aZUUvuYsvkeWGtqWOGcDhRCbdtMydPPqDcA6sKIf8zWPpVsNlUJzTtuO9JUkYNJj6lS1RnCIc3TsHP88Dtq7vsmULz/z/sryZTQzqMPx0yhMvig/DPT+sWVN/53PwH9qIR8JVkpdH86DAGdcgQaj4DfvwmfFRW1wd2l5jvDf8cA5e0VRqvlg5jUIcM4fCZC257HSo84DUAD/yjyPxH1YrR4JC5gFYZwuGtz+DuXf5zgeeKwG3Azwaqy1WfDuNPhwzh8vSHsOIjqP5yH3jvDNyzG347DEZ1U5utPh3GoA4ZQs0w4J5d5ut+bh946zP43jb4+7XQvZ3afE2h9IiV0tJSpk+fzsCBAxkyZAh33303M2fOBCArK4vU1NRm3e+iRYsYM2ZMi/MlZaZxavf7+Go8lB8pJrZdW+xOa9eidMgQDs8Umv+Yqvc+itsH75dCvkZ/sa488bnqCFpkCDXDgD/s959Igbn9TCGU16jJ1ZAO40+HDOFQWg1/Lwo8Ss3tgz8eUJOpMTqMQR0yhNrOYvj4C/8+4ANcHvh/RcpiBdBhDOqQIRz+38dQ5f1yUeVLbh8UlZv7hy50GH86ZAiHPzYyF/jnJ3CmWk2mhnQYfzpkCIfyGvhbvUWVc9w+c56o05FLOoxBHTKE2jufw3ul/vuAgTk/XPGRqlTNo3RETpkyhUmTJrFy5UpKSkpIS0tjwYIFF3XbBx54gHnz5pGens5jjz1Geno6ADU1NbzzzjsXdR+VlZUUFBTUbhse/xl+m07tcZfWHZPsLqugTccEqopLL+r+L8bevXuxxTiUZGhY20rbTlyBx4gLuNzt87Fl/0nsHU4qSBX4/IdbsNfAygyq9oFqn50jFRlBr7MbXja+9TH92qg5BrD+89/ae0Cw+lbZ7+pADL3xEFi7sAzeyn8bu4K/VlvdA+DC+4CVta304tkUXN6ugP8LXWPAa4cquba6IPgNw0zmAtb536n+1PjiAy53eQ22HDhF/LHjClJJH7CKz4APy4YEvc5heHnhrU8Y1LbM4lQmmQtY46PqdtiMNAgyFzhaabAzfx9xdl/gDcMs2npAsPpW2VzWFY/3Uhoe7+Ex4I1j1bztU/fXtv79+xMfH/ge1RhlCyvbtm2juLiYe++9F4Dk5GRSUlIYPnz4BW+7atUqevbsiWEYrFixgnHjxlFUVITD4eDZZ5/lu9/9Lr/5zW8ueD8FBQUMHTq0dtuBjeXdbqrddpeW40ysezKd7eOpLg3tP/ZGjBiBl7rlWCszNKxtpfQFb5Aw4KsBl9dUVfKnv+Ty0It/VZAq8PkPt2CvgZUZlO0DdgeZ/yzH7gxcXKusdvODm7NxHXnf+lz4P/+tvQcEq2+V+D5DSP/NduxtAt+wvFXlDB82NMitws/qHgAX3gesrG2lS775M1JuewxHkH3g/bd2MPThcQpSyVzASmkPv0jikPEBl3urq1j+t9/x6/V/VJBK+oCVMv5xFkd8h4DLK6pc/OQH/0flR3kKUslcwCptuqdzxaJ3sDsD/0Hvq3Hz1azh4LX+pEvR1gOC1bdK0tjbuez2hTjiEgKu+/TgXobecLXlmc7Jz89nyJDgi7/BKFtYycvLY8SIEbXbp0+f5tixYwwePPiCt+3ZsycANpuNGTNmMHfuXA4dOsTll1/OSy+9xD//+c+LWljp378/+fn5tduGx8t7k39bu13y9kdk3v9dbDEO4rt2oqbShc8d2sG9e/fugNVJqzI0rG2ltyo78swZL27Dv35c23jWPnIn7R77oZJcDZ//cAv2GliZQeU+8OyZcnZWOPHUW6G2YdAj3mD5uueUZAL/57+194Bg9a1iGDDvpJ0Srw+j3j4Qi4/rkip4ul5vtjSXxT0ALrwPWFnbSmXeGH5xIo6Gn/yLxccvrkvlqhv02Adaex9QuQ+8W9WBv37uo8bw/0tlmzZxrP7VdBIfulVJLukD1llTWsXr5QnUNJgLdGsXw/J/PKXsnHsyF7BO7ikfx2oMjHpHL8bgIyvxC5bv2a0kU7T1gGD1rVLpc/DzE21xN1jTcdq8/OzqrnxF0XwQzLWCplC2sJKcnMzatWvxer14vV7uvPNO0tPTcTqd572dy+WivLycpKQkADZv3ozD4aBHjx6sXbuWb37zmxedIT4+3m8Vylfj4b1617vPVlDwzEtMWJuLYRjseWhFkx7jxcjMzMQeW/cyWJmhYW0rZRpQeRBWF4HDbn6Oro0d/jjCzojkq5RkgsDnf+Tvf0zysHQczhiSrurDqz94PKT1gr0GVmZQuQ8M8JgnJ9t/xjxBoQF0bmPjLyPjSYm/+NXhUKv//Lf2HhCsvpWeKoc734RSt/nZ2hgbDE2yM/8rXYlzdFWSqeHzD9b3ASszqHz9AX53yvx2uHP/pHL74Htpdn4woI+yTDIXsM4QwFUAz3xkvg9U+8Bph98OszOq24X/0BYuVs8F4ML7QGudCwz0wtw882SV505W3D7Wxl9GtqFXgswFzmnNc4G/VJonMv/MZfaAWBsM6mzn1yOSiI9JUpIp2uYCwepb6YkSmL3H/NkAanzw7d4OfjSwNzZb5HwDlrLZ1NSpU1mzZg3p6en06tWLfv360aVL3RmOc3JyWL58OSUlJezfv59Zs2axa9cunE4nEyZMwO12Y7fb6dSpExs3biQ2NpYPPviA1157jWeffZZ3332Xv/71r/zoRz9qUc7C1a9SuPrVlj7ciM8Qajabebb3W1LhhUOw9EP4y9UwWLOTXL855ynVEbTIEA5tY8xvgCoohQ/LoFtbGJaEkvNqnI8O40+HDOHQMwFeGAtrP4Xfvge5mTDuMtWpAukwBnXIEA7XdIWXx8OOYnB5YUQyJAd+QlA5HcagDhnC4cf9Ycrl8J9D8NcP4MmrIUPmAlpmCIc2DvhTFnx0FgrOmuN/eLI+3wh1jg7jT4cM4XBpPPznOvjPp/Cb9+ChDJjQQ3WqQDqMQR0yhMPwZNh6vXnS8ooaGJZs/rsg0ihbWImLi2Pjxo2129OnT+faa6+t3c7JySEnJyfobfMbOSToV7/6Fb/61a8AGDNmTIsXVUT4dWsLo7uZCytBPl4pokD/juZ/Ijo5bDCok/lzz8CP14oo0DYGvpGiOoVQKSkORnU1F1biZC4Qlfommv+J6GS3wcAv5wK926vNItSIc8DXLlWdomWUft1yfXl5eQwbNixk9/faa6+F7L6EEEIIIYQQQgghgtHmC9APHjyoOoIQQgghhBBCCCFEk2izsBJJEi5L5saXf8eZg4dwxDn5ZN0bHFy2KeoyCBHNdBiDOmQQIpqpHoOq6wsR7XQYgzpkEELIwkqznX63iK0352Kz28l+fSEfPvcKnqrqqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBiGinzTlWIpWjrRO7MwabQ91TqUMGIaKZDmNQhwxCRDPVY1B1fSGinQ5jUIcMQkQrOWKlmboMTuX6tfPpfMXl7Fv0b2rKq6IyQ6tjtxHXpQOu02VhLxXXpUPw7xa2KEOj9cVF02EM6pChVbGwB0Aj41B6QERRPQZV12+VpA+IJtBhDOqQoVWJoh7QaH3RZLKw0kznDrnrdEUvhj14GweeeoHkYekkD+3LJ/95g8F330TRuh1+27sf/FvYMwx7aBrvP72ZuKREul09kLaXdPTbPvDUCyHN0NrYHQ6m7lsGPsOCYjbsjsDvlbQsQyP1xcWTPtD6WNoDIOg4lB4QWVT3AekBoSd9QDSF6h7QWAbpA80XVT2gkfqi6WRhpYXOHDxE5ckzdP96Jsde3UtSRh+yFtzB9rsW46lw+W1bkWHv46sZ8egMPFVu9sz7G444p9+2uDC7wwGKe4sOGcTFkz7Quugw/nTIIJpGdR+QHhBaOoxBHTKIi6e6BzTMIH2gZXQYfzpkEBdPPoAXAgeWbmTQXd8CoH2vrlSfKSc2oW3Q7XBn8LrcFO8p4NMNbwIEbAshwkP6gBBCdR+QHiCEWqp7QP0M0geEsJYsrDRD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8k1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLySR+whvQBoTPVfUB6gEl6gFBFdQ84X4bWRPqAiATyUaAQ+mDlS7U/vznnKb/rGm6HU+Ga1867HSluvPFGCgsLKSsrY/LkybU/T5w4sfZ3Nm3axHXXXRf09ldeeSXZ2dl+l23YsIHc3FwWL17M0aNH2bFjByNHjqSoqIhVq1YxZcoUli5dypw5c8L50EQrJn0gtKQPiEikQx+QHmCSHiBU0KEHgPSBc6QPCCvIworQVkVFBU888QQLFy70+7m+oqIixo8fz6ZNm1ixYkXt5c8///wF73/MmDFkZmaSlpZGamoq06ZNIyYmhrNnz4b8sQghmkf6gBDRTXqAEEL6gIgEsrAitHXfffeRlJTEkiVL2LJlC8OGDWPJkiVkZWWRlZUFQGpqKkeOHGHSpElMmjTJ7/ZHjhxh69atFBYWMmrUKAYNGsQNN9xAbm4uhmGQnJxMcnIyAH379mXx4sXMnDmTxMREyx+rECI46QNCRDfpAUII6QMiEtgMw7Doe6T056vxsKrnLZbWnHZ4NfbYuvUtKzM0rK1KQSnctg2eGw39Ozbtti6Xi+XLlzNr1qyQZFm9ejWjR48mJSUlJPcnIo/VfUBlDwhWX4WW9ACQPiBCS+YCashcQOhE9Xux6voqyFxARDr176RCtEBcXFzIGijALbdYO5kWQrSc9AEhopv0ACGE9AGhmiyshFjG7KnsW/Q8htcXlfVbA5/XCz4LDuSy28zvp1eV4Tz1RcuoHoeq60c6y3oANDoOpQdENtVjUHX91kD6gGgp1eNQdf1IFzU94Dz1RdPIwkqIJfTqSp/vjOHjf72mpJGprh/pfF4va666A9fpsrDXiuvSgan7lgU0MqsyNFZftJzqcai6fiSzsgdA8HEoPSDyqR6DqutHOukDIhRUj0PV9SNZNPWAxuqLpgvdl6gLAMoPnVLawFTXj3g+w7Im6jpdFnwV2qIMjdYXLaZ6HKquH9Es7AHQyDiUHhDxVI9B1fUjnvQBEQKqx6Hq+hEtinpAo/VFk8nCSoiVfXKCATMnYnOoeWpV1xdCqB+HqusLEe1Uj0HV9YUQ6seh6vpCRBv5KFCIFa3dHtX1hRDqx6Hq+kJEO9VjUHV9IYT6cai6vhDRRpYwhRBCCCGEEEIIIZpJFlaEEEIIIYQQQgghmkkWVoQQQgghhBBCCCGaSeuFlUceeYR+/fpht9tZt26d33Vjxoyhd+/eZGRkkJGRQW5ubsjrj/3Hg9yy/2kG/+zbIb/vSMoQLhUeeK4Qct8xt/NPg6HhCanTpo5h4guPMWH9o3Qe1DtqM4TDiUr44374wXaY9zYUlKpOFEiHMahDhnDZfwb+/L758z+K4FSV2jzB6DD+dMgQDoYB/z0Od+2EO96A1UVQ5VGdyp8O40+HDOFS5YF/FsEj75jbe0pkLqBzhnAoroI/HTDnAr/KN98XdKPDGNQhQ7gUnIWnCsyfn/vYnB/qRofxp0OGcDAM2HYSfrYLbn8Dni2E8hrVqZpO65PXjh07lltvvZUZM2YEvX7hwoVkZ2eHrf6O+54kZdRg4lO6hK1GJGQIhy9qYNo28820+stvgfvz+3CkAh4YrDZbfc7Edgy4fSKbJv2S+G6dGbXkLrZMnhd1GcLhw7Mw8w3wGFDjgwNnzH9gzc+Esd1Vp6ujwxjUIUM4bDwMv37XfP0BXjoGr52EFaMgtb3abOfoMP50yBAuue/Ay8fB5TW3D5bCvz+FZ0ZDO01mKDqMPx0yhEOlB76/HY5VQvWX+8BTH8DHX0BOJthsavOdo8MY1CFDOHz6BUzfDm5f3VzgfyfMueA3e6pOV0eHMahDhnD473Hzj2ueL+cCrxyH10/Csmugf6LabOfoMP50yBAuv98P6w/XzQXeLzXnAqtGQwenymRNo/yIldLSUqZPn87AgQMZMmQId999NzNnzgQgKyuL1NTUJt3fp59+Srdu3RgzZgzjxo1rUbbKE5+36PahoEOGcPjHx+Zfps8tqoD5pvrCYSi07mvjLygpM41Tu9/HV+Oh/Egxse3aYndaO9vXIUM4LHjXbKDn/lHtw9wHHt1Xd5kOdBiDOmQINZcHFrxnvubn/jjtMcx/aP3+PaXR/Ogw/nTIEA4HzpiLaecmUmC+JxyvNCdUutBh/OmQIRz+/Skcq6hbVAGzJ7xyHA6UqkoVSIcxqEOGcPj9frPvN5wLPP6eXkev6TAGdcgQajU+82g1t8987cGcC1R5YcE+lcn86TD+dMgQDkVfwNpDgXOBYhf8vUhdruZQ/mpMmTKFSZMmsXLlSkpKSkhLS2PBggUXddsHHniAefPmkZ6ezmOPPUZ6ejoA119/Pc8888wFb19ZWUlBQUHttuHxnue3w2Pv3r3YYhxKMjSsbaUXTl6B2xcXcLnX5+Ofb59gQodTClIFPv9tOrXHXVpRu+0uq6BNxwSqiktDUi/Ya2BlBlX7QI1h490zGUDgnyM9Xi//2V1IWpuKgOusYHUfUNkDgtW3ykFXewxfKtBg/wfyPjN4K38vdgV/rba6B8CF94HW2AMAXjh7KR5fNxr2gWof/OejSq4sKwh+wzCTuYB11p1Kp9rXLuByt89gzTsncSeeUJBK+oBVDAN2l2RiBJkLGD4vz+8pYmDcF5bnAvXvxarrW+Xj6na4vWk0nAsA7C812PnWO7SxW//ZwGjrAcHqW+XFL7pi+C6l4fEebh+8UOTiK5UHLc90Tv/+/YmPj7/o31e6sLJt2zaKi4u59957AUhOTiYlJYXhw4df8LarVq2iZ8+eGIbBihUrGDduHEVF5rLWK6+8wqhRo/jOd77D3Xff3eh9FBQUMHTo0NptBzaWd7uphY+qaUaMGIGXuoZhZYaGta00YNE7xPe+KuDymupq/rTwDzz4wkIFqQKff3dpOc7EugHlbB9PdWl5yOoFew2szKBqH7DFxJL5ryps9sAGXlnl4gfTbqOy8C3Lc4H1fUBlDwhW3yoJV4wi7aHNONomBFzn9dQwfNjQILcKP6t7AFx4H2iNPQCg23d+yaU3P4Q9tk3Ade+/t4+hE0cqSCVzASv1W7Cd9gOuCbjcW1PDsqee5JE1jypIJX3ASpnPu4L2gMrKSn7yyzso3/+6glTq34tV17dKfJ8h9Pv1NhxxgQushs/HV0dejVFTbXmuaOsBwepb5ZIb7yHle7/G0SZwAePTjz9i6CQ180GA/Px8hgwZctG/r3RhJS8vjxEjRtRunz59mmPHjjF48IVPstGzp/nBS5vNxowZM5g7dy6HDh2ie/fufPDBB7Rp04bs7Gyuu+46Bg4cGPQ++vfvT35+fu224fHy3uTftvBRNc3u3bsDVietytCwtpX++0Vn1p71UtNghTq2TRue+9UMujx8m5JcDZ//krc/IvP+72KLcRDftRM1lS587tAdmxrsNbAyg8p9YPFnX3DAlYivwV+qOsfH8vrqvyo5WgGs7wMqe0Cw+lbxGjDnRBwVDT72ZcfH0PblLK/Xm61kdQ+AC+8DrbUHnKppw/xTsTR8JE6blzuvTmGUJvuAFaJ1LvBGRRdWn/HibjAXcMbG8PR9t9Dt/m8pySV9wDrLTlfwdlUs3gZ/rW4f35b/PvNHYmQuoKS+VXwGPHAiltKAuYDBFW3LWbbrTcszQfT1gGD1rfK5J5ZfnYyj4TFasXj5/uCOfEPRXADMtYKmULqwkpyczNq1a/F6vXi9Xu68807S09NxOs9/lhqXy0V5eTlJSUkAbN68GYfDQY8ePYiNjaVNG3Ple9KkSRw4cKDRhZX4+Hi/VShfjYf6H+0f+fsfkzwsHYczhqSr+vDqDx5v2QMOIjMzE3ts3ctgZYaGta00yAcf7zLP/O7yQowN7Da4+wo7Y1OvVJIJAp9/99kKCp55iQlrczEMgz0PrQhpvWCvgZUZVO4DC6rg+9ug3GN+lhagjR3+cLWTjC4Xvzocalb3gQv1gHBnULkP/OEzuGeX+fEftw/aOiDRaeexUZ1JiuusJJPVPQAuvA+01h4AUPwR/PUD8PrACzjtMDTJwU+/0osYey8lmWQuYJ3BPvh4j/mtgC4vOL6cC/yon52J/YLP3awgfcA6j7rMExiXuuvmAk47/GFEDMOTZS5QX2vtA3/8HH6601xkqfZBnAMSYmwsGJ1It7Zq9oFo6wHB6lvp809g4QFzH/AaZg+4spODe6/uQay9h5JMzaF0YWXq1KmsWbOG9PR0evXqRb9+/ejSpe5M1zk5OSxfvpySkhL279/PrFmz2LVrF06nkwkTJuB2u7Hb7XTq1ImNGzcSGxvLF198Qfv25tdJ7Ny5k3vuuafZ+d6c81SLH2NL6ZAhHGLt8OTVsLMY3jgFCbEw8TLorck3gdRXuPpVCle/GvUZQq1rW/jPdfDScdhxCl49AX/8CmRodrJ7HcagDhnCYVgSrP8GbDwCJ6vgyo7wje7mpEonOow/HTKEw/S+8NWu8P8+hg1H4N6B8O3LUXbEWjA6jD8dMoRDjB0WjoC8z8xvAWnrgAmXQVoH1ckC6TAGdcgQal3i4Pmvm98Otv0k/PfLucDwZNXJ/OkwBnXIEA6DO8MLX84FjlbAgI4wvju0VX4mUH86jD8dMoTD1N7wlSTza5bXH4G7r4Dv9DYX2yOJ0l02Li6OjRs31m5Pnz6da6+9tnY7JyeHnJycoLfNb+SwoJ07d/KLX/yCuLg4rr32Wr9zqAi92G3mhPqrXVUnEarExcDknpDewVxYSYygr1QToZEUB9/vqzqFUCmtA9zc21xYGdRJr0UVEX52G4xINv8T0amNA27oAWntzYWVjjIXiDqd2sD30lSnECpd3t5cTFl/BDI6R96iCmjwrUD15eXlMXv27Bbdx7hx41r8NctCCCGEEEIIIYQQF0OrhZWDB9V9nZIQQgghhBBCCCFEU2m1sCJEpEi4LJkbX/4dZw4ewhHn5JN1b3Bw2aaoyyBENFM9BlXXFyLa6TAGdcggRDRTPQZV1xd1ZGFFiGY6/W4RW2/OxWa3k/36Qj587hU8VdVRl0GIaKZ6DKquL0S002EM6pBBiGimegyqri9M9gv/ihDifBxtndidMdgc6oaTDhmEiGaqx6Dq+kJEOx3GoA4ZhIhmqseg6vrRTo5Yqc9uI65LB1ynyywpF9elQ+DXH1iUIWht0SRdBqdy/dr5dL7icvYt+jc15VVRmaHVsbAPqOwBjdYXTaJ6DKqu3yrJXEA0gQ5jUIcMrY7q92LV9UWTqB6DqusLkyys1GN3OJi6bxn4DIsK2rA7HGoyBKktmubcYXedrujFsAdv48BTL5A8LJ3koX355D9vMPjumyhat8Nve/eDfwt7hmEPTeP9pzcTl5RIt6sH0vaSjn7bB556IaQZWhtL+4DKHtBIfdE0qvuA9IDQk7mAaArVPaCxDNIHWkb1e7Hq+qJpVPcB6QF6kIWVBuwOByjuLTpkEBfvzMFDVJ48Q/evZ3Ls1b0kZfQha8EdbL9rMZ4Kl9+2FRn2Pr6aEY/OwFPlZs+8v+GIc/ptiwtTPQZV1xdNp7oPSA8ILR3GoA4ZxMVT3QMaZpA+0HKqx6Dq+qLpVPcB6QFqyQewhAiBA0s3MuiubwHQvldXqs+UE5vQNuh2uDN4XW6K9xTw6YY3AQK2hRDhoboPSA8QQi3VPaB+BukDQqihug9ID1BHFlaEaIbyoyVsvTm3dru04DAvfush0qeP58jL+eyZt4LMuTczYOZEv+1QnkyqsQytyYYNG1i0aBGTJ09m/fr1tT9v3ry59ndcLhdLliwJevv9+/eTnZ1NYWFh7WV5eXnMnz+fnJwcdu7cydKlSzlw4AA5OTl4PB5Wr17N8ePHw/7YRORT3QekB5ikBwhVVPeA82VoTaQPCJ2p7gPSA0w69AD5KJAQIfTBypdqf35zzlN+1zXcDqfCNa+ddztS3HjjjRQWFlJWVsbkyZNrf544cWLt72zatInrrrsu6O2vvPJKsrOz/S7bsGEDubm5LF68mKNHj7Jjxw5GjhxJUVERq1atYsqUKSxdupQ5c+aE86GJVkyHPiA9wCQ9QKigQw8A6QPnSB8QKujQB6QHmKzqAbKwIoTQVkVFBU888QQLFy70+7m+oqIixo8fz6ZNm1ixYkXt5c8///wF73/MmDFkZmaSlpZGamoq06ZNIyYmhrNnz4b8sQghmk56gBBC+oAQ0S1SeoAsrAghtHXfffeRlJTEkiVL2LJlC8OGDWPJkiVkZWWRlZUFQGpqKkeOHGHSpElMmjTJ7/ZHjhxh69atFBYWMmrUKAYNGsQNN9xAbm4uhmGQnJxMcnIyAH379mXx4sXMnDmTxMREyx+rECKQ9AAhhPQBIaJbpPQAm2EYFn2foBD689V4WNXzFsvqTTu8Gnus//qmlRmC1VehoBRu2wbPjYb+HZt2W5fLxfLly5k1a1ZIsqxevZrRo0eTkpISkvsTkcXqHgCB41B6QNNuKz1AhJr0ATWkDwhdRFsPCFZfhUjvAeq7qBBCtEBcXFzImijALbdY+0YqhGgZ6QFCCOkDQkQ3HXqAfCuQECGWMXtqSM/4H2n1hYh2qseg6vpCCPXjUHV9IaKdDmNQhwzRRI5YacDn9YLPok9H2W3YHQ41GRqpLVouoVdX+nxnDB//6zUMry/q6rcGlvUBlT3gPPVFy6geg6rrtwYyFxAtpXocqq7fGqh+L1ZdX7SMDmNQhwzRRBZW6vF5vay56g5cp8ssqRfXpQNT9y3za2ZWZQhWW4RG+aFTShuY6vqRzso+oLIHNFZftJzqMai6fqSTuYAIBdXjUHX9SKf6vVh1fdFyOoxBHTJEEzk2qD6fYdlECjBrNVyJtihD0NoiJMo+OcGAmROVHXqnun7Es7APqOwBjdYXLaZ6DKquH/FkLiBCQPU4VF0/4ql+L1ZdX7SYDmNQhwzRRI5YESLEitZuj+r6QkQ71WNQdX0hhPpxqLq+ENFOhzGoQ4ZoIstXQgghhBBCCCGEEM0kCytCCCGEEEIIIYQQzSQLK0IIIYQQQgghhBDNpO3CyiOPPEK/fv2w2+2sW7fO77oxY8bQu3dvMjIyyMjIIDc3N2w50qaOYeILjzFh/aN0HtQ7bHV0zxAOhgFvfQZLDsLfPoRjFaoTBRr7jwe5Zf/TDP7Zt6M6Q7i4vfDSMfhHkbld4VGbJxgdxp8OGcLlrBv++Qn86SC8chw8Gp64XocxqEOGcDlSDusPmz9/cNZ8b9CNDmNQhwzhYBjwzmn480FY/qG5P+hGh/GnQ4Zw8fjM/n9uLlBeozZPMDqMPx0yhMsXNfD8l3OBF4+a80Pd6DAGdcgQLscr4YUv5wIHS/WcC1yItievHTt2LLfeeiszZswIev3ChQvJzs4OawZnYjsG3D6RTZN+SXy3zoxachdbJs8La00dM4SDxwez90D+Z1DtgxgbLPsQfj4IvtVLdbo6O+57kpRRg4lP6RLVGcLhMxf8YDuUuqHqyzfQe3bDX0fCwE5qs52jw/jTIUO4vHMa7toFBuDyQlsH/DkOVlwDHduoTldHhzGoQ4ZwWF0ETxys+0KK374Hb5yCBcPBYVOb7RwdxqAOGcLBa8Av3zJfc/eXc4GnP4S7B8B3+6hOV0eH8adDhnAodcOM7VDi8p8L/PlqyNDkoeow/nTIEC7vl8KP3zT7wbm5wJL34ZlRkBSnOl0dHcagDhnC4YXD8Jt36xZTfr8f/ncSFn4FYrQ9DCSQ0qilpaVMnz6dgQMHMmTIEO6++25mzpwJQFZWFqmpqU2+z1WrVvGNb3yDMWPGcOzYsRblS8pM49Tu9/HVeCg/Ukxsu7bYndauRemQIRzWHTaPVnH5zH9U1RhQ44PH34VTVarT1ak88bnqCFpkCIcF7/pPpMB8Q52bp8+3/ukw/nTIEA5ew3ytq7zm6w7mzycqzTdUnegwBnXIEGpHK+CJA2bv93455t0+2FkCm4+ozVafDmNQhwzh8OJR2FFs/oGl/lzgT+/rdeSKDuNPhwzhsHC/+Zfq+nOBah/MydPnCEYdxp8OGcLB+HIuUOHxnwuUuODX+9Rma0iHMahDhlArcZmLKjU+8NSbC+w9Df/+VGm0JlM6IqdMmcKkSZNYuXIlJSUlpKWlsWDBgou67QMPPMC8efNIT0/nscceIz09nWPHjvHGG2/wyiuvXNR9VFZWUlBQULttePyPO2vTqT3u0rrPp7jLKmjTMYGq4tKLuv+LsXfvXmwxDiUZGta20nOn+lPtiw9yjZeVe47zjfYllmeCwOc/3IK9BlZmULUPeAwbr5/MwCDwT9Kl1V7W7/6QXk41K2z1n//W3gOC1bfKR9XtqKhJA/xrewx4+ZiPb/EONgVHLFjdA+DC+4CVta20uawrPuNSGv6Nx+WF5w6W0/2zD5XkkrmAdZ4t7ofLmxBwuc/n45m3TjKpw0kFqaQPWMUw4KVjGXiC/J23qsbL87s/pl8bNStsMhewxmF3W05XpdPwfcBrwPZTBrvz3yHWZv1f26KtBwSrb5X/fpEMRgoN54MuL/yjoJK+pQXBb2iB/v37Ex8f7N+rwSlbWNm2bRvFxcXce++9ACQnJ5OSksLw4cMveNtVq1bRs2dPDMNgxYoVjBs3jqKiIl566SW8Xi/XXXcdV155JQsXLsRub/ygnIKCAoYOHVq77cDG8m431W67S8txJtY9mc728VSXhrbBjxgxAi91DcPKDA1rW2ngn98n7rL+AZdXuz0sXPwk9//74hbYQq3h8x9uwV4DKzOo2gdssW0Y8rwr6HVVlZV8b8YdVLy/w+JUpvrPf2vvAcHqW6X9Vd+gzwP/xhHfIeA6jw+GDR+m5AO2VvcAuPA+YGVtK136f/O5dMovsTkC36ffK/iIoROGBrlV+MlcwDr9/5BHu7RhAZd7vAZPPb2Ch557UEEq6QNWGvIfD7YgU/XKigp+9PDdlO19yfpQyFzAKu36X03fnJdwtG0fcJ3PgJFfvQZfdaXluaKtBwSrb5WuN/2clO/Ox+4MXNQpPHyUoZPUzAUA8vPzGTJkyEX/vrKFlby8PEaMGFG7ffr0aY4dO8bgwYMveNuePXsCYLPZmDFjBnPnzuXQoUOcOnWKmpoa/vvf/3L//fezceNGvvnNbzZ6P/379yc/P7922/B4eW/yb2u3S97+iMz7v4stxkF8107UVLrwuUN7ds3du3cHrE5alaFhbSutO5vI1i98AX+lcMbG8tScafT45XeU5Gr4/IdbsNfAygwq94Ffn6rg05p4aHDUSnx8PP99drGSv1CA//Pf2ntAsPpWqfbZue94AoHnKDRIj6tg2VtvWZ4JrO8BcOF9wMraVvq4uh1/LLEH7AOx+Pi/jEuYWO/92UoyF7DOlrKubCzzUtPgL5VOh41FP5lCn3snKMklfcA6fyip4IPq9jScC8TFJ7Bl6QLi7L9WkkvmAtaoMWzMPh6PK8iU73JnJcve3G55Joi+HhCsvlWOutvy62InDffmGHxkp3dglaK5AJhrBU2hbGElOTmZtWvX4vV68Xq93HnnnaSnp+N0Os97O5fLRXl5OUlJSQBs3rwZh8NBjx49SExM5NprrwXg61//Ou+88855F1bi4+P9VqF8NR7eq3e9+2wFBc+8xIS1uRiGwZ6HVjT/ATciMzMTe2zdy2Blhoa1rdTHDW+/Dmeqzc/SAjjtMK67ncmZA5RkgsDnf+Tvf0zysHQczhiSrurDqz94PKT1gr0GVmZQuQ/klsIPd9SdX8EGxNrhl4MdjOiZqSQT+D//rb0HBKtvpTmfwh/31/UAhw2cdhvzr25P38SL/wtBKDV8/sH6PmBlBpWvf6YBb+fD9lN1n61vY4fkODs/+2p3EmK7K8klcwHr9KuB/G3mudXqzwVGdbUzZVi6ko8DgvVzAbjwPtBa5wLzy8wT2Z87v8K5ucC9A+2M7J2hJBPIXMBKv7wEHt1n7gMG5gdCYh0wP6sdV3aSuYBVGVTtA0OAfe+Y3xJ6bi7gtEMnp505I7vRsU03yzM1l7KFlalTp7JmzRrS09Pp1asX/fr1o0uXujMc5+TksHz5ckpKSti/fz+zZs1i165dOJ1OJkyYgNvtxm6306lTJzZu3EhsbCwjR45kxQqz0bzzzjv07t3yryIrXP0qhatfbfH9RHqGUEt0wt+vhTWfwJajcKgC7ugH3++rOpm/N+c8pTqCFhnC4YqO5j7w7Mew/wx0j4fvpcFVnVUn86fD+NMhQzh8+3Lo3R6eKoC3T8PXusFdV0D3dqqT+dNhDOqQIdRsNnhsqHkC0/8cgkovjE2BKZdDQqzqdP50GIM6ZAi1hFhYNRqe/xQ2HoZPK2BGX5jRD2WLKsHoMP50yBAOaR3gn1+DZwvhnc/h0rZwax8YmqQ6mT8dxp8OGcJhYg+4rB08+T68dRpGdYO7r4CegadfUkqHMahDhnB48CrISjbfC8prYMylMLW3+e/FSKJsYSUuLo6NGzfWbk+fPr32aBMwF1ZycnKC3ja/kUOCMjIyiI2N5Wtf+xrJycncd999Ic0sQquDE25Ph2u6wm3b4OpL9JpIifDrmQC/ukp1CqHSkC5w30CzB3y/r36LKiK87DZzUj2xh+okQpWEWHPsZyWbfeCaruZ+IaJHSjzcf+EzAYhWbHBn+NmXc4Hb++m3qCLCy2aDsd3N/yKZNt/TlZeXx+zZs1t8P7///e9DkEYIIYQQQgghhBDiwrRZWDl48KDqCEIIIYQQQgghhBBNos3CSiRJuCyZG1/+HWcOHsIR5+STdW9wcNmmqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBCCELK812+t0itt6ci81uJ/v1hXz43Ct4qqqjLoMQ0UyHMahDBiGimeoxqLq+ENFOhzGoQwYhop1ddYBI52jrxO6MweZQ91TqkEGIaKbDGNQhgxDRTPUYVF1fiGinwxjUIYMQ0UqOWGmmLoNTuX7tfDpfcTn7Fv2bmvKqqMwgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBiGgny5nNdPrdIl686WG23PQQKaMHAZA8LJ0rfnQDbS/pyIhHZwRsW5Fh2EPTaNc9iS5X9WHgj78ZsC0uwG4jrksHS0rFdekQ/DslLcrQaH1x0aQPtEIW9gBoZBxKD4goqvuA9IAwkD4gmkB1D2gsg/SBFoiiHtBofdFkcsRKC505eIjKk2fo/vVMjr26l6SMPmQtuIPtdy3GU+Hy27Yiw97HVzPi0Rl4qtzsmfc3HHFOv21xfnaHg6n7loHPsKCYDbvDoS5DI/VF00kfaD0s7QEQdBxKD4hMqvuA9IDQkT4gmkN1D2iYQfpA80VVD2ikvmg6WVgJgQNLN5L1m9s59upe2vfqSvWZcmIT2uKpcAVsW5GheE8BZZ+eBMDrcvttiwuzOxyguLfokEE0jfSB1kOH8adDBtF0qvuA9IDQ0WEM6pBBNI3qHtAwg/SB5tNh/OmQQVw8+ShQM5QfLWHrzbm126UFh3nxWw+RPn08R17OZ8+8FWTOvZkBMyf6bYfyRFKNZWhNNmzYwKJFi5g8eTLr16+v/Xnz5s21v+NyuViyZEnQ2+/fv5/s7GwKCwtrL8vLy2P+/Pnk5OSwc+dOli5dyoEDB8jJycHj8bB69WqOHz8e9scmIp/0AWtIHxA6U90HpAeYpAcIVVT3gPNlaE2kD4hIIEeshNAHK1+q/fnNOU/5XddwO5wK17x23u1IceONN1JYWEhZWRmTJ0+u/XnixIm1v7Np0yauu+66oLe/8soryc7O9rtsw4YN5ObmsnjxYo4ePcqOHTsYOXIkRUVFrFq1iilTprB06VLmzJkTzocmWjHpA6ElfUBEIh36gPQAk/QAoYIOPQCkD5wjfUBYQRZWhLYqKip44oknWLhwod/P9RUVFTF+/Hg2bdrEihUrai9//vnnL3j/Y8aMITMzk7S0NFJTU5k2bRoxMTGcPXs25I9FCNE80geEiG7SA4QQ0gdEJJCFFaGt++67j6SkJJYsWcKWLVsYNmwYS5YsISsri6ysLABSU1M5cuQIkyZNYtKkSX63P3LkCFu3bqWwsJBRo0YxaNAgbrjhBnJzczEMg+TkZJKTkwHo27cvixcvZubMmSQmJlr+WIUQwUkfECK6SQ8QQkgfEJHAZhiGRac71p+vxsOqnrdYWnPa4dXYY+vWt6zM0LC2KgWlcNs2eG409O/YtNu6XC6WL1/OrFmzQpJl9erVjB49mpSUlJDcn4g8VvcBlT0gWH0VWtIDQPqACC2ZC6ghcwGhE9XvxarrqyBzARHp1L+TCtECcXFxIWugALfcYu1kWgjRctIHhIhu0gOEENIHhGryrUAhljF7akjP9B1p9YUQ6seh6vpCRDvVY1B1fSGE+nGour4Q0UaOWAmxhF5d6fOdMXz8r9cwvL6oq98a+Lxe8FnwCTm7zfx+elUZzlNftIzqcai6fqSzrAdAo+NQekBkUz0GVddvDaQPiJZSPQ5V1490UdMDzlNfNI0srIRY+aFTShuY6vqRzuf1suaqO3CdLgt7rbguHZi6b1lAI7MqQ2P1RcupHoeq60cyK3sABB+H0gMin+oxqLp+pJM+IEJB9ThUXT+SRVMPaKy+aDo5PizEyj45wYCZE5Udeqe6fsTzGZY1UdfpsuCr0BZlaLS+aDHV41B1/YhmYQ+ARsah9ICIp3oMqq4f8aQPiBBQPQ5V149oUdQDGq0vmkyOWAmxorXbo7q+EEL9OFRdX4hop3oMqq4vhFA/DlXXFyLayBKmEEIIIYQQQgghRDPJwooQQgghhBBCCCFEM8nCihBCCCGEEEIIIUQzab2w8sgjj9CvXz/sdjvr1q3zu27MmDH07t2bjIwMMjIyyM3NVRNStMjn1bC7xPzZIyctj0qffgFbj8G7n4Mh582KOoYBH541fz5RqTaLUMPthTdOwSvHobRadRqhQqkb9nw5F3DLXCAqHS435wLvnJa5QDQyDCj88jytx2QuEJVqfPBmsTkXOO1SnaZ5tD557dixY7n11luZMWNG0OsXLlxIdnZ2+Or/40G6DOrNweWbeXfRv8NWR/cM4fLXAljxEcR8ubz3k53wRBZkdlGbq6G0qWPod9tYDMNg94NP8/l7n0RlhlCr9sLP82DPZxBrN09Gfmlb+PPVcElb1enq6DAGdcgQDscr4ac74VSVuf2LfBh1FH49zNwndKHD+NMhQzjsKYG5eV/+Q8pmLrL8qD/8oK/qZHV0GH86ZAiXlR/BUwXgqDcX+P1wyLpEba6GdBiDOmQItRof/Coftp+EWIc5F0hqA0+OhJR41enq6DAGdcgQDiUu+MmbdQsqv8qH9Yfh8eEQp9G3/+ow/nTIEA7vnIb79tT9kd3tg+l94cfpYLOpzdYUyqeupaWlTJ8+nYEDBzJkyBDuvvtuZs6cCUBWVhapqalNur833niDMWPGMGbMGFJSUgKOdGmKHfc9yVu5zzb79qGgQ4ZweO0ErCoEjwEur3lZpRfu2gXlNWqz1edMbMeA2yfy4rcfZvusPzHi0eCLfK09Qzg8cRDyPjMnVZUecz84XGE2Vp3oMAZ1yBBqhgH37IJjFXV/ofYY5l8rnnxfbbb6dBh/OmQIhzPVcO9uqPCY/b/SY+4Dyz8w9wNd6DD+dMgQDruKYekHUFNvLuDywuw95v6hCx3GoA4ZwuGvBbDjlLkPnJsLHK+Eu3fpdeSKDmNQhwzhMGePOf+rPxd46zNYuF9trvp0GH86ZAiH8hrz339lNV/OBbzmPvD/PoZXT6hO1zTKj1iZMmUKkyZNYuXKlZSUlJCWlsaCBQsu6rYPPPAA8+bNIz09nccee4z09HSuueYaXnvtNQCuueYavvGNbzR6+8rKSgoKCmq3DY/X//oTnzf9ATXR3r17scXULcdamaFhbSs9VdyXal/7gMt9Pi9P7zzKqITTClIFPv9JmWmc2v0+vhoP5UeKiW3XFrszBp/bE5J6wV4DKzOo2gd8BvznWAY1DdZ2vQYUnvWxaff7XBqrZlZtdR+4UA8IdwZV+8Bhd1uOVqTja7APVPtgTZGXa1z7lPyVwuoeABfeB1pjDwD47xfJ+HwpgH/9ap/BX/eWEZf8sZJcMhewzlMlfaj2dQD8B7vP52PZrmN8o32JklzSB6zzz2ODqTb8/zniA46V+1i3+wN6OauU5JK5gDVO1bThg9IBeBvMBdw+WH/Ixzc87+CQuYAlGVTtA29UdMHnu4yGcwGXF5a+W06nkx9anumc/v37Ex9/8YfOKV1Y2bZtG8XFxdx7770AJCcnk5KSwvDhwy9421WrVtGzZ08Mw2DFihWMGzeOoqIiHA7zRTl69CgdO3YkISGh0fsoKChg6NChtdsObCzvdlMLH1XTjBgxAi91S/JWZmhY20oDn/qQuEsDF1ZcNT4WLFnGz/71mIJUgc9/m07tcZdW1G67yypo0zGBquLSkNQL9hpYmUHVPmBvE0/mmoqg11VXlnPLzJ9QfmCbxalMVvcBlT0gWH2rdMgcT+rP/4kjPjHgumrDwbCvDAef9SdbsLoHwIX3gdbYAwBSbnuUbt/+BbaAY2dt5H1wiKHXDw12s7CTuYB1BizcS3xqRsDlbsPGE0//P+5/9hfWh0L6gJWGrg9et6riC74/azZl+VssTmRS/V6sur5VEq64hrR5m3DEdwi4rsawkTXqWnxV5ZbnirYeEKy+VbpN+QWXfjcHe5BFnYOHTzF0gpq5AEB+fj5Dhgy56N9XurCSl5fHiBEjardPnz7NsWPHGDx48AVv27NnTwBsNhszZsxg7ty5HDp0qPajQ+vWrbvg+Vf69+9Pfn5+7bbh8fLe5N8245E03+7duwNWJ63K0LC2lVZ93ok3K30Bf62Oi7Xzu59N54oHrJ3UntPw+XeXluNMrFupdLaPp7o0dA0+2GtgZQZV+4BhwK9OVvOZt03AdW3iE9j8zJ9oZw/8a40VrO4DKntAsPpWKfPGcP+J9gR7lS+NqSI/L8/yTGB9D4AL7wOtsQcA7KtKZNnnBu4G8zgHPm4Y2I3n6r0/W0nmAtb555lLea3CF/DX6jZ2H4/86Dtk/GycklzSB6yTc7KK457AE6u1adeedX9ZQKLjUQWp1L8Xq65vlUqfgznHEwh2zEVSjJs9219XdvRqNPWAYPWtUuBKYMlpR8BcwI6Pr6UmslLRXADMtYKmULqwkpyczNq1a/F6vXi9Xu68807S09NxOp3nvZ3L5aK8vJykpCQANm/ejMPhoEePHrW/s2HDBp599vyfQ4yPj/dbhfLVeHivBY+nOTIzM7HH1r0MVmZoWNtKl1TA/70GVV5q10addujbwcGtV/dVdqKihs9/ydsfkXn/d7HFOIjv2omaSldID/sL9hpYmUHlPvDACfhlvv83QDjt8N1UO6OuuEpJJrC+D6jsAcHqW+nb78H6Q+bHf85x2uGBoW0Z0vXi/0IQSlb3ALjwPtBae8BVBmx9HQ6V1/UBGxAXY+e+qy+hW7yas5fKXMA63atg1//Mc2ucmwvE2qBngoPpI/so+QgASB+w0i+LzXOrNZwLTO5p52sX8YfWcFH9Xqy6vpW+dxD+UQSuBvvA/ZltGJoicwGrMqjaBzINeOUNKDjrPxdo47AzNyuJHglJlmdqLqULK1OnTmXNmjWkp6fTq1cv+vXrR5cudV8Jk5OTw/LlyykpKWH//v3MmjWLXbt24XQ6mTBhAm63G7vdTqdOndi4cSOxsbGAeUJct9vNJZe0bFI28vc/JnlYOg5nDElX9eHVHzzeovuL1AzhcFk7eGY0PHHAPEGV0wE39oA7++t19mf32QoKnnmJCWtzMQyDPQ+tiMoM4TDmUvOM739+Hz75wjxR1f+lwk8HqE7mT4cxqEOGcJhzJfSIh2c/hjNu6NMeZg3Q69tAdBh/OmQIB4cNln0V/lIAGw6bJ6zL7AK/ugq6afRtIDqMPx0yhEPXtvDsaPjTQdhZbH4b2MTL4CcDULaoEowOY1CHDOGQdQksGgGLD8JHZeZc4DuXwz0DVSfzp8MY1CFDOPxkAHRrCysK4XQ1XJ5gzgWv6ao6WR0dxp8OGcLBZoMnr4anPoD/HDJPaD+4E/ziKujR+Bk9tGQzDH3OuT19+nSuvfbaRr9e+WI999xznDx5kjlz5jTpdr4aD6t63tKi2k017fDqgNVJqzI0rC2s3weCvQbRuA8UlMJt2+C50dC/o9osqvcB1fWjnbwPqBHNPQBkH9CN7ANqRHMfkLmAXqKtBwSrr4JOPaA5tBpBeXl5zJ49u8X3c9ttt4UgjRBCCCGEEEIIIcT5abWwcvDgQdURhBBCCCGEEEIIIS6aVgsrQkSKhMuSufHl33Hm4CEccU4+WfcGB5dtiroMQkQz1WNQdX0hop0OY1CHDEJEM9VjUHV9UUcWVoRoptPvFrH15lxsdjvZry/kw+dewVNVHXUZhIhmqseg6vpCRDsdxqAOGYSIZqrHoOr6wmRXHUCISOdo68TujMHmUDecdMggRDRTPQZV1xci2ukwBnXIIEQ0Uz0GVdePdnLEihDN1GVwKtevnU/nKy5n36J/U1NeFZUZhIhmqseg6vpCRDsdxqAOGYSIZqrHoOr6wiTLWfXZbcR16WBZubguHcBuU5IhaG3RJKffLeLFmx5my00PkTJ6EADJw9K54kc30PaSjox4dEbAthUZhj00jXbdk+hyVR8G/vibAdviAizsAyp7QKP1RZOo7gPSA8JA5gKiCVT3gMYySB9oIdXvxarriyZR3QekB+hBjlipx+5wMHXfMvAZFhW0YXc41GQIUls0z5mDh6g8eYbuX8/k2Kt7ScroQ9aCO9h+12I8FS6/bSsy7H18NSMenYGnys2eeX/DEef02xbnZ2kfUNkDGqkvmkd1H5AeEDoyFxDNoboHNMwgfaBlVL8Xq64vmkd1H5AeoJYsrDRgdzhAcW/RIYNomgNLN5L1m9s59upe2vfqSvWZcmIT2uKpcAVsW5GheE8BZZ+eBMDrcvttiwtTPQZV1xfNo7oPSA8IHR3GoA4ZRNOo7gENM0gfaBnVY1B1fdE8qvuA9AB15KNAQjRD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8m1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLyqe4D0gNM0gOEKqp7wPkytCbSB4TOVPcB6QEmHXqAHLEiRAh9sPKl2p/fnPOU33UNt8OpcM1r592OFDfeeCOFhYWUlZUxefLk2p8nTpxY+zubNm3iuuuuC3r7K6+8kuzsbL/LNmzYQG5uLosXL+bo0aPs2LGDkSNHUlRUxKpVq5gyZQpLly5lzpw54XxoohXToQ9IDzBJDxAq6NADQPrAOdIHhAo69AHpASareoAsrAghtFVRUcETTzzBwoUL/X6ur6ioiPHjx7Np0yZWrFhRe/nzzz9/wfsfM2YMmZmZpKWlkZqayrRp04iJieHs2bMhfyxCiKaTHiCEkD4gRHSLlB4gCytCCG3dd999JCUlsWTJErZs2cKwYcNYsmQJWVlZZGVlAZCamsqRI0eYNGkSkyZN8rv9kSNH2Lp1K4WFhYwaNYpBgwZxww03kJubi2EYJCcnk5ycDEDfvn1ZvHgxM2fOJDEx0fLHKoQIJD1ACCF9QIjoFik9wGYYhkWnvRdCf74aD6t63mJZvWmHV2OP9V/ftDJDsPoqFJTCbdvgudHQv2PTbutyuVi+fDmzZs0KSZbVq1czevRoUlJSQnJ/IrJY3QMgcBxKD2jabaUHiFCTPqCG9AGhi2jrAcHqqxDpPUB9FxVCiBaIi4sLWRMFuOUWa99IhRAtIz1ACCF9QIjopkMPkG8FEiLEMmZPDekZ/yOtvhDRTvUYVF1fCKF+HKquL0S002EM6pAhmsgRKw34vF7wWfTpKLvN/I56FRkaqS1aLqFXV/p8Zwwf/+s1DK8v6uq3Bpb1AZU94Dz1RcuoHoOq67cGMhcQLaV6HKqu3xqofi9WXV+0jA5jUIcM0UQWVurxeb2sueoOXKfLLKkX16UDU/ct82tmVmUIVluERvmhU0obmOr6kc7KPqCyBzRWX7Sc6jGoun6kk7mACAXV41B1/Uin+r1YdX3RcjqMQR0yRBM5Nqg+n2HZRAowazVcibYoQ9DaIiTKPjnBgJkTlR16p7p+xLOwD6jsAY3WFy2megyqrh/xZC4gQkD1OFRdP+Kpfi9WXV+0mA5jUIcM0USOWBEixIrWbo/q+kJEO9VjUHV9IYT6cai6vhDRTocxqEOGaCLLV0IIIYQQQgghhBDNJAsrQgghhBBCCCGEEM0kCytCCCGEEEIIIYQQzaT1wsojjzxCv379sNvtrFu3zu+6MWPG0Lt3bzIyMsjIyCA3N1dNSNEiPgOOlMNnLtVJhCouLxyvVJ1CqFTmhkPlUO1VnUSocqba/L+cPzE6+Qw4WgHFVaqTCFWqvXBC5gJR7Ysa+LTcnBeK6BTpcwGtT147duxYbr31VmbMmBH0+oULF5KdnR3WDGlTx9DvtrEYhsHuB5/m8/c+CWs9XTOEw2sn4Dfvmo3Ua8AVHeHRIdC9nepkdcb+40G6DOrNweWbeXfRv6M2QzgYBiz7AFZ9bL7+AE++D48PhziNOpMO40+HDOFQ4YFH9sJrJ8FhA7sNZvSF7/cFm011ujo6jEEdMoTD4XL4VT58+OWXX9yzGx7OhGu6qs3VkA5jUIcM4fBmMTz6Dpxxm+8LfTvAo0OhV4LqZHV0GH86ZAgHw4BVhbD8Q/B8ORf400H43VegncwFtMsQDi4v/HofbD1mzgVsNritD/woXeYCOmYIhxOV5lzgQKm5PWsXPHgVfD1FaawmU37ESmlpKdOnT2fgwIEMGTKEu+++m5kzZwKQlZVFampqk+6voqKC66+/nmuvvZbp06djGM1f8nImtmPA7RN58dsPs33WnxjxaPAFnnDSIUM4vPc5/DIfTleD22f+w/rAGbj9DajR6KvWd9z3JG/lPhv1GcLhuY9h5cfmG+q51zzvM3jwbbW56tNh/OmQIVzuz4Ntp8zJdLUPqrzm5Pr5T1Un86fDGNQhQ6i5PDDjDfjgbN3i6hk3/DwPCs6qzVafDmNQhwzh8OFZmLMHil3m+4DHMPeHmW9AlUd1ujo6jD8dMoTD2kOw9AOz/5+bC7x92uwDutBh/OmQIVweehteOV43F3B54dlCc8FNJzqMQR0yhFqNz+z5+8/UzQXKasx/D+z7XG22plK+FjxlyhQmTZrEypUrKSkpIS0tjQULFlzUbR944AHmzZtHeno6jz32GOnp6bz00kuMHj2aX/7yl/zwhz9k3759ZGRkBL19ZWUlBQUFtduGx//Ys6TMNE7tfh9fjYfyI8XEtmuL3RmDzx26d/u9e/dii3EoydCwtpWWfJZKjS8RqFuK9gFlbi8r3jzEsPhSJbkaPv+VJ8I7ooO9BlZmULUP+AxYfnww1YZ/C6oxYPtJH6/sOUDnmBrLc4H/89/ae0Cw+lYp9rThrZIBeBqs71f74C8Hauhz5j3LM0Hg8w/W9wErM6h8H3izojOVNT3w4V+/xmewaM8ZftjlUyW5ZC5gneWne1Hj60zDuUBljZflO4/w1XZqZtVWzwXgwvtAa5wLAPzl+JVU+5x+l3kMyC/xsWX3+3SNrVaSS+YC1jjjjeX1EwPxBpkLPF3gYWDZu9gVHLUSbXOBYPWtkl/ZkbPVvQLmAm6fwaK3znJXUpHlmc7p378/8fHxF/37ShdWtm3bRnFxMffeey8AycnJpKSkMHz48AvedtWqVfTs2RPDMFixYgXjxo2jqKiIPn36kJ+fD0B5eTmdOnVq9D4KCgoYOnRo7bYDG8u73VS73aZTe9ylFbXb7rIK2nRMoKq4tKkPtVEjRozAS91RNVZmaFjbSgOf+oi4SzsGXO6q8fHwn/7GyX89Zn0oAp//cAv2GliZQdU+YG8TT+aaiqDXuSu/4FszZlF+YJvFqUz1n//W3gOC1bdKh8zx9J77T2LaJQZcV+aLZejw4eCz/vA1q3sAXHgfsLK2lVJue5RLv/OrgMsNbGx//xh/vWdokFuFn8wFrDNg0V7ie3cJuNxtOPjt8n9ybNUDClJJH7DS0PXB61ZXfMEtP/05ZfmbLU5kkrmANRKuuIa0eZtwxHcIuK7C52DEqDH4qr6wPFe09YBg9a3SbcovuPS7OdgDFnVsvPXpaYaOVzMXAMjPz2fIkCEX/ftKF1by8vIYMWJE7fbp06c5duwYgwcPvuBte/bsCYDNZmPGjBnMnTuXQ4cO0bdvX7Zt28aAAQPIzMykV69ejd5H//79axdhwFwZfG/yb2u33aXlOBPrVqmc7eOpLi1v0mO8kN27dwesTlqVoWFtK/35syTedRkY+C9Dx8XamX/3DIY9YG0zO6fh8x9uwV4DKzOo2gd8Bsw+4aHCF9iCnPHtWfe3JXRSeMTKuee/tfeAYPWtUuxxknOyPcH+1pZod5Ofp+Y4cKt7AFx4H7CytpXerOjM30u9uA3/+jYMRg/ozrP13p+tJHMB6yw/3YO8qsC5gNPm5f7bb+ar94xVkkv6gHV+ftxNaYMjVgDatGvP6j8/TtfYRxSkkrmAVUq9sfziRALBzlfbzu5l9/bXlB2xEk09IFh9q+RXduSZMw6qG6zp2DAYfnkXViqaC4C5VtAUShdWkpOTWbt2LV6vF6/Xy5133kl6ejpOZ2CDrc/lclFeXk5SUhIAmzdvxuFw0KNHD5YvX86UKVO45557uOeee9i2bRujR48Oej/x8fF+q1C+Gg/1Dz4vefsjMu//LrYYB/FdO1FT6QrpYX8AmZmZ2GPrXgYrMzSsbaV7z8APd5jnVznHDnRo4+AHI1OJVXT2n4bPf7gFew2szKByH/hhIfylAFz19gGnHb7a1c51wwcpyQT+z39r7wHB6ltp805467R/H2hjhzsHOhnS++L/QhBKVvcAuPA+YGVtK13hgfWvgMdtfvzjHKfdxs++0pn0xM5KcslcwDr3noXp2/17gA2Ij3Vwx9WXExdzuZJc0ges85PO8If95kc/znHaYUgXOxNGDFSSCWQuYKWvfXm+Nb+5gANuT49hWJrMBVTVt8pgH6x7xfyG2PoLbLF2Gz8b1pHBndXsA82hdGFl6tSprFmzhvT0dHr16kW/fv3o0qXukNCcnByWL19OSUkJ+/fvZ9asWezatQun08mECRNwu93Y7XY6derExo0biY2Nxefz0bmzORnr3LkzpaWlzc7nPltBwTMvMWFtLoZhsOehFS19yBGZIRyu7AS/GQa/2QelbvPztGkd4A9fQdmiSjAjf/9jkoel43DGkHRVH179weNRmSEc/q+PebK6lYXmyaoMA8amwC+uUp2sjg7jT4cM4bJgODy2zzxpndeAOAf8MB2+fbnqZP50GIM6ZAi1uBhYMcr8JoCCs+a3QnV2wq8yID3wE2LK6DAGdcgQDn0Tzff9R98xT2bvMaB3gnmZTt8Op8P40yFDOHyrl/kNccs+BI/PPKL12m4wL0N1sjo6jD8dMoRLzhBY8C68eNTsAW3sMD0NvtdHdTJ/OoxBHTKEWowdnr7GPFnt/jPmN0ElxsIDg2Gwmr+vNJvNaMnX5oTY9OnTufbaaxv9euWLcebMGaZOnUpNTQ2JiYmsWbOGNm3aXNRtfTUeVvW8pdm1m2Pa4dUBq5NWZWhYWwWfAW+chPvy4LnR0L+j0jiW7wPBXoNo2weqvVBcBZ3aQEKs0iiA+n1AdX0V3v4MfvgmrLgGBil+E5X3ATU+c5m9ICVe/ddryj5gPcOA7VE8FwDZB9xe89uhEp3QXuYCyuurcG4u8Ldr1P+DOtp6QLD6KnxeDZUecy6g4iNgLaV+NlVPXl4es2fPbtF9dOrUiZdffjlEiUS42W1wSVvVKYRKbRzQI0F1CqFS/JfvRDodrSaslRSnOoFQySZzgajndMBl7VSnECqdmws4ZS4QtTq3Mf+LVFotrBw8eFB1BCGEEEIIIYQQQoiLptXCSqRIuCyZG1/+HWcOHsIR5+STdW9wcNmmqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBCCELK812+t0itt6ci81uJ/v1hXz43Ct4qqqjLoMQ0UyHMahDBiGimeoxqLq+ENFOhzGoQwYhop18iq2FHG2d2J0x2BzqnkodMggRzXQYgzpkECKaqR6DqusLEe10GIM6ZBAiWskRK83UZXAq16+dT+crLmffon9TU14VlRmEiGY6jEEdMggRzVSPQdX1hYh2OoxBHTIIEe1kObOZTr9bxIs3PcyWmx4iZfQgAJKHpXPFj26g7SUdGfHojIBtKzIMe2ga7bon0eWqPgz88TcDtsUF2G3EdelgSam4Lh2Cf5eYRRkarS8umvSBVsjCHgCNjEPpARFFdR+QHhAG0gdEE6juAY1lkD7QAlHUAxqtL5pMjlhpoTMHD1F58gzdv57JsVf3kpTRh6wFd7D9rsV4Klx+21Zk2Pv4akY8OgNPlZs98/6GI87pty3Oz+5wMHXfMvAZFhSzYXc41GVopL5oOukDrYelPQCCjkPpAZFJdR+QHhA60gdEc6juAQ0zSB9ovqjqAY3UF00nCyshcGDpRrJ+czvHXt1L+15dqT5TTmxCWzwVroBtKzIU7ymg7NOTAHhdbr9tcWF2hwMU9xYdMoimkT7Qeugw/nTIIJpOdR+QHhA6OoxBHTKIplHdAxpmkD7QfDqMPx0yiIsnCyvNUH60hK0359ZulxYc5sVvPUT69PEceTmfkrc+5Cu53+fM+4f9tnfevxTD6wtrBiGENaQPCCFU9wHpAUKopboHnC+DEMJasrASQh+sfKn25zfnPOV3XcPtcCpc89p5tyPFhg0b+Pjjj/nf//7HjBkz+OSTT/jf//7Hj370IyZOnAiAy+Vi+fLlzJo1K+D2+/fv58EHH+T3v/89aWlpAOTl5bF582YMw2D8+PG89957fPWrX+Vf//oXDz74IM8//zyjR48mJSXF0scqWg/pA6ElfUBEIh36gPQAk/QAoYIOPQCkD5wjfUBYQU5eK7R14403csMNNzB06FAmT55c+/O5BgqwadMmrrvuuqC3v/LKK8nOzva7bMOGDTz88MN06dKFo0ePsmPHDgzDoKioiFWrVjFx4kT+/ve/h/NhCSGaQPqAENFNeoAQQvqAiARyxIrQVkVFBU888QQLFy70+7m+oqIixo///+3dbXBU9RXH8d9uHo0KRbJAYUgKIgm0YIBgIvKQaVEqMHampQyjDFR4U1usDQwzzNShNE61Ok61NZYXQlOpVoY6GdviE047PLUQQzQdHgxjRDAiD2kqaAghye7ti5UEko2Qy+49N93vZ4YXu8u95+xmzrn/PXv37hy9+uqrqqio6Lz/5ZdfvuL+S0pKNGnSJI0ZM0ajR4/WkiVLlJqaqrNnz8b9uQBwhz4AJDd6AAD6APoDBivwrZUrVyo7O1vl5eV6/fXXVVhYqPLychUXF6u4uFiSNHr0aDU0NGjevHmaN2/eZds3NDRo27Ztqq+v14wZMzRhwgTNnz9fZWVlchxHoVBIoVBIknTLLbfomWee0fLlyzVw4EDPnyuA2OgDQHKjBwCgD6A/CDiO49HvSPlfpL1Dm3IWeRpzyUebFUzrmm95mUP32FbqzkiLd0ovzJTyv9K3bb/s+5RubN68me9TJjmv+4BlD4gV38K19ACJPoD4Yi1gg7UA/MT6WGwd3wJrAfR3XGMlzgpWLVQgxe5ltY7vtczMzLg1UElatGgRDRTXzLoOreN7jT4Av7GuQev4XqMHwI+s69A6vtfoA7CWPNXmkRtyh+rm75eYNTLr+ADs69A6PpDsrGvQOj4A+zq0jg8kGyotzpqPndIHf94et9+m72/xAdjXoXV8INlZ16B1fAD2dWgdH0g2DFbi7LMPT2jc8rlm02Hr+ADs69A6PpDsrGvQOj4A+zq0jg8kG/urlf2fOVK5K6njA7CvQ+v4QLKzrkHr+ADs69A6PpBsGGECAAAAAAC4xGAFAAAAAADAJQYrAAAAAAAALvl6sPLII49o7NixCgaDeuWVVy57rKSkRKNGjVJBQYEKCgpUVlZmkyQAAAAAAEhavh6s3HnnnXrjjTc0c+bMmI8/9dRTqq2tVW1trdauXRv/+C89rEUHNmriT78X9333pxwSpf4z6cE90g++uLbWH+ullg7bnIDu/FCDfsghESKO9MIH0oN7o7d/ViPtOW2bE9CdH+rPDzkkytFmqbSqay1Q8b7U3G6bE9CdH2rQDzkkguNIWz6UflIVvb1mn7TzpG1OgBvmvwp05swZPfTQQ9q3b58yMjI0ffp0nTt3Ths3blRxcXGf99fW1qZ7771XjY2Nmj9/vlavXu06t3+u/J2Gz5iorOGDXe/jWvkhh0RoaJbu3yW1hiXni/v+fkJqaJH+MEMKBkzTAzr5oQb9kEMiPLlf+mtDtA9I0rFz0qq3pSemStOH2uYGXOSH+vNDDolw8ry0dGf0Q5WLa4EdJ6Wju6UXZ0mpvv74D8nEDzXohxwS4dn3pJc+lC58sRb4uCU6XCmbJM0eYZsb0Bfmh6wFCxaooKBABw8e1Jtvvqnnn39ehYWFV7XtmjVrNGHCBC1YsECHDx+WJFVWVmratGnasWOHqqqq1NjY6Dq3lhP/db1tvPghh0SoqJfaIl0LKUnqcKQjn0tvu/+TAXHnhxr0Qw7x1tQqVR7rGqpc1BaRnj5okxMQix/qzw85JMKL9dE3U93XAp+0SLtPmaUF9OCHGvRDDvH2ebv0pyNdQ5WL2iLS04eiZ7MA/YXpGSs7d+7U6dOnVVpaKkkKhUIaPny4pk6desVtN23apJycHDmOo4qKCt111106cuSIjh49qsmTJ0uSxo0bp+rqas2dOzfmPlpaWlRXV9d52+kIx/x/ifTuu+8qkJpikkP32F7ac2K8wk5mj/vbwhG9deik0j/mHEDY8LoPWPaAWPG9cqB1gFI1Sh3qGftos7Sv5h3OXIMJ1gLe2XUqXx1OVo/7z4cdvfXeKQ048YlBVoD9sdg6vlfev3C9As4YKcZa4OR5R3tq/q3MYMTzvABJys/PV1ZWz2NUb0wHK9XV1SoqKuq83dTUpOPHj2vixIlX3DYnJ0eSFAgEtGzZMq1evVrHjh1TXl6edu3apdmzZ2v37t0aP358r/uoq6vTlClTOm+nKKANw757Dc+o74qKihS+5LMaL3PoHttLYx/doRu/3vPaOe3nW/Sb8rVa+9ZGg6wA7/uAZQ+IFd8r1426VfmP/0vBjJ4HrHDLZ5paOCXGVkDisRbwzs0P/00Dp8xVIHj5CdSRC+e14bnH9OjW35rkBVgfi63jeyXjq2M0/rf7FUzvOViJXGjVHUWFUsT7YTcgSTU1NZ0nbFwN08FKKBRSZWWlwuGwwuGwHnjgAeXl5Sk9Pf1Lt2ttbVVzc7Oys7MlSa+99ppSUlI0cuRI5ebmatu2bZozZ46GDh2qIUOG9Lqf/Px81dTUdN52OsLa/53H4/PkrlJVVVWPCbVXOXSP7aXa8wP1XFNE7d2+jZaVdZ3+8ugKXferH5nkBXjdByx7QKz4XnEcad2pgE52OHLUdWpKWiCsbw9t0cZLejPgJdYC3jnUeqOebZLau72fy8jM1Ja1y3XjL5aa5AVYH4ut43vpsVNhfdQeUfiS9wRpiuiOmz7Xhuq3TXICpOisoC9MBysLFy7Uli1blJeXp9zcXI0dO1aDB3ddkGndunXasGGDGhsbdeDAAa1YsUJ79+5Venq67r77brW1tSkYDGrQoEHaunWr0tLSJEnr169XJBLR4sWLdfvtt/caPysr67IpVKS9Q/sveXzakz9UqDBPKempyr71Zv3j/ifi/hpMmjRJwbSuP4OXOXSP7aXJksKHpd+/L6UFo2+y0oLSr29LUcHgApOcAMn7PnClHpDoHCz7wHMt0o/3SKdaoxesbg9LM4el6OdThiktOMwkJ4C1gHcmS1K99GxddA0gJ9oLnpga1G2hK5+9DCQKawHvrG+NrgU+bpFSAlJ7RCoKBfXLwiHKSOn9A3LAbwKO45/LAi1dulSzZs3SsmXLXO/j+PHjuu+++xQIBFRaWqp77rnnqreNtHdoU84i17HdWPLR5h6N1Kscuse28OkF6Z0m6fpUqTCbXwCAPa/7gGUPiBXfa44j7f9UOt0q5Q2QRt5glgogibWAhbNtUs1/pMxUqXCwFONbAYCnrI/F1vG95jjSwTPRXwobM0D6GmsB9EPmP7d8qerqaq1ateqa9jFixAht3749Pgkh4QZlSN8abp0FACuBgDTxJussAFgamC59k7UAkLQCAekbg6L/gP7KV4OVQ4cOWacAAAAAAABw1fjiBQAAAAAAgEsMVgAAAAAAAFxisAIAAAAAAOASgxUAAAAAAACXGKxcKhhQ5uABnoXLHDxACgZMcogZG4CnfcCyB/QaH0h2rAUAWB+LreMD6LOA4ziOdRJ+EgmHpYhHL0kwoGBKik0OvcQG4GEfsOwBXxIfSHasBQBYH4ut4wPoGwYrAAAAAAAALvFVIAAAAAAAAJcYrAAAAAAAALjEYAUAAAAAAMAlBisAAAAAAAAuMVgBAAAAAABwicEKAAAAAACASwxWAAAAAAAAXGKwAgAAAAAA4BKDFQAAAAAAAJcYrAAAAAAAALjEYAUAAAAAAMAlBisAAAAAAAAuMVgBAAAAAABwicEKAAAAAACASwxWAAAAAAAAXGKwAgAAAAAA4NL/AHbu9LjM4ifmAAAAAElFTkSuQmCC", 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" ] }, - "execution_count": 20, + "execution_count": 12, "metadata": {}, "output_type": "execute_result" } @@ -473,9 +484,6 @@ "source": [ "t = Parameter('t')\n", "\n", - "# ## Create the time-evo op circuit\n", - "# evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=1)) #MatrixExponential exact matrix exp, SuzukiTrotter(order=2) for order-2 Trotter evo op\n", - "\n", "# Create instruction for rotation about XX+YY-ZZ:\n", "Rxyz_circ = QuantumCircuit(2)\n", "Rxyz_circ.rxx(t,0,1)\n", @@ -508,7 +516,7 @@ }, { "cell_type": "code", - "execution_count": 21, + "execution_count": 14, "metadata": {}, "outputs": [ { @@ -518,7 +526,7 @@ "
" ] }, - "execution_count": 21, + "execution_count": 14, "metadata": {}, "output_type": "execute_result" } @@ -545,17 +553,17 @@ }, { "cell_type": "code", - "execution_count": 22, + "execution_count": 15, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" ] }, - "execution_count": 22, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" } @@ -594,21 +602,23 @@ }, { "cell_type": "code", - "execution_count": 23, + "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 96\n" + "The optimized circuit has 2Q gates depth: 96\n", + "Compared to the unoptimized circuit depth of 78772\n" ] } ], "source": [ "circuit_trans_opt = transpile(S_real_circ.decompose().decompose(), Fake20QV1())\n", "\n", - "print('The circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))" + "print('The optimized circuit has 2Q gates depth: ', circuit_trans_opt.depth(lambda x: x[0].num_qubits ==2))\n", + "print('Compared to the unoptimized circuit depth of', circuit_trans_unopt.depth(lambda x: x[0].num_qubits == 2))" ] }, { From 202b1be5a1278cc8ab06113548232e2ae6105215 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 29 Feb 2024 20:47:54 -0700 Subject: [PATCH 18/22] rename --- ... the quantum krylov subspace method.ipynb => krylov.ipynb} | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) rename docs/notebooks/{Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb => krylov.ipynb} (99%) diff --git a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb b/docs/notebooks/krylov.ipynb similarity index 99% rename from docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb rename to docs/notebooks/krylov.ipynb index 09ac02b..1b46098 100644 --- a/docs/notebooks/Calculating ground states on large scale systems with the quantum krylov subspace method.ipynb +++ b/docs/notebooks/krylov.ipynb @@ -74,7 +74,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -142,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": {}, "outputs": [ { From 73fba0fe68dc7468fac2664ed5dbcef48426688d Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 11 Mar 2024 12:18:17 -0600 Subject: [PATCH 19/22] small changes --- docs/notebooks/krylov.ipynb | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/notebooks/krylov.ipynb b/docs/notebooks/krylov.ipynb index 1b46098..b190c08 100644 --- a/docs/notebooks/krylov.ipynb +++ b/docs/notebooks/krylov.ipynb @@ -258,7 +258,7 @@ "source": [ "t = Parameter('t')\n", "\n", - " ## Create the time-evo op circuit\n", + "## Create the time-evo op circuit\n", "evol_gate = PauliEvolutionGate(H_op, time=t, synthesis=SuzukiTrotter(order=num_trotter_steps) )\n", "\n", "qr = QuantumRegister(n_qubits)\n", From d502a79b134ed607db944df8ba6f860b905bd799 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Fri, 22 Mar 2024 11:37:28 -0600 Subject: [PATCH 20/22] add changes from review --- docs/notebooks/krylov.ipynb | 13 +++++-------- 1 file changed, 5 insertions(+), 8 deletions(-) diff --git a/docs/notebooks/krylov.ipynb b/docs/notebooks/krylov.ipynb index b190c08..ca42b22 100644 --- a/docs/notebooks/krylov.ipynb +++ b/docs/notebooks/krylov.ipynb @@ -13,7 +13,7 @@ "source": [ "## Step 1: Map problem to quantum native format\n", "\n", - "Across disciplines, we're interested in learning ground state properties of quantum systems. Examples include understanding the fundamental nature of particles and forces, predicting and undestanding the behavior of complex materials and understanding bio-chemical interactions and reactions. Because of the exponential growth of the Hilbert space and the correlation that arise in entangled systems, classical algorithm struggle to solve this problem for quantum systems of increasing size. At one end of the spectrum, existing approach that take advantage of the quantum hardware focus on variational quantum methods (e. g. variational quantum eigen-solver). These techniques face challenges with current devices because of the high number of function calls required in the optimization process, which is incompatible with advanced error mitigation techniques, thus limiting their efficacy to small systems. At the other end of the spectrum, there are fault-tolerant quantum methods with performance guarantees (e.g. [quantum phase estimation](https://arxiv.org/pdf/quant-ph/0604193.pdf)) which require require deep circuits that can be executed only on a fault-tolerant device. For these reasons, we introduce here a quantum algorithm based on subspace methods (as reviewed [here](https://arxiv.org/pdf/2312.00178.pdf)), the quantum Krylov algorithm. This algorithm performs well at large scale on existing quantum hardware, shares similar [performance guarantees](https://arxiv.org/pdf/2110.07492.pdf) as phase estimation, are compatible with advanced error mitigation techniques and could provide results that are classically inaccessible.\n", + "Across disciplines, we're interested in learning ground state properties of quantum systems. Examples include understanding the fundamental nature of particles and forces, predicting and undestanding the behavior of complex materials and understanding bio-chemical interactions and reactions. Because of the exponential growth of the Hilbert space and the correlation that arise in entangled systems, classical algorithm struggle to solve this problem for quantum systems of increasing size. At one end of the spectrum, existing approach that take advantage of the quantum hardware focus on variational quantum methods (e. g. [variational quantum eigen-solver](https://learning.quantum.ibm.com/tutorial/variational-quantum-eigensolver)). These techniques face challenges with current devices because of the high number of function calls required in the optimization process, which is incompatible with advanced error mitigation techniques, thus limiting their efficacy to small systems. At the other end of the spectrum, there are fault-tolerant quantum methods with performance guarantees (e.g. [quantum phase estimation](https://arxiv.org/pdf/quant-ph/0604193.pdf)) which require deep circuits that can be executed only on a fault-tolerant device. For these reasons, we introduce here a quantum algorithm based on subspace methods (as reviewed [here](https://arxiv.org/pdf/2312.00178.pdf)), the quantum Krylov algorithm. This algorithm performs well at large scale on existing quantum hardware, shares similar [performance guarantees](https://arxiv.org/pdf/2110.07492.pdf) as phase estimation, are compatible with advanced error mitigation techniques and could provide results that are classically inaccessible.\n", "\n", "Let us now go into more details of how subspace methods, and the quantum Krylov algorithm in particular, work. Given a matrix $H$ for which we want to know its lowest eigenvalue, subspace methods construct of a smaller representation $\\tilde{H}$ of $H$, which captures its properties of interest. In the case of the quantum Krylov algorithm, the Krylov subspace is used to construct the effective representation.\n", "\n", @@ -58,10 +58,10 @@ "\n", "We can implement the algorithm on a quantum computer by using the Hadamard test to calculate the matrix elements of $\\tilde{H}$ and $\\tilde{S}$ as expectation values:\n", "\n", - "$$\\langle \\psi_m \\vert H \\vert \\psi_n \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i H t_m} H e^{-i H t_n} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert e^{i H m \\delta t} H e^{-i H n \\delta t} \\vert \\psi \\rangle$$\n", - "$$\\langle \\psi \\vert H e^{-i H (n-m) \\delta t} \\vert \\psi \\rangle$$" + "$$\\langle \\psi_m \\vert H \\vert \\psi_n \\rangle = $$\n", + "$$= \\langle \\psi \\vert e^{i H t_m} H e^{-i H t_n} \\vert \\psi \\rangle$$\n", + "$$= \\langle \\psi \\vert e^{i H m \\delta t} H e^{-i H n \\delta t} \\vert \\psi \\rangle$$\n", + "$$= \\langle \\psi \\vert H e^{-i H (n-m) \\delta t} \\vert \\psi \\rangle$$" ] }, { @@ -842,16 +842,13 @@ "\n", "H_real_results_list, H_imag_results_list = [], []\n", "for i in range(len(job_idxs)-1):\n", - " # print('executing circuits: ', job_size*job_idxs[i], 'to', job_size*job_idxs[i+1])\n", "\n", "\n", " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_real.job_id()}\")\n", " jobs['H']['real'].append(job_real.job_id())\n", " H_real_results = job_real.result()\n", "\n", " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " # print(f\"job id: {job_imag.job_id()}\")\n", " jobs['H']['imag'].append(job_imag.job_id())\n", " H_imag_results = job_imag.result()\n", "\n", From 9ce3a8a9c652b798b38edd6d45824aca66ddb86e Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Mon, 25 Mar 2024 15:18:00 -0600 Subject: [PATCH 21/22] use estimator v2 --- docs/notebooks/krylov.ipynb | 319 +++++++++++++----------------------- 1 file changed, 118 insertions(+), 201 deletions(-) diff --git a/docs/notebooks/krylov.ipynb b/docs/notebooks/krylov.ipynb index ca42b22..519933c 100644 --- a/docs/notebooks/krylov.ipynb +++ b/docs/notebooks/krylov.ipynb @@ -74,7 +74,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -86,13 +86,13 @@ "import warnings\n", "warnings.filterwarnings('ignore')\n", "\n", - "from qiskit.quantum_info import SparsePauliOp, Operator\n", + "from qiskit.quantum_info import SparsePauliOp\n", "from qiskit.circuit import Parameter\n", "from qiskit import QuantumCircuit, QuantumRegister, transpile\n", "from qiskit.circuit.library import PauliEvolutionGate\n", - "from qiskit.synthesis import SuzukiTrotter, MatrixExponential\n", + "from qiskit.synthesis import SuzukiTrotter\n", "from qiskit.providers.fake_provider import Fake20QV1\n", - "from qiskit.primitives import Estimator\n", + "from qiskit.primitives import StatevectorEstimator\n", "\n", "def solve_regularized_gen_eig(h: np.ndarray, s:np.ndarray, threshold: float, k: int =1, return_dimn: bool = False) -> Union[float, List[float]]:\n", " \"\"\"\n", @@ -142,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 4, "metadata": {}, "outputs": [ { @@ -186,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "metadata": {}, "outputs": [], "source": [ @@ -207,7 +207,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "metadata": {}, "outputs": [ { @@ -217,7 +217,7 @@ "
" ] }, - "execution_count": 8, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -241,16 +241,16 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "" + "" ] }, - "execution_count": 9, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -267,17 +267,11 @@ ] }, { - "attachments": { - "H_test.PNG": { - "image/png": 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" - } - }, "cell_type": "markdown", "metadata": {}, "source": [ "### Hadamard test\n", "\n", - "![H_test.PNG](attachment:H_test.PNG)\n", "\n", "\n", "\\begin{equation}\n", @@ -302,7 +296,7 @@ }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 8, "metadata": {}, "outputs": [ { @@ -319,7 +313,7 @@ "
" ] }, - "execution_count": 10, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -365,14 +359,14 @@ }, { "cell_type": "code", - "execution_count": 11, + "execution_count": 29, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The circuit has 2Q gates depth: 78772\n" + "The circuit has 2Q gates depth: 96\n" ] } ], @@ -466,17 +460,17 @@ }, { "cell_type": "code", - "execution_count": 12, + "execution_count": 9, "metadata": {}, "outputs": [ { "data": { - "image/png": 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qx6Hq+kJEGzliJcQSenWlz3fG8PG/XsPw+qKufmvg83rBZ8En5Ow27A6HugznqS9aRvU4VF0/0lnWA6DRcSg9ILKpHoOq67cG0gdES6keh6rrR7qo6QHnqS+aRhZWQqz80CmlDUx1/Ujn83pZc9UduE6Xhb1WXJcOTN23LKCRWZWhsfqi5VSPQ9X1I5mVPQCCj0PpAZFP9RhUXT/SSR8QoaB6HKquH8miqQc0Vl80nRwfFmJln5xgwMyJyg69U10/4vkMy5qo63RZ8FVoizI0Wl+0mOpxqLp+RLOwB0Aj41B6QMRTPQZV14940gdECKgeh6rrR7Qo6gGN1hdNJkeshFjR2u1RXV8IoX4cqq4vRLRTPQZV1xdCqB+HqusLEW1kCVMIIYQQQgghhBCimWRhRQghhBBCCCGEEKKZZGFFCCGEEEIIIYQQopm0Xlh55JFH6NevH3a7nXXr1vldN2bMGHr37k1GRgYZGRnk5uaGvP7YfzzILfufZvDPvh3y+46kDOF0sBReOGz+XOpWGqVRaVPHMPGFx5iw/lE6D+odtRnCwWvA9pOw/EPYeARcHtWJAukwBnXIEC6VHth20vx53+d6njtNh/GnQ4ZwKa6CfxTBMx/BB2dVpwmkw/jTIUM4fXC2bi7webXaLI3RYQzqkCEcfAbsOAVPf2juB5UyF9A2Q7i4PPDGKfPnt0+b80Pd6DD+dMgQLqddsLoIVnwEB86oTtM8Wp+8duzYsdx6663MmDEj6PULFy4kOzs7bPV33PckKaMGE5/SJWw1IiFDOHgNeDAfXj9Z1zx/thvmZ8L4y9Rmq8+Z2I4Bt09k06RfEt+tM6OW3MWWyfOiLkM4lLrh9jfgVBW4feC0wx/3w19HQt9E1enq6DAGdcgQDu+Xwp1vQs2X3wT5p4Pwn0Ow7BpoH6s0Wi0dxp8OGcLlhcPwm3fNv/J4DVj6AYxNgYczwW5Tnc6kw/jTIUM4GAbkvgMvHaubC9y3Bx4YDNm9lEbzo8MY1CFDOJTXwB074EiF+V7gtMMf9sNfRsIVHVWnq6PDGNQhQzgUlsEPd0C119z+8/vw70Pw9FehYxu12c7RYfzpkCFcth6Dh/fWzQWW2WBUV/j1MHBoMhe4GMqPWCktLWX69OkMHDiQIUOGcPfddzNz5kwAsrKySE1NbdL9lZSUMGTIEOLi4lqcrfLE5y2+j9aQIRw2HDaPVHD76iZTHgNy3oHPXEqj+UnKTOPU7vfx1XgoP1JMbLu22J3WrkfqkCEcfvsuHK2AKq+5D1R54YsamJ1nTrZ1ocMY1CFDqPkMuHc3lHug+suFlWofHKowF9h0ocP40yFDOJyoNBdVanzma+8xzPeE/54wJ1m60GH86ZAhHLYeh5ePB84FfvseHK9Um60+HcagDhnCYdEB+LQcXPXmAhUeuG+3Xkct6DAGdcgQaoYBc/aY87/6c4FjFeb7gy50GH86ZAiH0y5zUaXhXGBHcd2RjJFC+asxZcoUJk2axMqVKykpKSEtLY0FCxZc1G0feOAB5s2bR3p6Oo899hjp6ekkJibyyiuvcNNNN13w9pWVlRQUFNRuGx5vsx9Hc+3duxdbjENJhoa1rbTqVDouX7vAK3w+Vuw+xnXtS6wPReDz36ZTe9ylFbXb7rIK2nRMoKq4NCT1gr0GVmZQtQ94DPjv8Ux8+C9DG0BJpY/1uz+gp7PK8lxgfR9Q2QOC1bfKx9XtKHOnAf61a3yw5YiPG3zvYFPwVwqrewBceB9ojT0A4MWyrhi+S2n4Nx6XF57Z/wWXFH+kJJfMBayzsrgvLm/7gMsNn48Ve04wocMpBamkD1jFMGDTsQxqgvydt8zt5fldhfRtUxHkluGn+r1YdX2rHHW35VRlOkaDfcBjwP9OGOzJf4cYm/UrbNHWA4LVt8r/ypOw+brTcD7o8sKqg5X0Ol0Q/IYW6N+/P/Hx8Rf9+0oXVrZt20ZxcTH33nsvAMnJyaSkpDB8+PAL3nbVqlX07NkTwzBYsWIF48aNo6ioCKfTSefOnS+qfkFBAUOHDq3ddmBjebcLL8iE0ogRI/BS1zCszNCwtpUGPllAXPf0gMurazz8cclf+Pnzv1GQKvD5d5eW40ysG1DO9vFUl5aHrF6w18DKDKr2AZszjiH/Cr5w4qos53szf0j5wTcsTmWyug+o7AHB6lulfcZY+tz/PI74DgHX1RgwbPgwJYcuWd0D4ML7QGvsAQAp/5dLtym/xBZkHvfuB0UMnTA08AoLyFzAOgP+mE98nyEBl9f44MmnV/Lgc79SkEr6gJWG/MeLLcjx81UVFfww52eUvf2i9aFQ/16sur5V2vUfSd+cF3G0DVxg9Rpw9TWj8LmsX1yLth4QrL5Vun77flK+Ox97bOBk4KNDxxg6Uc1cACA/P58hQwLfoxqjdGElLy+PESNG1G6fPn2aY8eOMXjw4AvetmfPngDYbDZmzJjB3LlzOXToUJM+OtS/f3/y8/Nrtw2Pl/cm/7YJj6Dldu/eHbA6aVWGhrWt9HxpIv8t9+FtsELdJjaGP8+exuW/mKIkV8Pnv+Ttj8i8/7vYYhzEd+1ETaULnzt0Z1UL9hpYmUHlPvDIqUqO1ASuArdt146tK/9EG7uaSZ7VfUBlDwhW3ypVPjuzjycQuCcb9GlTybK33rI8E1jfA+DC+0Br7QEfVifwp8/A3WCox+Bj6uBkvlnv/dlKMhewzsaybmwp8wUcseC0w+9/MoX0e69Xkkv6gHUeL66g0J0ADY5gbROfwKa//oZ4+2NKcql+L1Zd3ypuw8Z9x+MD3gcAejirWLZjm+WZIPp6QLD6VjnkbsvjxbHUNLg8Bh839uvAKkVzATDXCppC6cJKcnIya9euxev14vV6ufPOO0lPT8fpdJ73di6Xi/LycpKSkgDYvHkzDoeDHj16NKl+fHy83yqUr8bDe/WuH/n7H5M8LB2HM4akq/rw6g8eb9L9X4zMzEzssXUvg5UZGta20uXVkP8alLnNv04DxDngq5fYuWl403biUGr4/LvPVlDwzEtMWJuLYRjseWhFSOsFew2szKByH3j4NPx0p/mXyS8/VkusHe4d6ODq3plKMoH1feBCPSDcGVTuA3cVwpMFdZ+rtgNOh42HRyQwsNPF/4UglKzuAXDhfaC19oBMA3buhrc+q9sHYmzQuY2dn301hY7OFCW5ZC5gnTQ37Hnd/CYg95f7QJwdhiTZuWVEPyUfBwTpA1Z6uNQ8eW2NF8598CHWDj/pb+eatAwlmUDmAlaa08U8YXH9uUCsHR7+SjyZXWQuYFUGVfvAEGDPW7D9lPnxHzDnAh1i7cwe2ZWkuK6WZ2oupQsrU6dOZc2aNaSnp9OrVy/69etHly51Z7rOyclh+fLllJSUsH//fmbNmsWuXbtwOp1MmDABt9uN3W6nU6dObNy4kdjY0H6NxJtzngrp/UVqhnDo3Ab+fi089zG8dhLaxcCUy+HGnqqTBSpc/SqFq1+N+gyhltEFVo6Gv30I73wOxS64byB8R7Nvj9NhDOqQIRxuTYNe7eHZQvPboQZ1hh/0hdTAI4KV0mH86ZAh1Gw2+MNXYN0h+HsRHK6ACZfBPVdAx/P/fcVSOow/HTKEQwcnPHct/L+P4b/HzT+wfKuX+Z+qRZXG6DAGdcgQagM6wnOj4emPIP8zcy5w9wD4bh/VyfzpMAZ1yBAON10O3dvByo/gWKX5bVAz+ur1DZGgx/jTIUM4PDrU/GKT5z42T2Y9NgV+NhC6tPy7aCyldGElLi6OjRs31m5Pnz6da6+9tnY7JyeHnJycoLfNb+SwIJ/Px7hx49i3bx/f+MY3+N3vfkdmprq/fovGdYmDewaa/4nolNbB/Cq1glK4bRsM6qQ6kbDaNV3N/0R0irHDlN5wZSezB9zcW5+v1xTW6OiEnw4w/xPR6fL28MiQurlAZuv6NmFxEUYkm/+J6OSwQXYv6J9o9oBb+0Teogpo8K1A9eXl5TF79uwW3YfdbueVV14JUSIhhBBCCCGEEEKIxmm1sHLw4EHVEYQQQgghhBBCCCEumlYLK0JEioTLkrnx5d9x5uAhHHFOPln3BgeXbYq6DEJEM9VjUHV9IaKdDmNQhwxCRDPVY1B1fVFHFlaEaKbT7xax9eZcbHY72a8v5MPnXsFTVR11GYSIZqrHoOr6QkQ7HcagDhmEiGaqx6Dq+sJkVx1AiEjnaOvE7ozB5lA3nHTIIEQ0Uz0GVdcXItrpMAZ1yCBENFM9BlXXj3ZyxIoQzdRlcCrXr51P5ysuZ9+if1NTXhWVGYSIZqrHoOr6QkQ7HcagDhmEiGaqx6Dq+sIky1n12W3EdelgWbm4Lh3AblOSIWht0SSn3y3ixZseZstND5EyehAAycPSueJHN9D2ko6MeHRGwLYVGYY9NI123ZPoclUfBv74mwHb4gIs7AMqe0Cj9UWTqO4D0gPCQOYCoglU94DGMkgfaCHV78Wq64smUd0HpAfoQY5YqcfucDB13zLwGRYVtGF3ONRkCFJbNM+Zg4eoPHmG7l/P5Nire0nK6EPWgjvYftdiPBUuv20rMux9fDUjHp2Bp8rNnnl/wxHn9NsW52dpH1DZAxqpL5pHdR+QHhA6MhcQzaG6BzTMIH2gZVS/F6uuL5pHdR+QHqCWLKw0YHc4QHFv0SGDaJoDSzeS9ZvbOfbqXtr36kr1mXJiE9riqXAFbFuRoXhPAWWfngTA63L7bYsLUz0GVdcXzaO6D0gPCB0dxqAOGUTTqO4BDTNIH2gZ1WNQdX3RPKr7gPQAdeSjQEI0Q/nRErbenFu7XVpwmBe/9RDp08dz5OV89sxbQebcmxkwc6LfdihPJtVYhtZkw4YNLFq0iMmTJ7N+/franzdv3lz7Oy6XiyVLlgS9/f79+8nOzqawsLD2sry8PObPn09OTg47d+5k6dKlHDhwgJycHDweD6tXr+b48eNhf2wi8qnuA9IDTNIDhCqqe8D5MrQm0geEzlT3AekBJh16gByxIkQIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIV06EPSA8wSQ8QKujQA0D6wDnSB4QKOvQB6QEmq3qALKwIIbRVUVHBE088wcKFC/1+rq+oqIjx48ezadMmVqxYUXv5888/f8H7HzNmDJmZmaSlpZGamsq0adOIiYnh7NmzIX8sQoimkx4ghJA+IER0i5QeIAsrQght3XfffSQlJbFkyRK2bNnCsGHDWLJkCVlZWWRlZQGQmprKkSNHmDRpEpMmTfK7/ZEjR9i6dSuFhYWMGjWKQYMGccMNN5Cbm4thGCQnJ5OcnAxA3759Wbx4MTNnziQxMdHyxyqECCQ9QAghfUCI6BYpPcBmGIZFp70XQn++Gg+ret5iWb1ph1djj/Vf37QyQ7D6KhSUwm3b4LnR0L9j027rcrlYvnw5s2bNCkmW1atXM3r0aFJSUkJyfyKyWN0DIHAcSg9o2m2lB4hQkz6ghvQBoYto6wHB6qsQ6T1AfRcVQogWiIuLC1kTBbjlFmvfSIUQLSM9QAghfUCI6KZDD5BvBRIixDJmTw3pGf8jrb4Q0U71GFRdXwihfhyqri9EtNNhDOqQIZrIESsN+Lxe8Fn06Si7zfyOehUZGqktWi6hV1f6fGcMH//rNQyvL+rqtwaW9QGVPeA89UXLqB6Dquu3BjIXEC2lehyqrt8aqH4vVl1ftIwOY1CHDNFEFlbq8Xm9rLnqDlynyyypF9elA1P3LfNrZlZlCFZbhEb5oVNKG5jq+pHOyj6gsgc0Vl+0nOoxqLp+pJO5gAgF1eNQdf1Ip/q9WHV90XI6jEEdMkQTOTaoPp9h2UQKMGs1XIm2KEPQ2iIkyj45wYCZE5Udeqe6fsSzsA+o7AGN1hctpnoMqq4f8WQuIEJA9ThUXT/iqX4vVl1ftJgOY1CHDNFEjlgRIsSK1m6P6vpCRDvVY1B1fSGE+nGour4Q0U6HMahDhmgiy1dCCCGEEEIIIYQQzSQLK0IIIYQQQgghhBDNJAsrQgghhBBCCCGEEM2k9cLKI488Qr9+/bDb7axbt87vujFjxtC7d28yMjLIyMggNzdXTUjRIuU1sOMU7D0NXjlvVlQ6WWm+/iJ6fXgW3jgFp6pUJxEqeHxQUGr+XOVRGkUoUuGBN4sh/zNzfxDRp7iqbi5gyHwwKhWWmXOBE5WqkwgVvAZ8cNb8uSJC5wJan7x27Nix3HrrrcyYMSPo9QsXLiQ7OzusGdKmjqHfbWMxDIPdDz7N5+99EtZ6umYIh+cK4ckCiLGbb6LxMfDHr8DATqqT1Rn7jwfpMqg3B5dv5t1F/47aDOFQ44OH34b/nTD3AYCH3oanvgqd26jNVp8O40+HDOFQ4oJ7dsGhcnMfqPbC+O4wL6Nun9CBDmNQhwzh8M5pmJsHlV9Oon6yC+4dCFN7q83VkA5jUIcM4fCvT2DRAXB8ORdo44DfD4eMLqqT1dFh/OmQIRw8Pnh0H7x4FGK/7Pu/ehueGgmXtFWbrT4dxp8OGcLhTDX8bDd8VGbuA24vjLkUcofU7RM60GEM6pAhHN4vhXt3wxc15vZPd8JPBsC0NKWxmkz57lpaWsr06dMZOHAgQ4YM4e6772bmzJkAZGVlkZqa2qT7e/nll8nKyuLqq6/mD3/4Q4uyORPbMeD2ibz47YfZPutPjHg0+AJPOOmQIRzeOAV/KQC3z5xQV3nhdDX8ZGfdBFsHO+57krdyn436DOHw5/fh9ZNQY5ivP8ChCpizR22u+nQYfzpkCJef7YKPv4Bqn/nXCY8BrxyH5R+qTuZPhzGoQ4ZQK3PDXbvgjNvcB8BccH3iAOSVqM1Wnw5jUIcM4ZD/GSw8YL7+5+YCpW6YtQvOulWnq6PD+NMhQzis+AhePmb2/3NzgaMVcM9utbnq02H86ZAhXObmmUcquL+cC9QYsO0k/Omg6mT+dBiDOmQItSoP3PkmfFZdNxfwGPDXAth+Um22plJ+xMqUKVOYNGkSK1eupKSkhLS0NBYsWHBRt33ggQeYN28e6enpPPbYY6SnpzNgwAC2b99OTEwMY8aM4Uc/+hEJCQlBb19ZWUlBQUHttuHx+l2flJnGqd3v46vxUH6kmNh2bbE7Y/C5Q/cv/71792KLcSjJ0LC2lZ4s7ku1r33A5TVeL0/vPMJX232uIFXg8195Irw5gr0GVmZQtQ/4DFhz/Crchn9trwEHz/jYsvt9usZWW54L/J//1t4DgtW3ytGaOIrK+uNtsL5f7YP/95GHr1S+a3kmCHz+wfo+YGUGle8D/ytPwuvtDvjXr/YZPLm3jLuSPlaSS+YC1vnzZ6m4fYmAze9yr9fLsl3H+XqCmhU2q+cCcOF9oDXOBQCePTaYasP/nyM+4NMyH+t3fUAPp5rPiMpcwBrFHif7P78CT5C5wL8/8TK6eh8OWyM3DqNomwsEq2+VNys6U+PtQeBcAJ585wvaXfKR5ZnO6d+/P/Hx8Rf9+0oXVrZt20ZxcTH33nsvAMnJyaSkpDB8+PAL3nbVqlX07NkTwzBYsWIF48aNo6ioiMsuu6z2d2JiYrDbGz8op6CggKFDh9ZuO7CxvNtNtdttOrXHXVpRu+0uq6BNxwSqikub8jDPa8SIEXip+zCplRka1rbSwKc+JO7SwIWV6hofv168nJP/ekxBqsDnP9yCvQZWZlC1D9jbxJO5piLoddWV5Uyd+RPKD2yzOJWp/vPf2ntAsPpW6ZA5ntS5/8TRLjHguiojhqHDh4PP+pMtWN0D4ML7gJW1rZRy26N0m/JLbAGTZhu7Cw7xzD1Dg90s7GQuYJ0Bi/YS3zsj4PIaHCxc/v+Y++wvrA+F9AErDV0fvK6r8gumzZpNWf4WixOZZC5gjYQrriFt3iYc8R0Crqv22ckadS2+qnLLc0VbDwhW3yrdpvyCS7+bgz3Ios7+w8UMnaBmLgCQn5/PkCFDLvr3lS6s5OXlMWLEiNrt06dPc+zYMQYPHnzB2/bs2RMAm83GjBkzmDt3LocOHar96NCLL75IWlraeVeZ+vfvT35+fu224fHy3uTf1m67S8txJtbd3tk+nurS0A7u3bt3B6xOWpWhYW0r/e10Z/ZUGfga/JWqTaydBfd8n0EPWNvMzmn4/IdbsNfAygyq9gHDgAdOujnjdQZc54xPYOOKP9HeEbhSb4X6z39r7wHB6lul1BvDL060J9irfEmMi/y8PMszgfU9AC68D1hZ20pvV3Xkb5/7Ao5cc+BjwsBLea7e+7OVZC5gnb+fSWF7hS/gyDWnzUvOD6cy9GfjlOSSPmCdeSddnPLEBVzujG/P2r/8lk6ORxWkkrmAVSp8DuYeTyDYcTedHDXs2f56kMX38Iu2HhCsvlUOuNrzl9MO3A3WdOwYjOrdkZWK5gJgrhU0hdKFleTkZNauXYvX68Xr9XLnnXeSnp6O0xn4j636XC4X5eXlJCUlAbB582YcDgc9evQA4PDhw/zud7/jhRdeOO/9xMfH+61C+Wo8vFfv+pK3PyLz/u9ii3EQ37UTNZWukB72B5CZmYk9tu5lsDJDw9pW6lwOt70Ornr/qoqxQa/2Dr43Mg27giYKgc9/uAV7DazMoHIfmHMU5r9jfqb2nDZ2yO5l59pBVynJBP7Pf2vvAcHqW2nSO/DS0brP1AI47fDzzDiGXHrxfyEIJat7AFx4H7CytpUG+2DLa3C8wvxMPZgfCHE67Nyblcxl7ZKV5JK5gHW6VcLu/5lzgXNzaocNusU7+MHIVGUnsZY+YJ37T8IDbwXOBcZ3t3Nd5iAlmUDmAlb6zn74zyH/fxM47TD7KidDe8hcQFV9q2QY8OLrUFRunmftHKfDxtysLvRur9GZzC9A6cLK1KlTWbNmDenp6fTq1Yt+/frRpUvdk5eTk8Py5cspKSlh//79zJo1i127duF0OpkwYQJutxu73U6nTp3YuHEjsbGxVFZWMn36dJYtW0a7du1alM99toKCZ15iwtpcDMNgz0MrWvqQIzJDOFyeAMu/Cr/fD/s+NydU13SFnEyULaoEM/L3PyZ5WDoOZwxJV/Xh1R88HpUZwmH8Zea3QCw5CEcrIdEJ0/rA9zQ6A7gO40+HDOHyq6sgJR6eLTRPWHdpW5h9pfltADrRYQzqkCHUYuzwt2tg4X7YetycUA1NgtkD4bKWvX2HlA5jUIcM4ZASDytGwR/2w1ufmXOBq5MhZ4he3wymw/jTIUM4jO4GC4aZJ60+VAEdYuG7qTCjn+pkdXQYfzpkCJd7B0JSG3im0PxWmEvizMvGdledzJ8OY1CHDKFmt8FfvwpPHITNR8xF1qs6m/PB3oFnjdCazTD0+bb46dOnc+211zb69coXY/HixSxYsIC+ffsCdediuRi+Gg+ret7S7NrNMe3w6oDVSasyNKytyvtn4Hvb4bnR0L+j2ixW7wPBXoNo3AcMAyWHegajeh9QXV+FglK4bVt09gCQ9wEwewDo0QdkH1AjmucCIPsAyFxA5gIyF4j2fUCnuUBzqO+i9eTl5TF79uwW3cddd93FXXfdFaJEwgqROnhE6Mg+IER0kx4gZB8Qsg8IEd0ivQdotbBy8KBmX1guhBBCCCGEEEIIcR5aLaxEioTLkrnx5d9x5uAhHHFOPln3BgeXbYq6DEJEMx3GoA4ZhIhmqseg6vpCRDsdxqAOGYQQsrDSbKffLWLrzbnY7HayX1/Ih8+9gqeqOuoyCBHNdBiDOmQQIpqpHoOq6wsR7XQYgzpkECLaaXTO9cjkaOvE7ozB5lD3VOqQQYhopsMY1CGDENFM9RhUXV+IaKfDGNQhgxDRSo5YaaYug1O5fu18Ol9xOfsW/Zua8qqozCBENNNhDOqQQYhopnoMqq4vRLTTYQzqkEGIaCfLmc10+t0iXrzpYbbc9BApowcBkDwsnSt+dANtL+nIiEdnBGxbkWHYQ9No1z2JLlf1YeCPvxmwLS7AbiOuSwdLSsV16WB+ebuiDI3WFxdN+kArZGEPgEbGofSAiKK6D0gPCAPpA6IJVPeAxjJIH2iBKOoBjdYXTSZHrLTQmYOHqDx5hu5fz+TYq3tJyuhD1oI72H7XYjwVLr9tKzLsfXw1Ix6dgafKzZ55f8MR5/TbFudndziYum8Z+AwLitmwOxzqMjRSXzSd9IHWw9IeAEHHofSAyKS6D0gPCB3pA6I5VPeAhhmkDzRfVPWARuqLppOFlRA4sHQjWb+5nWOv7qV9r65UnyknNqEtngpXwLYVGYr3FFD26UkAvC6337a4MLvDAYp7iw4ZRNNIH2g9dBh/OmQQTae6D0gPCB0dxqAOGUTTqO4BDTNIH2g+HcafDhnExZOPAjVD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8k1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLySR+whvQBoTPVfUB6gEl6gFBFdQ84X4bWRPqAiARyxEoIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIVkz4QWtIHRCTSoQ9IDzBJDxAq6NADQPrAOdIHhBVkYUVoq6KigieeeIKFCxf6/VxfUVER48ePZ9OmTaxYsaL28ueff/6C9z9mzBgyMzNJS0sjNTWVadOmERMTw9mzZ0P+WIQQzSN9QIjoJj1ACCF9QEQCWVgR2rrvvvtISkpiyZIlbNmyhWHDhrFkyRKysrLIysoCIDU1lSNHjjBp0iQmTZrkd/sjR46wdetWCgsLGTVqFIMGDeKGG24gNzcXwzBITk4mOTkZgL59+7J48WJmzpxJYmKi5Y9VCBGc9AEhopv0ACGE9AERCWyGYVh0umP9+Wo8rOp5i6U1px1ejT22bn3LygwNa6tSUAq3bYPnRkP/jk27rcvlYvny5cyaNSskWVavXs3o0aNJSUkJyf2JyGN1H1DZA4LVV6ElPQCkD4jQkrmAGjIXEDpR/V6sur4KMhcQkU79O6kQLRAXFxeyBgpwyy3WTqaFEC0nfUCI6CY9QAghfUCoJt8KFGIZs6eG9EzfkVZfCKF+HKquL0S0Uz0GVdcXQqgfh6rrCxFt5IiVEEvo1ZU+3xnDx/96DcPri7r6rYHP6wWfBZ+Qs9vM76dXleE89UXLqB6HqutHOst6ADQ6DqUHRDbVY1B1/dZA+oBoKdXjUHX9SBc1PeA89UXTyMJKiJUfOqW0gamuH+l8Xi9rrroD1+mysNeK69KBqfuWBTQyqzI0Vl+0nOpxqLp+JLOyB0DwcSg9IPKpHoOq60c66QMiFFSPQ9X1I1k09YDG6oumk+PDQqzskxMMmDlR2aF3qutHPJ9hWRN1nS4LvgptUYZG64sWUz0OVdePaBb2AGhkHEoPiHiqx6Dq+hFP+oAIAdXjUHX9iBZFPaDR+qLJ5IiVECtauz2q6wsh1I9D1fWFiHaqx6Dq+kII9eNQdX0hoo0sYQohhBBCCCGEEEI0kyysCCGEEEIIIYQQQjSTLKwIIYQQQgghhBBCNJPWCyuPPPII/fr1w263s27dOr/rxowZQ+/evcnIyCAjI4Pc3Fw1IUWLGAaUulWnECp5fFDiApdXdRKhSvWXr71XzpsWtb6ogdMu8z1BRB/DgLMyF4hqtXMBj+okQhX3l3MBj3yJUdQqr4HPInguoPXJa8eOHcutt97KjBkzgl6/cOFCsrOzw1f/Hw/SZVBvDi7fzLuL/h22OrpnCJddxfCbd+FElbn92/fg8eGQHKc2V0NpU8fQ77axGIbB7gef5vP3PonKDKFmGPD3Ilj2gbmoYrfBN3vCfQPBqdG3vekwBnXIEA4uL/zuPdh0xNz+yU746QCY2lttroZ0GH86ZAiHk5WQsxf2fm5ud4+HX14Fw5LU5qpPh/GnQ4Zwyf8MHtsHRyvM7cf2mXOBS+PV5mpIhzGoQ4ZweP4T+EsBVHjAZoMJl8HPB0GczAW0yxAONT5YuB/+c8jc/slO+FE6/F8fc3/QhQ7jT4cM4fCZC+bvhT2fmdtd4+AXV8HVl6jN1VTKF1ZKS0u55557eOutt2jTpg3XXHMNFRUVPP3002RlZTX5/j788EO+//3v43A46Nu3L08//TS2Zo7KHfc9ScqowcSndGnW7UNBhwzhUFAKs/dAdb1V6YNnYMZ2+M91EKPJsVTOxHYMuH0imyb9kvhunRm15C62TJ4XdRnC4flP4cn36+0DBmw4bP7l+rGhKpP502EM6pAhHB7MhzeLwfPlXyYqPPDEAXMy/c2earOdo8P40yFDOFR74QdvwOcuOHfA2uEKuGcXrBwNaR2Uxqulw/jTIUM4FH0Bd+/ynwt8cBZ+sB3WfUOff1jrMAZ1yBAOGw/DwgP+c4EXj0JpNfxxhNJofnQYgzpkCIdH3oH/HoeaL+cClV54sgAcdrglVWm0WjqMPx0yhIPHBzPfgJNVdUcuH68y/524/Bq4oqPSeE2i/J+vU6ZMISMjgwMHDvDSSy+xcuVKhg0bdlG3feCBBxg0aBBTpkzhgw8+ACA1NZUdO3awfft2bDYb77zzTrOzVZ74vNm3DRUdMoTD0x+Bu8Ghfl7MjwVtO6kkUlBJmWmc2v0+vhoP5UeKiW3XFrvT2vVIHTKEmmHA0g/8J9Ngbv/3uHk4sC50GIM6ZAi145XwxqnAPlDtg6cK1GQKRofxp0OGcPjvcfOw34afAvT4YGWhkkhB6TD+dMgQDqs+qltYPceHucj63+NKIgWlwxjUIUM4PBVkLuD2wc7iuqOYdKDDGNQhQ6h95oKXjwWfDy77EHyafCREh/GnQ4ZweOMUfF4d+HHwGh/87UM1mZpL6auxbds2iouLuffeewFITk4mJSWF4cOHX/C2q1atomfPnhiGwYoVKxg3bhxFRUXExNQ9pNjYWLp3797ofVRWVlJQUDeDNzzWn+Rh79692GLq/iRjZYaGta20v/gKDAI/81PtNdjx4Qk6nlSzutLw+W/TqT3u0rp3dndZBW06JlBVXBqSesFeAyszqNoHqn12zrgzgl4Xg5dX9n5Meptya0N9yeo+oLIHBKtvlf2uDsRwOZ4gb0PFLngr/23sCg4BtroHwIX3gdbYAwB2nk2hytsV8H+hvcC+k1W8/fb7SnLJXMA6e0/2x2sEfuanygtvfnSSS0vUrK5IH7CGYcDJqiFBr3Pg5ZV3PmFw2zKLU5lUvxerrm+Vj6rb4SCNGgJrn3Ub7MzfR1u79SddibYeEKy+Vd4o64rbeykNj/cwgP0l1bz99gHLM53Tv39/4uMv/nOpShdW8vLyGDGi7ji/06dPc+zYMQYPHnzB2/bsaR4nbrPZmDFjBnPnzuXQoUOkpqby4osvMmfOHPr160enTp0avY+CggKGDq37zIEDG8u73dSCR9R0I0aMwEvdEp2VGRrWtlLavI10GDIBm91/ENVUlbPwD3N4aNs/lORq+Py7S8txJtYNKGf7eKpLQ/cP/mCvgZUZlO0DNhtXPXeamITA8Vnp9vD9yWNxlxy2PhfW9wGVPSBYfau0SenLFX96D3ts4NtQTWkxwyer+TyY1T0ALrwPtMoeAHT5xgx63P4EjrYJfpcbXi/7d2xk6ONTleSSuYB1es/5Bx1HTsHu8O8D3qpyli6Zx69fXq4kl/QB6wx+5jixnS4NuLyyuoYf33wD1cc+UJBK/Xux6vpWiU26jCufKsQeG/gPem9FGdeMGAo+6xdWoq0HBKtvlU7XTKXXrOU42rb3u9zw+fj47f8xdP4EyzOdk5+fz5AhwRd/g1G6sJKcnMzatWvxer14vV7uvPNO0tPTcTqd572dy+WivLycpCTz7HabN2/G4XDQo0cPAK6//nquv/567rrrLl588UVuvPHGoPfTv39/8vPza7cNj5f3Jv82RI/u4uzevTtgddKqDA1rW+mj6nYsKoGaepfZ8NGxXRxP/XEusbY5SnI1fP5L3v6IzPu/iy3GQXzXTtRUuvC5Q3fK+mCvgZUZVO4Dm8sq2VzWAXe9v1I48HFlgovlL/5HSSawvg+o7AHB6lvp9yVuiqpj8dT7K0Wszct3elWzol5vtpLVPQAuvA+01h7g8tl54EQcVYaBUe+oFafDxu++NYjeN+uxD1ghWucCn7rjebzYTv292YZB+/g41v/6p8QtuFNJLukD1vnvFx7WnvVRU+99wIGPvgk1LH/h70oygfr3YtX1rbTksyoOuvznAk68jL+0gqfz8pRkirYeEKy+VWoMG784EccXPh9G/X3ADrnjU0n/ppq5AJhrBU2hdGFl6tSprFmzhvT0dHr16kW/fv3o0qXuhEw5OTksX76ckpIS9u/fz6xZs9i1axdOp5MJEybgdrux2+106tSJjRs3EhsbS3V1NW3atAGgQ4cOxMU1/hUz8fHxfqtQvhoP79W7fuTvf0zysHQczhiSrurDqz94POTPQWZmpt9fbK3M0LC2lYYAHY+a3wTk9pmfq7s8wc6CYXZ6JWQqyQSBz7/7bAUFz7zEhLW5GIbBnodWhLResNfAygwq94EMA9ofhH9+Yn4QoNoHmV3s/GFEIu1iLn51ONSs7gMX6gHhzqByH/hrDcx72/yGsFi7+Vnq29Ic/Di9BzZbDyWZrO4BcOF9oLX2AIBnvoAH3oLD5ea5NhJi4KEMO19PadpkJpRkLmCdIUDnE/DoPqjymId+d4+3sWBYDH06ZCjJBNIHrJRpQPsP4Nkvz6tU7YMrO9lZlNWe9rEyF6ivtfaBJR54eC9sP2nOBbwGTO3t4O4rUrDbUpRkirYeEKy+lVaWw/1vmSc09xjQLgYeGGRnQo9+SvI0l80w9Pmm6OnTp3Pttdc2+vXKF2Pr1q089thjAPTt25elS5dib/Bxk8b4ajys6nlLs2s3x7TDqwMGkVUZGtZWweODT76AtjFwWTulUQDr94Fgr0G07QPlNbDjFPzqbXhuNPTvqDSO8n1AdX0VPnPB6Wro0Q7iFZ+HTd4H1HjtBMzJg1Wj4IrGP8FrCdkHrOc1zLlAGzv0SLjw74eb7APWq/SY/7CWuYAe9VX4vNr88oLu8ZAQqzRK1PWAYPVV2HYC7suDZ66BKzsrjdIs6mdT9eTl5TF79uwW3ce4ceMYN25ciBKJcIuxQ99E1SmESgmx0EuDibRQJynO/E9Er25tzf+rOGGxUM9h0+frtYUa8TEyF4h2nduY/4nodcmXc4EY5d9b3DxaLawcPHhQdQQhhBBCCCGEEEKIixah60FCCCGEEEIIIYQQ6ml1xIoQkSLhsmRufPl3nDl4CEeck0/WvcHBZZuiLoMQ0Uz1GFRdX4hop8MY1CGDENFM9RhUXV/UkYUVIZrp9LtFbL05F5vdTvbrC/nwuVfwVFVHXQYhopnqMai6vhDRTocxqEMGIaKZ6jGour4wyUeBhGghR1sndmcMNoe64aRDBiGimeoxqLq+ENFOhzGoQwYhopnqMai6frSTI1bqs9uI69IB1+kyS8rFdekQ+BUIFmUIWls0SZfBqVy/dj6dr7icfYv+TU15VVRmaHUs7AMqe0Cj9UWTqB6Dquu3SjIXEE2gwxjUIUOro/q9WHV90SSqx6Dq+sIkCyv12B0Opu5bBj7DooI27A6HmgxBaoumOXfYXacrejHswds48NQLJA9LJ3loXz75zxsMvvsmitbt8Nve/eDfwp5h2EPTeP/pzcQlJdLt6oG0vaSj3/aBp14IaYbWxtI+oLIHNFJfNI3qPiA9IPRkLiCaQnUPaCyD9IGWUf1erLq+aBrVfUB6gB5kYaUBu8MBinuLDhnExTtz8BCVJ8/Q/euZHHt1L0kZfchacAfb71qMp8Llt21Fhr2Pr2bEozPwVLnZM+9vOOKcftviwlSPQdX1RdOp7gPSA0JLhzGoQwZx8VT3gIYZpA+0nOoxqLq+aDrVfUB6gFryASwhQuDA0o0MuutbALTv1ZXqM+XEJrQNuh3uDF6Xm+I9BXy64U2AgG0hRHio7gPSA4RQS3UPqJ9B+oAQaqjuA9ID1JGFFSGaofxoCVtvzq3dLi04zIvfeoj06eM58nI+e+atIHPuzQyYOdFvO5Qnk2osQ2uyYcMGFi1axOTJk1m/fn3tz5s3b679HZfLxZIlS4Lefv/+/WRnZ1NYWFh7WV5eHvPnzycnJ4edO3eydOlSDhw4QE5ODh6Ph9WrV3P8+PGwPzYR+VT3AekBJukBQhXVPeB8GVoT6QNCZ6r7gPQAkw49QD4KJEQIfbDypdqf35zzlN91DbfDqXDNa+fdjhQ33ngjhYWFlJWVMXny5NqfJ06cWPs7mzZt4rrrrgt6+yuvvJLs7Gy/yzZs2EBubi6LFy/m6NGj7Nixg5EjR1JUVMSqVauYMmUKS5cuZc6cOeF8aKIV06EPSA8wSQ8QKujQA0D6wDnSB4QKOvQB6QEmq3qALKwIIbRVUVHBE088wcKFC/1+rq+oqIjx48ezadMmVqxYUXv5888/f8H7HzNmDJmZmaSlpZGamsq0adOIiYnh7NmzIX8sQoimkx4ghJA+IER0i5QeIAsrQght3XfffSQlJbFkyRK2bNnCsGHDWLJkCVlZWWRlZQGQmprKkSNHmDRpEpMmTfK7/ZEjR9i6dSuFhYWMGjWKQYMGccMNN5Cbm4thGCQnJ5OcnAxA3759Wbx4MTNnziQxMdHyxyqECCQ9QAghfUCI6BYpPcBmGIZF3ycohP58NR5W9bzFsnrTDq/GHuu/vmllhmD1VSgohdu2wXOjoX/Hpt3W5XKxfPlyZs2aFZIsq1evZvTo0aSkpITk/kRksboHQOA4lB7QtNtKDxChJn1ADekDQhfR1gOC1Vch0nuAnLxWiBDLmD01pCemi7T6VouLiwtZEwW45ZZbZCIlWkT1GFRd32rSA4SOVI9D1fWtJn1A6EaHMahDBqvo0APUL09rxuf1gs+ig3jsNvM76lVkaKS2aLmEXl3p850xfPyv1zC8vqir3xpY1gdU9oDz1Bcto3oMqq7fGshcQLSU6nGoun5roPq9WHV90TI6jEEdMkQTWVipx+f1suaqO3CdLrOkXlyXDkzdt8yvmVmVIVhtERrlh04pbWCq60c6K/uAyh7QWH3RcqrHoOr6kU7mAiIUVI9D1fUjner3YtX1RcvpMAZ1yBBNouPYoIvlMyybSAFmrYYr0RZlCFpbhETZJycYMHOiskPvVNePeBb2AZU9oNH6osVUj0HV9SOezAVECKgeh6rrRzzV78Wq64sW02EM6pAhmsgRK0KEWNHa7VFdX4hop3oMqq4vhFA/DlXXFyLa6TAGdcgQTWT5SgghhBBCCCGEEKKZZGFFCCGEEEIIIYQQoplkYUUIIYQQQgghhBCimWRhRQghhBBCCCGEEKKZtF1YeeSRR+jXrx92u51169b5XTdmzBh69+5NRkYGGRkZ5Obmhi1H2tQxTHzhMSasf5TOg3qHrY7uGcLhSDk88BaM2QzXvwRPFUC1V3Uqf2P/8SC37H+awT/7dlRnCJe3PoMZ2+H2Heb2tpNgaHZieh3Gnw4ZwsEwYN0huOm/cO1muP0N2HtadapAOoxBHTKEQ5UHlhyEn+40t//8PhyrUJspGB3GoA4ZwuF4JTyYD1/bDONegsUHzf1CJzqMPx0yhMs7p+GOHeZ/AK8el7mArhnCwTBg0xGY8qo5F/jBdsgrUZ0qkA5jUIcM4VDthaUFMGuXuf3EQThcrjZTc2j7rUBjx47l1ltvZcaMGUGvX7hwIdnZ2WHN4Exsx4DbJ7Jp0i+J79aZUUvuYsvkeWGtqWOGcDhRCbdtMydPPqDcA6sKIf8zWPpVsNlUJzTtuO9JUkYNJj6lS1RnCIc3TsHP88Dtq7vsmULz/z/sryZTQzqMPx0yhMvig/DPT+sWVN/53PwH9qIR8JVkpdH86DAGdcgQaj4DfvwmfFRW1wd2l5jvDf8cA5e0VRqvlg5jUIcM4fCZC257HSo84DUAD/yjyPxH1YrR4JC5gFYZwuGtz+DuXf5zgeeKwG3Azwaqy1WfDuNPhwzh8vSHsOIjqP5yH3jvDNyzG347DEZ1U5utPh3GoA4ZQs0w4J5d5ut+bh946zP43jb4+7XQvZ3afE2h9IiV0tJSpk+fzsCBAxkyZAh33303M2fOBCArK4vU1NRm3e+iRYsYM2ZMi/MlZaZxavf7+Go8lB8pJrZdW+xOa9eidMgQDs8Umv+Yqvc+itsH75dCvkZ/sa488bnqCFpkCDXDgD/s959Igbn9TCGU16jJ1ZAO40+HDOFQWg1/Lwo8Ss3tgz8eUJOpMTqMQR0yhNrOYvj4C/8+4ANcHvh/RcpiBdBhDOqQIRz+38dQ5f1yUeVLbh8UlZv7hy50GH86ZAiHPzYyF/jnJ3CmWk2mhnQYfzpkCIfyGvhbvUWVc9w+c56o05FLOoxBHTKE2jufw3ul/vuAgTk/XPGRqlTNo3RETpkyhUmTJrFy5UpKSkpIS0tjwYIFF3XbBx54gHnz5pGens5jjz1Geno6ADU1NbzzzjsXdR+VlZUUFBTUbhse/xl+m07tcZfWHZPsLqugTccEqopLL+r+L8bevXuxxTiUZGhY20rbTlyBx4gLuNzt87Fl/0nsHU4qSBX4/IdbsNfAygyq9oFqn50jFRlBr7MbXja+9TH92qg5BrD+89/ae0Cw+lbZ7+pADL3xEFi7sAzeyn8bu4K/VlvdA+DC+4CVta304tkUXN6ugP8LXWPAa4cquba6IPgNw0zmAtb536n+1PjiAy53eQ22HDhF/LHjClJJH7CKz4APy4YEvc5heHnhrU8Y1LbM4lQmmQtY46PqdtiMNAgyFzhaabAzfx9xdl/gDcMs2npAsPpW2VzWFY/3Uhoe7+Ex4I1j1bztU/fXtv79+xMfH/ge1RhlCyvbtm2juLiYe++9F4Dk5GRSUlIYPnz4BW+7atUqevbsiWEYrFixgnHjxlFUVITD4eDZZ5/lu9/9Lr/5zW8ueD8FBQUMHTq0dtuBjeXdbqrddpeW40ysezKd7eOpLg3tP/ZGjBiBl7rlWCszNKxtpfQFb5Aw4KsBl9dUVfKnv+Ty0It/VZAq8PkPt2CvgZUZlO0DdgeZ/yzH7gxcXKusdvODm7NxHXnf+lz4P/+tvQcEq2+V+D5DSP/NduxtAt+wvFXlDB82NMitws/qHgAX3gesrG2lS775M1JuewxHkH3g/bd2MPThcQpSyVzASmkPv0jikPEBl3urq1j+t9/x6/V/VJBK+oCVMv5xFkd8h4DLK6pc/OQH/0flR3kKUslcwCptuqdzxaJ3sDsD/0Hvq3Hz1azh4LX+pEvR1gOC1bdK0tjbuez2hTjiEgKu+/TgXobecLXlmc7Jz89nyJDgi7/BKFtYycvLY8SIEbXbp0+f5tixYwwePPiCt+3ZsycANpuNGTNmMHfuXA4dOsTll1/OSy+9xD//+c+LWljp378/+fn5tduGx8t7k39bu13y9kdk3v9dbDEO4rt2oqbShc8d2sG9e/fugNVJqzI0rG2ltyo78swZL27Dv35c23jWPnIn7R77oZJcDZ//cAv2GliZQeU+8OyZcnZWOPHUW6G2YdAj3mD5uueUZAL/57+194Bg9a1iGDDvpJ0Srw+j3j4Qi4/rkip4ul5vtjSXxT0ALrwPWFnbSmXeGH5xIo6Gn/yLxccvrkvlqhv02Adaex9QuQ+8W9WBv37uo8bw/0tlmzZxrP7VdBIfulVJLukD1llTWsXr5QnUNJgLdGsXw/J/PKXsnHsyF7BO7ikfx2oMjHpHL8bgIyvxC5bv2a0kU7T1gGD1rVLpc/DzE21xN1jTcdq8/OzqrnxF0XwQzLWCplC2sJKcnMzatWvxer14vV7uvPNO0tPTcTqd572dy+WivLycpKQkADZv3ozD4aBHjx6sXbuWb37zmxedIT4+3m8Vylfj4b1617vPVlDwzEtMWJuLYRjseWhFkx7jxcjMzMQeW/cyWJmhYW0rZRpQeRBWF4HDbn6Oro0d/jjCzojkq5RkgsDnf+Tvf0zysHQczhiSrurDqz94PKT1gr0GVmZQuQ8M8JgnJ9t/xjxBoQF0bmPjLyPjSYm/+NXhUKv//Lf2HhCsvpWeKoc734RSt/nZ2hgbDE2yM/8rXYlzdFWSqeHzD9b3ASszqHz9AX53yvx2uHP/pHL74Htpdn4woI+yTDIXsM4QwFUAz3xkvg9U+8Bph98OszOq24X/0BYuVs8F4ML7QGudCwz0wtw882SV505W3D7Wxl9GtqFXgswFzmnNc4G/VJonMv/MZfaAWBsM6mzn1yOSiI9JUpIp2uYCwepb6YkSmL3H/NkAanzw7d4OfjSwNzZb5HwDlrLZ1NSpU1mzZg3p6en06tWLfv360aVL3RmOc3JyWL58OSUlJezfv59Zs2axa9cunE4nEyZMwO12Y7fb6dSpExs3biQ2NpYPPviA1157jWeffZZ3332Xv/71r/zoRz9qUc7C1a9SuPrVlj7ciM8Qajabebb3W1LhhUOw9EP4y9UwWLOTXL855ynVEbTIEA5tY8xvgCoohQ/LoFtbGJaEkvNqnI8O40+HDOHQMwFeGAtrP4Xfvge5mTDuMtWpAukwBnXIEA7XdIWXx8OOYnB5YUQyJAd+QlA5HcagDhnC4cf9Ycrl8J9D8NcP4MmrIUPmAlpmCIc2DvhTFnx0FgrOmuN/eLI+3wh1jg7jT4cM4XBpPPznOvjPp/Cb9+ChDJjQQ3WqQDqMQR0yhMPwZNh6vXnS8ooaGJZs/rsg0ihbWImLi2Pjxo2129OnT+faa6+t3c7JySEnJyfobfMbOSToV7/6Fb/61a8AGDNmTIsXVUT4dWsLo7uZCytBPl4pokD/juZ/Ijo5bDCok/lzz8CP14oo0DYGvpGiOoVQKSkORnU1F1biZC4Qlfommv+J6GS3wcAv5wK926vNItSIc8DXLlWdomWUft1yfXl5eQwbNixk9/faa6+F7L6EEEIIIYQQQgghgtHmC9APHjyoOoIQQgghhBBCCCFEk2izsBJJEi5L5saXf8eZg4dwxDn5ZN0bHFy2KeoyCBHNdBiDOmQQIpqpHoOq6wsR7XQYgzpkEELIwkqznX63iK0352Kz28l+fSEfPvcKnqrqqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBiGinzTlWIpWjrRO7MwabQ91TqUMGIaKZDmNQhwxCRDPVY1B1fSGinQ5jUIcMQkQrOWKlmboMTuX6tfPpfMXl7Fv0b2rKq6IyQ6tjtxHXpQOu02VhLxXXpUPw7xa2KEOj9cVF02EM6pChVbGwB0Aj41B6QERRPQZV12+VpA+IJtBhDOqQoVWJoh7QaH3RZLKw0kznDrnrdEUvhj14GweeeoHkYekkD+3LJ/95g8F330TRuh1+27sf/FvYMwx7aBrvP72ZuKREul09kLaXdPTbPvDUCyHN0NrYHQ6m7lsGPsOCYjbsjsDvlbQsQyP1xcWTPtD6WNoDIOg4lB4QWVT3AekBoSd9QDSF6h7QWAbpA80XVT2gkfqi6WRhpYXOHDxE5ckzdP96Jsde3UtSRh+yFtzB9rsW46lw+W1bkWHv46sZ8egMPFVu9sz7G444p9+2uDC7wwGKe4sOGcTFkz7Quugw/nTIIJpGdR+QHhBaOoxBHTKIi6e6BzTMIH2gZXQYfzpkEBdPPoAXAgeWbmTQXd8CoH2vrlSfKSc2oW3Q7XBn8LrcFO8p4NMNbwIEbAshwkP6gBBCdR+QHiCEWqp7QP0M0geEsJYsrDRD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8k1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLySR+whvQBoTPVfUB6gEl6gFBFdQ84X4bWRPqAiATyUaAQ+mDlS7U/vznnKb/rGm6HU+Ga1867HSluvPFGCgsLKSsrY/LkybU/T5w4sfZ3Nm3axHXXXRf09ldeeSXZ2dl+l23YsIHc3FwWL17M0aNH2bFjByNHjqSoqIhVq1YxZcoUli5dypw5c8L50EQrJn0gtKQPiEikQx+QHmCSHiBU0KEHgPSBc6QPCCvIworQVkVFBU888QQLFy70+7m+oqIixo8fz6ZNm1ixYkXt5c8///wF73/MmDFkZmaSlpZGamoq06ZNIyYmhrNnz4b8sQghmkf6gBDRTXqAEEL6gIgEsrAitHXfffeRlJTEkiVL2LJlC8OGDWPJkiVkZWWRlZUFQGpqKkeOHGHSpElMmjTJ7/ZHjhxh69atFBYWMmrUKAYNGsQNN9xAbm4uhmGQnJxMcnIyAH379mXx4sXMnDmTxMREyx+rECI46QNCRDfpAUII6QMiEtgMw7Doe6T056vxsKrnLZbWnHZ4NfbYuvUtKzM0rK1KQSnctg2eGw39Ozbtti6Xi+XLlzNr1qyQZFm9ejWjR48mJSUlJPcnIo/VfUBlDwhWX4WW9ACQPiBCS+YCashcQOhE9Xux6voqyFxARDr176RCtEBcXFzIGijALbdYO5kWQrSc9AEhopv0ACGE9AGhmiyshFjG7KnsW/Q8htcXlfVbA5/XCz4LDuSy28zvp1eV4Tz1RcuoHoeq60c6y3oANDoOpQdENtVjUHX91kD6gGgp1eNQdf1IFzU94Dz1RdPIwkqIJfTqSp/vjOHjf72mpJGprh/pfF4va666A9fpsrDXiuvSgan7lgU0MqsyNFZftJzqcai6fiSzsgdA8HEoPSDyqR6DqutHOukDIhRUj0PV9SNZNPWAxuqLpgvdl6gLAMoPnVLawFTXj3g+w7Im6jpdFnwV2qIMjdYXLaZ6HKquH9Es7AHQyDiUHhDxVI9B1fUjnvQBEQKqx6Hq+hEtinpAo/VFk8nCSoiVfXKCATMnYnOoeWpV1xdCqB+HqusLEe1Uj0HV9YUQ6seh6vpCRBv5KFCIFa3dHtX1hRDqx6Hq+kJEO9VjUHV9IYT6cai6vhDRRpYwhRBCCCGEEEIIIZpJFlaEEEIIIYQQQgghmkkWVoQQQgghhBBCCCGaSeuFlUceeYR+/fpht9tZt26d33Vjxoyhd+/eZGRkkJGRQW5ubsjrj/3Hg9yy/2kG/+zbIb/vSMoQLhUeeK4Qct8xt/NPg6HhCanTpo5h4guPMWH9o3Qe1DtqM4TDiUr44374wXaY9zYUlKpOFEiHMahDhnDZfwb+/L758z+K4FSV2jzB6DD+dMgQDoYB/z0Od+2EO96A1UVQ5VGdyp8O40+HDOFS5YF/FsEj75jbe0pkLqBzhnAoroI/HTDnAr/KN98XdKPDGNQhQ7gUnIWnCsyfn/vYnB/qRofxp0OGcDAM2HYSfrYLbn8Dni2E8hrVqZpO65PXjh07lltvvZUZM2YEvX7hwoVkZ2eHrf6O+54kZdRg4lO6hK1GJGQIhy9qYNo28820+stvgfvz+3CkAh4YrDZbfc7Edgy4fSKbJv2S+G6dGbXkLrZMnhd1GcLhw7Mw8w3wGFDjgwNnzH9gzc+Esd1Vp6ujwxjUIUM4bDwMv37XfP0BXjoGr52EFaMgtb3abOfoMP50yBAuue/Ay8fB5TW3D5bCvz+FZ0ZDO01mKDqMPx0yhEOlB76/HY5VQvWX+8BTH8DHX0BOJthsavOdo8MY1CFDOHz6BUzfDm5f3VzgfyfMueA3e6pOV0eHMahDhnD473Hzj2ueL+cCrxyH10/Csmugf6LabOfoMP50yBAuv98P6w/XzQXeLzXnAqtGQwenymRNo/yIldLSUqZPn87AgQMZMmQId999NzNnzgQgKyuL1NTUJt3fp59+Srdu3RgzZgzjxo1rUbbKE5+36PahoEOGcPjHx+Zfps8tqoD5pvrCYSi07mvjLygpM41Tu9/HV+Oh/Egxse3aYndaO9vXIUM4LHjXbKDn/lHtw9wHHt1Xd5kOdBiDOmQINZcHFrxnvubn/jjtMcx/aP3+PaXR/Ogw/nTIEA4HzpiLaecmUmC+JxyvNCdUutBh/OmQIRz+/Skcq6hbVAGzJ7xyHA6UqkoVSIcxqEOGcPj9frPvN5wLPP6eXkev6TAGdcgQajU+82g1t8987cGcC1R5YcE+lcn86TD+dMgQDkVfwNpDgXOBYhf8vUhdruZQ/mpMmTKFSZMmsXLlSkpKSkhLS2PBggUXddsHHniAefPmkZ6ezmOPPUZ6ejoA119/Pc8888wFb19ZWUlBQUHttuHxnue3w2Pv3r3YYhxKMjSsbaUXTl6B2xcXcLnX5+Ofb59gQodTClIFPv9tOrXHXVpRu+0uq6BNxwSqiktDUi/Ya2BlBlX7QI1h490zGUDgnyM9Xi//2V1IWpuKgOusYHUfUNkDgtW3ykFXewxfKtBg/wfyPjN4K38vdgV/rba6B8CF94HW2AMAXjh7KR5fNxr2gWof/OejSq4sKwh+wzCTuYB11p1Kp9rXLuByt89gzTsncSeeUJBK+oBVDAN2l2RiBJkLGD4vz+8pYmDcF5bnAvXvxarrW+Xj6na4vWk0nAsA7C812PnWO7SxW//ZwGjrAcHqW+XFL7pi+C6l4fEebh+8UOTiK5UHLc90Tv/+/YmPj7/o31e6sLJt2zaKi4u59957AUhOTiYlJYXhw4df8LarVq2iZ8+eGIbBihUrGDduHEVF5rLWK6+8wqhRo/jOd77D3Xff3eh9FBQUMHTo0NptBzaWd7uphY+qaUaMGIGXuoZhZYaGta00YNE7xPe+KuDymupq/rTwDzz4wkIFqQKff3dpOc7EugHlbB9PdWl5yOoFew2szKBqH7DFxJL5ryps9sAGXlnl4gfTbqOy8C3Lc4H1fUBlDwhW3yoJV4wi7aHNONomBFzn9dQwfNjQILcKP6t7AFx4H2iNPQCg23d+yaU3P4Q9tk3Ade+/t4+hE0cqSCVzASv1W7Cd9gOuCbjcW1PDsqee5JE1jypIJX3ASpnPu4L2gMrKSn7yyzso3/+6glTq34tV17dKfJ8h9Pv1NhxxgQushs/HV0dejVFTbXmuaOsBwepb5ZIb7yHle7/G0SZwAePTjz9i6CQ180GA/Px8hgwZctG/r3RhJS8vjxEjRtRunz59mmPHjjF48IVPstGzp/nBS5vNxowZM5g7dy6HDh2ie/fufPDBB7Rp04bs7Gyuu+46Bg4cGPQ++vfvT35+fu224fHy3uTftvBRNc3u3bsDVietytCwtpX++0Vn1p71UtNghTq2TRue+9UMujx8m5JcDZ//krc/IvP+72KLcRDftRM1lS587tAdmxrsNbAyg8p9YPFnX3DAlYivwV+qOsfH8vrqvyo5WgGs7wMqe0Cw+lbxGjDnRBwVDT72ZcfH0PblLK/Xm61kdQ+AC+8DrbUHnKppw/xTsTR8JE6blzuvTmGUJvuAFaJ1LvBGRRdWn/HibjAXcMbG8PR9t9Dt/m8pySV9wDrLTlfwdlUs3gZ/rW4f35b/PvNHYmQuoKS+VXwGPHAiltKAuYDBFW3LWbbrTcszQfT1gGD1rfK5J5ZfnYyj4TFasXj5/uCOfEPRXADMtYKmULqwkpyczNq1a/F6vXi9Xu68807S09NxOs9/lhqXy0V5eTlJSUkAbN68GYfDQY8ePYiNjaVNG3Ple9KkSRw4cKDRhZX4+Hi/VShfjYf6H+0f+fsfkzwsHYczhqSr+vDqDx5v2QMOIjMzE3ts3ctgZYaGta00yAcf7zLP/O7yQowN7Da4+wo7Y1OvVJIJAp9/99kKCp55iQlrczEMgz0PrQhpvWCvgZUZVO4DC6rg+9ug3GN+lhagjR3+cLWTjC4Xvzocalb3gQv1gHBnULkP/OEzuGeX+fEftw/aOiDRaeexUZ1JiuusJJPVPQAuvA+01h4AUPwR/PUD8PrACzjtMDTJwU+/0osYey8lmWQuYJ3BPvh4j/mtgC4vOL6cC/yon52J/YLP3awgfcA6j7rMExiXuuvmAk47/GFEDMOTZS5QX2vtA3/8HH6601xkqfZBnAMSYmwsGJ1It7Zq9oFo6wHB6lvp809g4QFzH/AaZg+4spODe6/uQay9h5JMzaF0YWXq1KmsWbOG9PR0evXqRb9+/ejSpe5M1zk5OSxfvpySkhL279/PrFmz2LVrF06nkwkTJuB2u7Hb7XTq1ImNGzcSGxvLF198Qfv25tdJ7Ny5k3vuuafZ+d6c81SLH2NL6ZAhHGLt8OTVsLMY3jgFCbEw8TLorck3gdRXuPpVCle/GvUZQq1rW/jPdfDScdhxCl49AX/8CmRodrJ7HcagDhnCYVgSrP8GbDwCJ6vgyo7wje7mpEonOow/HTKEw/S+8NWu8P8+hg1H4N6B8O3LUXbEWjA6jD8dMoRDjB0WjoC8z8xvAWnrgAmXQVoH1ckC6TAGdcgQal3i4Pmvm98Otv0k/PfLucDwZNXJ/OkwBnXIEA6DO8MLX84FjlbAgI4wvju0VX4mUH86jD8dMoTD1N7wlSTza5bXH4G7r4Dv9DYX2yOJ0l02Li6OjRs31m5Pnz6da6+9tnY7JyeHnJycoLfNb+SwoJ07d/KLX/yCuLg4rr32Wr9zqAi92G3mhPqrXVUnEarExcDknpDewVxYSYygr1QToZEUB9/vqzqFUCmtA9zc21xYGdRJr0UVEX52G4xINv8T0amNA27oAWntzYWVjjIXiDqd2sD30lSnECpd3t5cTFl/BDI6R96iCmjwrUD15eXlMXv27Bbdx7hx41r8NctCCCGEEEIIIYQQF0OrhZWDB9V9nZIQQgghhBBCCCFEU2m1sCJEpEi4LJkbX/4dZw4ewhHn5JN1b3Bw2aaoyyBENFM9BlXXFyLa6TAGdcggRDRTPQZV1xd1ZGFFiGY6/W4RW2/OxWa3k/36Qj587hU8VdVRl0GIaKZ6DKquL0S002EM6pBBiGimegyqri9M9gv/ihDifBxtndidMdgc6oaTDhmEiGaqx6Dq+kJEOx3GoA4ZhIhmqseg6vrRTo5Yqc9uI65LB1ynyywpF9elQ+DXH1iUIWht0SRdBqdy/dr5dL7icvYt+jc15VVRmaHVsbAPqOwBjdYXTaJ6DKqu3yrJXEA0gQ5jUIcMrY7q92LV9UWTqB6DqusLkyys1GN3OJi6bxn4DIsK2rA7HGoyBKktmubcYXedrujFsAdv48BTL5A8LJ3koX355D9vMPjumyhat8Nve/eDfwt7hmEPTeP9pzcTl5RIt6sH0vaSjn7bB556IaQZWhtL+4DKHtBIfdE0qvuA9IDQk7mAaArVPaCxDNIHWkb1e7Hq+qJpVPcB6QF6kIWVBuwOByjuLTpkEBfvzMFDVJ48Q/evZ3Ls1b0kZfQha8EdbL9rMZ4Kl9+2FRn2Pr6aEY/OwFPlZs+8v+GIc/ptiwtTPQZV1xdNp7oPSA8ILR3GoA4ZxMVT3QMaZpA+0HKqx6Dq+qLpVPcB6QFqyQewhAiBA0s3MuiubwHQvldXqs+UE5vQNuh2uDN4XW6K9xTw6YY3AQK2hRDhoboPSA8QQi3VPaB+BukDQqihug9ID1BHFlaEaIbyoyVsvTm3dru04DAvfush0qeP58jL+eyZt4LMuTczYOZEv+1QnkyqsQytyYYNG1i0aBGTJ09m/fr1tT9v3ry59ndcLhdLliwJevv9+/eTnZ1NYWFh7WV5eXnMnz+fnJwcdu7cydKlSzlw4AA5OTl4PB5Wr17N8ePHw/7YRORT3QekB5ikBwhVVPeA82VoTaQPCJ2p7gPSA0w69AD5KJAQIfTBypdqf35zzlN+1zXcDqfCNa+ddztS3HjjjRQWFlJWVsbkyZNrf544cWLt72zatInrrrsu6O2vvPJKsrOz/S7bsGEDubm5LF68mKNHj7Jjxw5GjhxJUVERq1atYsqUKSxdupQ5c+aE86GJVkyHPiA9wCQ9QKigQw8A6QPnSB8QKujQB6QHmKzqAbKwIoTQVkVFBU888QQLFy70+7m+oqIixo8fz6ZNm1ixYkXt5c8///wF73/MmDFkZmaSlpZGamoq06ZNIyYmhrNnz4b8sQghmk56gBBC+oAQ0S1SeoAsrAghtHXfffeRlJTEkiVL2LJlC8OGDWPJkiVkZWWRlZUFQGpqKkeOHGHSpElMmjTJ7/ZHjhxh69atFBYWMmrUKAYNGsQNN9xAbm4uhmGQnJxMcnIyAH379mXx4sXMnDmTxMREyx+rECKQ9AAhhPQBIaJbpPQAm2EYFn2foBD689V4WNXzFsvqTTu8Gnus//qmlRmC1VehoBRu2wbPjYb+HZt2W5fLxfLly5k1a1ZIsqxevZrRo0eTkpISkvsTkcXqHgCB41B6QNNuKz1AhJr0ATWkDwhdRFsPCFZfhUjvAeq7qBBCtEBcXFzImijALbdY+0YqhGgZ6QFCCOkDQkQ3HXqAfCuQECGWMXtqSM/4H2n1hYh2qseg6vpCCPXjUHV9IaKdDmNQhwzRRI5YacDn9YLPok9H2W3YHQ41GRqpLVouoVdX+nxnDB//6zUMry/q6rcGlvUBlT3gPPVFy6geg6rrtwYyFxAtpXocqq7fGqh+L1ZdX7SMDmNQhwzRRBZW6vF5vay56g5cp8ssqRfXpQNT9y3za2ZWZQhWW4RG+aFTShuY6vqRzso+oLIHNFZftJzqMai6fqSTuYAIBdXjUHX9SKf6vVh1fdFyOoxBHTJEEzk2qD6fYdlECjBrNVyJtihD0NoiJMo+OcGAmROVHXqnun7Es7APqOwBjdYXLaZ6DKquH/FkLiBCQPU4VF0/4ql+L1ZdX7SYDmNQhwzRRI5YESLEitZuj+r6QkQ71WNQdX0hhPpxqLq+ENFOhzGoQ4ZoIstXQgghhBBCCCGEEM0kCytCCCGEEEIIIYQQzSQLK0IIIYQQQgghhBDNpO3CyiOPPEK/fv2w2+2sW7fO77oxY8bQu3dvMjIyyMjIIDc3N2w50qaOYeILjzFh/aN0HtQ7bHV0zxAOhgFvfQZLDsLfPoRjFaoTBRr7jwe5Zf/TDP7Zt6M6Q7i4vfDSMfhHkbld4VGbJxgdxp8OGcLlrBv++Qn86SC8chw8Gp64XocxqEOGcDlSDusPmz9/cNZ8b9CNDmNQhwzhYBjwzmn480FY/qG5P+hGh/GnQ4Zw8fjM/n9uLlBeozZPMDqMPx0yhMsXNfD8l3OBF4+a80Pd6DAGdcgQLscr4YUv5wIHS/WcC1yItievHTt2LLfeeiszZswIev3ChQvJzs4OawZnYjsG3D6RTZN+SXy3zoxachdbJs8La00dM4SDxwez90D+Z1DtgxgbLPsQfj4IvtVLdbo6O+57kpRRg4lP6RLVGcLhMxf8YDuUuqHqyzfQe3bDX0fCwE5qs52jw/jTIUO4vHMa7toFBuDyQlsH/DkOVlwDHduoTldHhzGoQ4ZwWF0ETxys+0KK374Hb5yCBcPBYVOb7RwdxqAOGcLBa8Av3zJfc/eXc4GnP4S7B8B3+6hOV0eH8adDhnAodcOM7VDi8p8L/PlqyNDkoeow/nTIEC7vl8KP3zT7wbm5wJL34ZlRkBSnOl0dHcagDhnC4YXD8Jt36xZTfr8f/ncSFn4FYrQ9DCSQ0qilpaVMnz6dgQMHMmTIEO6++25mzpwJQFZWFqmpqU2+z1WrVvGNb3yDMWPGcOzYsRblS8pM49Tu9/HVeCg/Ukxsu7bYndauRemQIRzWHTaPVnH5zH9U1RhQ44PH34VTVarT1ak88bnqCFpkCIcF7/pPpMB8Q52bp8+3/ukw/nTIEA5ew3ytq7zm6w7mzycqzTdUnegwBnXIEGpHK+CJA2bv93455t0+2FkCm4+ozVafDmNQhwzh8OJR2FFs/oGl/lzgT+/rdeSKDuNPhwzhsHC/+Zfq+nOBah/MydPnCEYdxp8OGcLB+HIuUOHxnwuUuODX+9Rma0iHMahDhlArcZmLKjU+8NSbC+w9Df/+VGm0JlM6IqdMmcKkSZNYuXIlJSUlpKWlsWDBgou67QMPPMC8efNIT0/nscceIz09nWPHjvHGG2/wyiuvXNR9VFZWUlBQULttePyPO2vTqT3u0rrPp7jLKmjTMYGq4tKLuv+LsXfvXmwxDiUZGta20nOn+lPtiw9yjZeVe47zjfYllmeCwOc/3IK9BlZmULUPeAwbr5/MwCDwT9Kl1V7W7/6QXk41K2z1n//W3gOC1bfKR9XtqKhJA/xrewx4+ZiPb/EONgVHLFjdA+DC+4CVta20uawrPuNSGv6Nx+WF5w6W0/2zD5XkkrmAdZ4t7ofLmxBwuc/n45m3TjKpw0kFqaQPWMUw4KVjGXiC/J23qsbL87s/pl8bNStsMhewxmF3W05XpdPwfcBrwPZTBrvz3yHWZv1f26KtBwSrb5X/fpEMRgoN54MuL/yjoJK+pQXBb2iB/v37Ex8f7N+rwSlbWNm2bRvFxcXce++9ACQnJ5OSksLw4cMveNtVq1bRs2dPDMNgxYoVjBs3jqKiIl566SW8Xi/XXXcdV155JQsXLsRub/ygnIKCAoYOHVq77cDG8m431W67S8txJtY9mc728VSXhrbBjxgxAi91DcPKDA1rW2ngn98n7rL+AZdXuz0sXPwk9//74hbYQq3h8x9uwV4DKzOo2gdssW0Y8rwr6HVVlZV8b8YdVLy/w+JUpvrPf2vvAcHqW6X9Vd+gzwP/xhHfIeA6jw+GDR+m5AO2VvcAuPA+YGVtK136f/O5dMovsTkC36ffK/iIoROGBrlV+MlcwDr9/5BHu7RhAZd7vAZPPb2Ch557UEEq6QNWGvIfD7YgU/XKigp+9PDdlO19yfpQyFzAKu36X03fnJdwtG0fcJ3PgJFfvQZfdaXluaKtBwSrb5WuN/2clO/Ox+4MXNQpPHyUoZPUzAUA8vPzGTJkyEX/vrKFlby8PEaMGFG7ffr0aY4dO8bgwYMveNuePXsCYLPZmDFjBnPnzuXQoUOcOnWKmpoa/vvf/3L//fezceNGvvnNbzZ6P/379yc/P7922/B4eW/yb2u3S97+iMz7v4stxkF8107UVLrwuUN7ds3du3cHrE5alaFhbSutO5vI1i98AX+lcMbG8tScafT45XeU5Gr4/IdbsNfAygwq94Ffn6rg05p4aHDUSnx8PP99drGSv1CA//Pf2ntAsPpWqfbZue94AoHnKDRIj6tg2VtvWZ4JrO8BcOF9wMraVvq4uh1/LLEH7AOx+Pi/jEuYWO/92UoyF7DOlrKubCzzUtPgL5VOh41FP5lCn3snKMklfcA6fyip4IPq9jScC8TFJ7Bl6QLi7L9WkkvmAtaoMWzMPh6PK8iU73JnJcve3G55Joi+HhCsvlWOutvy62InDffmGHxkp3dglaK5AJhrBU2hbGElOTmZtWvX4vV68Xq93HnnnaSnp+N0Os97O5fLRXl5OUlJSQBs3rwZh8NBjx49SExM5NprrwXg61//Ou+88855F1bi4+P9VqF8NR7eq3e9+2wFBc+8xIS1uRiGwZ6HVjT/ATciMzMTe2zdy2Blhoa1rdTHDW+/Dmeqzc/SAjjtMK67ncmZA5RkgsDnf+Tvf0zysHQczhiSrurDqz94PKT1gr0GVmZQuQ/klsIPd9SdX8EGxNrhl4MdjOiZqSQT+D//rb0HBKtvpTmfwh/31/UAhw2cdhvzr25P38SL/wtBKDV8/sH6PmBlBpWvf6YBb+fD9lN1n61vY4fkODs/+2p3EmK7K8klcwHr9KuB/G3mudXqzwVGdbUzZVi6ko8DgvVzAbjwPtBa5wLzy8wT2Z87v8K5ucC9A+2M7J2hJBPIXMBKv7wEHt1n7gMG5gdCYh0wP6sdV3aSuYBVGVTtA0OAfe+Y3xJ6bi7gtEMnp505I7vRsU03yzM1l7KFlalTp7JmzRrS09Pp1asX/fr1o0uXujMc5+TksHz5ckpKSti/fz+zZs1i165dOJ1OJkyYgNvtxm6306lTJzZu3EhsbCwjR45kxQqz0bzzzjv07t3yryIrXP0qhatfbfH9RHqGUEt0wt+vhTWfwJajcKgC7ugH3++rOpm/N+c8pTqCFhnC4YqO5j7w7Mew/wx0j4fvpcFVnVUn86fD+NMhQzh8+3Lo3R6eKoC3T8PXusFdV0D3dqqT+dNhDOqQIdRsNnhsqHkC0/8cgkovjE2BKZdDQqzqdP50GIM6ZAi1hFhYNRqe/xQ2HoZPK2BGX5jRD2WLKsHoMP50yBAOaR3gn1+DZwvhnc/h0rZwax8YmqQ6mT8dxp8OGcJhYg+4rB08+T68dRpGdYO7r4CegadfUkqHMahDhnB48CrISjbfC8prYMylMLW3+e/FSKJsYSUuLo6NGzfWbk+fPr32aBMwF1ZycnKC3ja/kUOCMjIyiI2N5Wtf+xrJycncd999Ic0sQquDE25Ph2u6wm3b4OpL9JpIifDrmQC/ukp1CqHSkC5w30CzB3y/r36LKiK87DZzUj2xh+okQpWEWHPsZyWbfeCaruZ+IaJHSjzcf+EzAYhWbHBn+NmXc4Hb++m3qCLCy2aDsd3N/yKZNt/TlZeXx+zZs1t8P7///e9DkEYIIYQQQgghhBDiwrRZWDl48KDqCEIIIYQQQgghhBBNos3CSiRJuCyZG1/+HWcOHsIR5+STdW9wcNmmqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBCCELK812+t0itt6ci81uJ/v1hXz43Ct4qqqjLoMQ0UyHMahDBiGimeoxqLq+ENFOhzGoQwYhop1ddYBI52jrxO6MweZQ91TqkEGIaKbDGNQhgxDRTPUYVF1fiGinwxjUIYMQ0UqOWGmmLoNTuX7tfDpfcTn7Fv2bmvKqqMwgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBiGgny5nNdPrdIl686WG23PQQKaMHAZA8LJ0rfnQDbS/pyIhHZwRsW5Fh2EPTaNc9iS5X9WHgj78ZsC0uwG4jrksHS0rFdekQ/DslLcrQaH1x0aQPtEIW9gBoZBxKD4goqvuA9IAwkD4gmkB1D2gsg/SBFoiiHtBofdFkcsRKC505eIjKk2fo/vVMjr26l6SMPmQtuIPtdy3GU+Hy27Yiw97HVzPi0Rl4qtzsmfc3HHFOv21xfnaHg6n7loHPsKCYDbvDoS5DI/VF00kfaD0s7QEQdBxKD4hMqvuA9IDQkT4gmkN1D2iYQfpA80VVD2ikvmg6WVgJgQNLN5L1m9s59upe2vfqSvWZcmIT2uKpcAVsW5GheE8BZZ+eBMDrcvttiwuzOxyguLfokEE0jfSB1kOH8adDBtF0qvuA9IDQ0WEM6pBBNI3qHtAwg/SB5tNh/OmQQVw8+ShQM5QfLWHrzbm126UFh3nxWw+RPn08R17OZ8+8FWTOvZkBMyf6bYfyRFKNZWhNNmzYwKJFi5g8eTLr16+v/Xnz5s21v+NyuViyZEnQ2+/fv5/s7GwKCwtrL8vLy2P+/Pnk5OSwc+dOli5dyoEDB8jJycHj8bB69WqOHz8e9scmIp/0AWtIHxA6U90HpAeYpAcIVVT3gPNlaE2kD4hIIEeshNAHK1+q/fnNOU/5XddwO5wK17x23u1IceONN1JYWEhZWRmTJ0+u/XnixIm1v7Np0yauu+66oLe/8soryc7O9rtsw4YN5ObmsnjxYo4ePcqOHTsYOXIkRUVFrFq1iilTprB06VLmzJkTzocmWjHpA6ElfUBEIh36gPQAk/QAoYIOPQCkD5wjfUBYQRZWhLYqKip44oknWLhwod/P9RUVFTF+/Hg2bdrEihUrai9//vnnL3j/Y8aMITMzk7S0NFJTU5k2bRoxMTGcPXs25I9FCNE80geEiG7SA4QQ0gdEJJCFFaGt++67j6SkJJYsWcKWLVsYNmwYS5YsISsri6ysLABSU1M5cuQIkyZNYtKkSX63P3LkCFu3bqWwsJBRo0YxaNAgbrjhBnJzczEMg+TkZJKTkwHo27cvixcvZubMmSQmJlr+WIUQwUkfECK6SQ8QQkgfEJHAZhiGRac71p+vxsOqnrdYWnPa4dXYY+vWt6zM0LC2KgWlcNs2eG409O/YtNu6XC6WL1/OrFmzQpJl9erVjB49mpSUlJDcn4g8VvcBlT0gWH0VWtIDQPqACC2ZC6ghcwGhE9XvxarrqyBzARHp1L+TCtECcXFxIWugALfcYu1kWgjRctIHhIhu0gOEENIHhGryrUAhljF7akjP9B1p9YUQ6seh6vpCRDvVY1B1fSGE+nGour4Q0UaOWAmxhF5d6fOdMXz8r9cwvL6oq98a+Lxe8FnwCTm7zfx+elUZzlNftIzqcai6fqSzrAdAo+NQekBkUz0GVddvDaQPiJZSPQ5V1490UdMDzlNfNI0srIRY+aFTShuY6vqRzuf1suaqO3CdLgt7rbguHZi6b1lAI7MqQ2P1RcupHoeq60cyK3sABB+H0gMin+oxqLp+pJM+IEJB9ThUXT+SRVMPaKy+aDo5PizEyj45wYCZE5Udeqe6fsTzGZY1UdfpsuCr0BZlaLS+aDHV41B1/YhmYQ+ARsah9ICIp3oMqq4f8aQPiBBQPQ5V149oUdQDGq0vmkyOWAmxorXbo7q+EEL9OFRdX4hop3oMqq4vhFA/DlXXFyLayBKmEEIIIYQQQgghRDPJwooQQgghhBBCCCFEM8nCihBCCCGEEEIIIUQzab2w8sgjj9CvXz/sdjvr1q3zu27MmDH07t2bjIwMMjIyyM3NVRNStMjn1bC7xPzZIyctj0qffgFbj8G7n4Mh582KOoYBH541fz5RqTaLUMPthTdOwSvHobRadRqhQqkb9nw5F3DLXCAqHS435wLvnJa5QDQyDCj88jytx2QuEJVqfPBmsTkXOO1SnaZ5tD557dixY7n11luZMWNG0OsXLlxIdnZ2+Or/40G6DOrNweWbeXfRv8NWR/cM4fLXAljxEcR8ubz3k53wRBZkdlGbq6G0qWPod9tYDMNg94NP8/l7n0RlhlCr9sLP82DPZxBrN09Gfmlb+PPVcElb1enq6DAGdcgQDscr4ac74VSVuf2LfBh1FH49zNwndKHD+NMhQzjsKYG5eV/+Q8pmLrL8qD/8oK/qZHV0GH86ZAiXlR/BUwXgqDcX+P1wyLpEba6GdBiDOmQItRof/Coftp+EWIc5F0hqA0+OhJR41enq6DAGdcgQDiUu+MmbdQsqv8qH9Yfh8eEQp9G3/+ow/nTIEA7vnIb79tT9kd3tg+l94cfpYLOpzdYUyqeupaWlTJ8+nYEDBzJkyBDuvvtuZs6cCUBWVhapqalNur833niDMWPGMGbMGFJSUgKOdGmKHfc9yVu5zzb79qGgQ4ZweO0ErCoEjwEur3lZpRfu2gXlNWqz1edMbMeA2yfy4rcfZvusPzHi0eCLfK09Qzg8cRDyPjMnVZUecz84XGE2Vp3oMAZ1yBBqhgH37IJjFXV/ofYY5l8rnnxfbbb6dBh/OmQIhzPVcO9uqPCY/b/SY+4Dyz8w9wNd6DD+dMgQDruKYekHUFNvLuDywuw95v6hCx3GoA4ZwuGvBbDjlLkPnJsLHK+Eu3fpdeSKDmNQhwzhMGePOf+rPxd46zNYuF9trvp0GH86ZAiH8hrz339lNV/OBbzmPvD/PoZXT6hO1zTKj1iZMmUKkyZNYuXKlZSUlJCWlsaCBQsu6rYPPPAA8+bNIz09nccee4z09HSuueYaXnvtNQCuueYavvGNbzR6+8rKSgoKCmq3DY/X//oTnzf9ATXR3r17scXULcdamaFhbSs9VdyXal/7gMt9Pi9P7zzKqITTClIFPv9JmWmc2v0+vhoP5UeKiW3XFrszBp/bE5J6wV4DKzOo2gd8BvznWAY1DdZ2vQYUnvWxaff7XBqrZlZtdR+4UA8IdwZV+8Bhd1uOVqTja7APVPtgTZGXa1z7lPyVwuoeABfeB1pjDwD47xfJ+HwpgH/9ap/BX/eWEZf8sZJcMhewzlMlfaj2dQD8B7vP52PZrmN8o32JklzSB6zzz2ODqTb8/zniA46V+1i3+wN6OauU5JK5gDVO1bThg9IBeBvMBdw+WH/Ixzc87+CQuYAlGVTtA29UdMHnu4yGcwGXF5a+W06nkx9anumc/v37Ex9/8YfOKV1Y2bZtG8XFxdx7770AJCcnk5KSwvDhwy9421WrVtGzZ08Mw2DFihWMGzeOoqIiHA7zRTl69CgdO3YkISGh0fsoKChg6NChtdsObCzvdlMLH1XTjBgxAi91S/JWZmhY20oDn/qQuEsDF1ZcNT4WLFnGz/71mIJUgc9/m07tcZdW1G67yypo0zGBquLSkNQL9hpYmUHVPmBvE0/mmoqg11VXlnPLzJ9QfmCbxalMVvcBlT0gWH2rdMgcT+rP/4kjPjHgumrDwbCvDAef9SdbsLoHwIX3gdbYAwBSbnuUbt/+BbaAY2dt5H1wiKHXDw12s7CTuYB1BizcS3xqRsDlbsPGE0//P+5/9hfWh0L6gJWGrg9et6riC74/azZl+VssTmRS/V6sur5VEq64hrR5m3DEdwi4rsawkTXqWnxV5ZbnirYeEKy+VbpN+QWXfjcHe5BFnYOHTzF0gpq5AEB+fj5Dhgy56N9XurCSl5fHiBEjardPnz7NsWPHGDx48AVv27NnTwBsNhszZsxg7ty5HDp0qPajQ+vWrbvg+Vf69+9Pfn5+7bbh8fLe5N8245E03+7duwNWJ63K0LC2lVZ93ok3K30Bf62Oi7Xzu59N54oHrJ3UntPw+XeXluNMrFupdLaPp7o0dA0+2GtgZQZV+4BhwK9OVvOZt03AdW3iE9j8zJ9oZw/8a40VrO4DKntAsPpWKfPGcP+J9gR7lS+NqSI/L8/yTGB9D4AL7wOtsQcA7KtKZNnnBu4G8zgHPm4Y2I3n6r0/W0nmAtb555lLea3CF/DX6jZ2H4/86Dtk/GycklzSB6yTc7KK457AE6u1adeedX9ZQKLjUQWp1L8Xq65vlUqfgznHEwh2zEVSjJs9219XdvRqNPWAYPWtUuBKYMlpR8BcwI6Pr6UmslLRXADMtYKmULqwkpyczNq1a/F6vXi9Xu68807S09NxOp3nvZ3L5aK8vJykpCQANm/ejMPhoEePHrW/s2HDBp599vyfQ4yPj/dbhfLVeHivBY+nOTIzM7HH1r0MVmZoWNtKl1TA/70GVV5q10addujbwcGtV/dVdqKihs9/ydsfkXn/d7HFOIjv2omaSldID/sL9hpYmUHlPvDACfhlvv83QDjt8N1UO6OuuEpJJrC+D6jsAcHqW+nb78H6Q+bHf85x2uGBoW0Z0vXi/0IQSlb3ALjwPtBae8BVBmx9HQ6V1/UBGxAXY+e+qy+hW7yas5fKXMA63atg1//Mc2ucmwvE2qBngoPpI/so+QgASB+w0i+LzXOrNZwLTO5p52sX8YfWcFH9Xqy6vpW+dxD+UQSuBvvA/ZltGJoicwGrMqjaBzINeOUNKDjrPxdo47AzNyuJHglJlmdqLqULK1OnTmXNmjWkp6fTq1cv+vXrR5cudV8Jk5OTw/LlyykpKWH//v3MmjWLXbt24XQ6mTBhAm63G7vdTqdOndi4cSOxsbGAeUJct9vNJZe0bFI28vc/JnlYOg5nDElX9eHVHzzeovuL1AzhcFk7eGY0PHHAPEGV0wE39oA7++t19mf32QoKnnmJCWtzMQyDPQ+tiMoM4TDmUvOM739+Hz75wjxR1f+lwk8HqE7mT4cxqEOGcJhzJfSIh2c/hjNu6NMeZg3Q69tAdBh/OmQIB4cNln0V/lIAGw6bJ6zL7AK/ugq6afRtIDqMPx0yhEPXtvDsaPjTQdhZbH4b2MTL4CcDULaoEowOY1CHDOGQdQksGgGLD8JHZeZc4DuXwz0DVSfzp8MY1CFDOPxkAHRrCysK4XQ1XJ5gzgWv6ao6WR0dxp8OGcLBZoMnr4anPoD/HDJPaD+4E/ziKujR+Bk9tGQzDH3OuT19+nSuvfbaRr9e+WI999xznDx5kjlz5jTpdr4aD6t63tKi2k017fDqgNVJqzI0rC2s3weCvQbRuA8UlMJt2+C50dC/o9osqvcB1fWjnbwPqBHNPQBkH9CN7ANqRHMfkLmAXqKtBwSrr4JOPaA5tBpBeXl5zJ49u8X3c9ttt4UgjRBCCCGEEEIIIcT5abWwcvDgQdURhBBCCCGEEEIIIS6aVgsrQkSKhMuSufHl33Hm4CEccU4+WfcGB5dtiroMQkQz1WNQdX0hop0OY1CHDEJEM9VjUHV9UUcWVoRoptPvFrH15lxsdjvZry/kw+dewVNVHXUZhIhmqseg6vpCRDsdxqAOGYSIZqrHoOr6wmRXHUCISOdo68TujMHmUDecdMggRDRTPQZV1xci2ukwBnXIIEQ0Uz0GVdePdnLEihDN1GVwKtevnU/nKy5n36J/U1NeFZUZhIhmqseg6vpCRDsdxqAOGYSIZqrHoOr6wiTLWfXZbcR16WBZubguHcBuU5IhaG3RJKffLeLFmx5my00PkTJ6EADJw9K54kc30PaSjox4dEbAthUZhj00jXbdk+hyVR8G/vibAdviAizsAyp7QKP1RZOo7gPSA8JA5gKiCVT3gMYySB9oIdXvxarriyZR3QekB+hBjlipx+5wMHXfMvAZFhW0YXc41GQIUls0z5mDh6g8eYbuX8/k2Kt7ScroQ9aCO9h+12I8FS6/bSsy7H18NSMenYGnys2eeX/DEef02xbnZ2kfUNkDGqkvmkd1H5AeEDoyFxDNoboHNMwgfaBlVL8Xq64vmkd1H5AeoJYsrDRgdzhAcW/RIYNomgNLN5L1m9s59upe2vfqSvWZcmIT2uKpcAVsW5GheE8BZZ+eBMDrcvttiwtTPQZV1xfNo7oPSA8IHR3GoA4ZRNOo7gENM0gfaBnVY1B1fdE8qvuA9AB15KNAQjRD+dEStt6cW7tdWnCYF7/1EOnTx3Pk5Xz2zFtB5tybGTBzot92KE8m1ViG1mTDhg0sWrSIyZMns379+tqfN2/eXPs7LpeLJUuWBL39/v37yc7OprCwsPayvLw85s+fT05ODjt37mTp0qUcOHCAnJwcPB4Pq1ev5vjx42F/bCLyqe4D0gNM0gOEKqp7wPkytCbSB4TOVPcB6QEmHXqAHLEiRAh9sPKl2p/fnPOU33UNt8OpcM1r592OFDfeeCOFhYWUlZUxefLk2p8nTpxY+zubNm3iuuuuC3r7K6+8kuzsbL/LNmzYQG5uLosXL+bo0aPs2LGDkSNHUlRUxKpVq5gyZQpLly5lzpw54XxoohXToQ9IDzBJDxAq6NADQPrAOdIHhAo69AHpASareoAsrAghtFVRUcETTzzBwoUL/X6ur6ioiPHjx7Np0yZWrFhRe/nzzz9/wfsfM2YMmZmZpKWlkZqayrRp04iJieHs2bMhfyxCiKaTHiCEkD4gRHSLlB4gCytCCG3dd999JCUlsWTJErZs2cKwYcNYsmQJWVlZZGVlAZCamsqRI0eYNGkSkyZN8rv9kSNH2Lp1K4WFhYwaNYpBgwZxww03kJubi2EYJCcnk5ycDEDfvn1ZvHgxM2fOJDEx0fLHKoQIJD1ACCF9QIjoFik9wGYYhkWnvRdCf74aD6t63mJZvWmHV2OP9V/ftDJDsPoqFJTCbdvgudHQv2PTbutyuVi+fDmzZs0KSZbVq1czevRoUlJSQnJ/IrJY3QMgcBxKD2jabaUHiFCTPqCG9AGhi2jrAcHqqxDpPUB9FxVCiBaIi4sLWRMFuOUWa99IhRAtIz1ACCF9QIjopkMPkG8FEiLEMmZPDekZ/yOtvhDRTvUYVF1fCKF+HKquL0S002EM6pAhmsgRKw34vF7wWfTpKLvN/I56FRkaqS1aLqFXV/p8Zwwf/+s1DK8v6uq3Bpb1AZU94Dz1RcuoHoOq67cGMhcQLaV6HKqu3xqofi9WXV+0jA5jUIcM0UQWVurxeb2sueoOXKfLLKkX16UDU/ct82tmVmUIVluERvmhU0obmOr6kc7KPqCyBzRWX7Sc6jGoun6kk7mACAXV41B1/Uin+r1YdX3RcjqMQR0yRBM5Nqg+n2HZRAowazVcibYoQ9DaIiTKPjnBgJkTlR16p7p+xLOwD6jsAY3WFy2megyqrh/xZC4gQkD1OFRdP+Kpfi9WXV+0mA5jUIcM0USOWBEixIrWbo/q+kJEO9VjUHV9IYT6cai6vhDRTocxqEOGaCLLV0IIIYQQQgghhBDNJAsrQgghhBBCCCGEEM0kCytCCCGEEEIIIYQQzaT1wsojjzxCv379sNvtrFu3zu+6MWPG0Lt3bzIyMsjIyCA3N1dNSNEiPgOOlMNnLtVJhCouLxyvVJ1CqFTmhkPlUO1VnUSocqba/L+cPzE6+Qw4WgHFVaqTCFWqvXBC5gJR7Ysa+LTcnBeK6BTpcwGtT147duxYbr31VmbMmBH0+oULF5KdnR3WDGlTx9DvtrEYhsHuB5/m8/c+CWs9XTOEw2sn4Dfvmo3Ua8AVHeHRIdC9nepkdcb+40G6DOrNweWbeXfRv6M2QzgYBiz7AFZ9bL7+AE++D48PhziNOpMO40+HDOFQ4YFH9sJrJ8FhA7sNZvSF7/cFm011ujo6jEEdMoTD4XL4VT58+OWXX9yzGx7OhGu6qs3VkA5jUIcM4fBmMTz6Dpxxm+8LfTvAo0OhV4LqZHV0GH86ZAgHw4BVhbD8Q/B8ORf400H43VegncwFtMsQDi4v/HofbD1mzgVsNritD/woXeYCOmYIhxOV5lzgQKm5PWsXPHgVfD1FaawmU37ESmlpKdOnT2fgwIEMGTKEu+++m5kzZwKQlZVFampqk+6voqKC66+/nmuvvZbp06djGM1f8nImtmPA7RN58dsPs33WnxjxaPAFnnDSIUM4vPc5/DIfTleD22f+w/rAGbj9DajR6KvWd9z3JG/lPhv1GcLhuY9h5cfmG+q51zzvM3jwbbW56tNh/OmQIVzuz4Ntp8zJdLUPqrzm5Pr5T1Un86fDGNQhQ6i5PDDjDfjgbN3i6hk3/DwPCs6qzVafDmNQhwzh8OFZmLMHil3m+4DHMPeHmW9AlUd1ujo6jD8dMoTD2kOw9AOz/5+bC7x92uwDutBh/OmQIVweehteOV43F3B54dlCc8FNJzqMQR0yhFqNz+z5+8/UzQXKasx/D+z7XG22plK+FjxlyhQmTZrEypUrKSkpIS0tjQULFlzUbR944AHmzZtHeno6jz32GOnp6bz00kuMHj2aX/7yl/zwhz9k3759ZGRkBL19ZWUlBQUFtduGx//Ys6TMNE7tfh9fjYfyI8XEtmuL3RmDzx26d/u9e/dii3EoydCwtpWWfJZKjS8RqFuK9gFlbi8r3jzEsPhSJbkaPv+VJ8I7ooO9BlZmULUP+AxYfnww1YZ/C6oxYPtJH6/sOUDnmBrLc4H/89/ae0Cw+lYp9rThrZIBeBqs71f74C8Hauhz5j3LM0Hg8w/W9wErM6h8H3izojOVNT3w4V+/xmewaM8ZftjlUyW5ZC5gneWne1Hj60zDuUBljZflO4/w1XZqZtVWzwXgwvtAa5wLAPzl+JVU+5x+l3kMyC/xsWX3+3SNrVaSS+YC1jjjjeX1EwPxBpkLPF3gYWDZu9gVHLUSbXOBYPWtkl/ZkbPVvQLmAm6fwaK3znJXUpHlmc7p378/8fHxF/37ShdWtm3bRnFxMffeey8AycnJpKSkMHz48AvedtWqVfTs2RPDMFixYgXjxo2jqKiIPn36kJ+fD0B5eTmdOnVq9D4KCgoYOnRo7bYDG8u73VS73aZTe9ylFbXb7rIK2nRMoKq4tKkPtVEjRozAS91RNVZmaFjbSgOf+oi4SzsGXO6q8fHwn/7GyX89Zn0oAp//cAv2GliZQdU+YG8TT+aaiqDXuSu/4FszZlF+YJvFqUz1n//W3gOC1bdKh8zx9J77T2LaJQZcV+aLZejw4eCz/vA1q3sAXHgfsLK2lVJue5RLv/OrgMsNbGx//xh/vWdokFuFn8wFrDNg0V7ie3cJuNxtOPjt8n9ybNUDClJJH7DS0PXB61ZXfMEtP/05ZfmbLU5kkrmANRKuuIa0eZtwxHcIuK7C52DEqDH4qr6wPFe09YBg9a3SbcovuPS7OdgDFnVsvPXpaYaOVzMXAMjPz2fIkCEX/ftKF1by8vIYMWJE7fbp06c5duwYgwcPvuBte/bsCYDNZmPGjBnMnTuXQ4cO0bdvX7Zt28aAAQPIzMykV69ejd5H//79axdhwFwZfG/yb2u33aXlOBPrVqmc7eOpLi1v0mO8kN27dwesTlqVoWFtK/35syTedRkY+C9Dx8XamX/3DIY9YG0zO6fh8x9uwV4DKzOo2gd8Bsw+4aHCF9iCnPHtWfe3JXRSeMTKuee/tfeAYPWtUuxxknOyPcH+1pZod5Ofp+Y4cKt7AFx4H7CytpXerOjM30u9uA3/+jYMRg/ozrP13p+tJHMB6yw/3YO8qsC5gNPm5f7bb+ar94xVkkv6gHV+ftxNaYMjVgDatGvP6j8/TtfYRxSkkrmAVUq9sfziRALBzlfbzu5l9/bXlB2xEk09IFh9q+RXduSZMw6qG6zp2DAYfnkXViqaC4C5VtAUShdWkpOTWbt2LV6vF6/Xy5133kl6ejpOZ2CDrc/lclFeXk5SUhIAmzdvxuFw0KNHD5YvX86UKVO45557uOeee9i2bRujR48Oej/x8fF+q1C+Gg/1Dz4vefsjMu//LrYYB/FdO1FT6QrpYX8AmZmZ2GPrXgYrMzSsbaV7z8APd5jnVznHDnRo4+AHI1OJVXT2n4bPf7gFew2szKByH/hhIfylAFz19gGnHb7a1c51wwcpyQT+z39r7wHB6ltp805467R/H2hjhzsHOhnS++L/QhBKVvcAuPA+YGVtK13hgfWvgMdtfvzjHKfdxs++0pn0xM5KcslcwDr3noXp2/17gA2Ij3Vwx9WXExdzuZJc0ges85PO8If95kc/znHaYUgXOxNGDFSSCWQuYKWvfXm+Nb+5gANuT49hWJrMBVTVt8pgH6x7xfyG2PoLbLF2Gz8b1pHBndXsA82hdGFl6tSprFmzhvT0dHr16kW/fv3o0qXukNCcnByWL19OSUkJ+/fvZ9asWezatQun08mECRNwu93Y7XY6derExo0biY2Nxefz0bmzORnr3LkzpaWlzc7nPltBwTMvMWFtLoZhsOehFS19yBGZIRyu7AS/GQa/2QelbvPztGkd4A9fQdmiSjAjf/9jkoel43DGkHRVH179weNRmSEc/q+PebK6lYXmyaoMA8amwC+uUp2sjg7jT4cM4bJgODy2zzxpndeAOAf8MB2+fbnqZP50GIM6ZAi1uBhYMcr8JoCCs+a3QnV2wq8yID3wE2LK6DAGdcgQDn0Tzff9R98xT2bvMaB3gnmZTt8Op8P40yFDOHyrl/kNccs+BI/PPKL12m4wL0N1sjo6jD8dMoRLzhBY8C68eNTsAW3sMD0NvtdHdTJ/OoxBHTKEWowdnr7GPFnt/jPmN0ElxsIDg2Gwmr+vNJvNaMnX5oTY9OnTufbaaxv9euWLcebMGaZOnUpNTQ2JiYmsWbOGNm3aXNRtfTUeVvW8pdm1m2Pa4dUBq5NWZWhYWwWfAW+chPvy4LnR0L+j0jiW7wPBXoNo2weqvVBcBZ3aQEKs0iiA+n1AdX0V3v4MfvgmrLgGBil+E5X3ATU+c5m9ICVe/ddryj5gPcOA7VE8FwDZB9xe89uhEp3QXuYCyuurcG4u8Ldr1P+DOtp6QLD6KnxeDZUecy6g4iNgLaV+NlVPXl4es2fPbtF9dOrUiZdffjlEiUS42W1wSVvVKYRKbRzQI0F1CqFS/JfvRDodrSaslRSnOoFQySZzgajndMBl7VSnECqdmws4ZS4QtTq3Mf+LVFotrBw8eFB1BCGEEEIIIYQQQoiLptXCSqRIuCyZG1/+HWcOHsIR5+STdW9wcNmmqMsgRDTTYQzqkEGIaKZ6DKquL0S002EM6pBBCCELK812+t0itt6ci81uJ/v1hXz43Ct4qqqjLoMQ0UyHMahDBiGimeoxqLq+ENFOhzGoQwYhop18iq2FHG2d2J0x2BzqnkodMggRzXQYgzpkECKaqR6DqusLEe10GIM6ZBAiWskRK83UZXAq16+dT+crLmffon9TU14VlRmEiGY6jEEdMggRzVSPQdX1hYh2OoxBHTIIEe1kObOZTr9bxIs3PcyWmx4iZfQgAJKHpXPFj26g7SUdGfHojIBtKzIMe2ga7bon0eWqPgz88TcDtsUF2G3EdelgSam4Lh2Cf5eYRRkarS8umvSBVsjCHgCNjEPpARFFdR+QHhAG0gdEE6juAY1lkD7QAlHUAxqtL5pMjlhpoTMHD1F58gzdv57JsVf3kpTRh6wFd7D9rsV4Klx+21Zk2Pv4akY8OgNPlZs98/6GI87pty3Oz+5wMHXfMvAZFhSzYXc41GVopL5oOukDrYelPQCCjkPpAZFJdR+QHhA60gdEc6juAQ0zSB9ovqjqAY3UF00nCyshcGDpRrJ+czvHXt1L+15dqT5TTmxCWzwVroBtKzIU7ymg7NOTAHhdbr9tcWF2hwMU9xYdMoimkT7Qeugw/nTIIJpOdR+QHhA6OoxBHTKIplHdAxpmkD7QfDqMPx0yiIsnCyvNUH60hK0359ZulxYc5sVvPUT69PEceTmfkrc+5Cu53+fM+4f9tnfevxTD6wtrBiGENaQPCCFU9wHpAUKopboHnC+DEMJasrASQh+sfKn25zfnPOV3XcPtcCpc89p5tyPFhg0b+Pjjj/nf//7HjBkz+OSTT/jf//7Hj370IyZOnAiAy+Vi+fLlzJo1K+D2+/fv58EHH+T3v/89aWlpAOTl5bF582YMw2D8+PG89957fPWrX+Vf//oXDz74IM8//zyjR48mJSXF0scqWg/pA6ElfUBEIh36gPQAk/QAoYIOPQCkD5wjfUBYQU5eK7R14403csMNNzB06FAmT55c+/O5BgqwadMmrrvuuqC3v/LKK8nOzva7bMOGDTz88MN06dKFo0ePsmPHDgzDoKioiFWrVjFx4kT+/ve/h/NhCSGaQPqAENFNeoAQQvqAiARyxIrQVkVFBU888QQLFy70+7m+oqIixo///+3dbXBU9RXH8d9uHo0KRbJAYUgKIgm0YIBgIvKQaVEqMHampQyjDFR4U1usDQwzzNShNE61Ok61NZYXQlOpVoY6GdviE047PLUQQzQdHgxjRDAiD2kqaAghye7ti5UEko2Qy+49N93vZ4YXu8u95+xmzrn/PXv37hy9+uqrqqio6Lz/5ZdfvuL+S0pKNGnSJI0ZM0ajR4/WkiVLlJqaqrNnz8b9uQBwhz4AJDd6AAD6APoDBivwrZUrVyo7O1vl5eV6/fXXVVhYqPLychUXF6u4uFiSNHr0aDU0NGjevHmaN2/eZds3NDRo27Ztqq+v14wZMzRhwgTNnz9fZWVlchxHoVBIoVBIknTLLbfomWee0fLlyzVw4EDPnyuA2OgDQHKjBwCgD6A/CDiO49HvSPlfpL1Dm3IWeRpzyUebFUzrmm95mUP32FbqzkiLd0ovzJTyv9K3bb/s+5RubN68me9TJjmv+4BlD4gV38K19ACJPoD4Yi1gg7UA/MT6WGwd3wJrAfR3XGMlzgpWLVQgxe5ltY7vtczMzLg1UElatGgRDRTXzLoOreN7jT4Av7GuQev4XqMHwI+s69A6vtfoA7CWPNXmkRtyh+rm75eYNTLr+ADs69A6PpDsrGvQOj4A+zq0jg8kGyotzpqPndIHf94et9+m72/xAdjXoXV8INlZ16B1fAD2dWgdH0g2DFbi7LMPT2jc8rlm02Hr+ADs69A6PpDsrGvQOj4A+zq0jg8kG/urlf2fOVK5K6njA7CvQ+v4QLKzrkHr+ADs69A6PpBsGGECAAAAAAC4xGAFAAAAAADAJQYrAAAAAAAALvl6sPLII49o7NixCgaDeuWVVy57rKSkRKNGjVJBQYEKCgpUVlZmkyQAAAAAAEhavh6s3HnnnXrjjTc0c+bMmI8/9dRTqq2tVW1trdauXRv/+C89rEUHNmriT78X9333pxwSpf4z6cE90g++uLbWH+ullg7bnIDu/FCDfsghESKO9MIH0oN7o7d/ViPtOW2bE9CdH+rPDzkkytFmqbSqay1Q8b7U3G6bE9CdH2rQDzkkguNIWz6UflIVvb1mn7TzpG1OgBvmvwp05swZPfTQQ9q3b58yMjI0ffp0nTt3Ths3blRxcXGf99fW1qZ7771XjY2Nmj9/vlavXu06t3+u/J2Gz5iorOGDXe/jWvkhh0RoaJbu3yW1hiXni/v+fkJqaJH+MEMKBkzTAzr5oQb9kEMiPLlf+mtDtA9I0rFz0qq3pSemStOH2uYGXOSH+vNDDolw8ry0dGf0Q5WLa4EdJ6Wju6UXZ0mpvv74D8nEDzXohxwS4dn3pJc+lC58sRb4uCU6XCmbJM0eYZsb0Bfmh6wFCxaooKBABw8e1Jtvvqnnn39ehYWFV7XtmjVrNGHCBC1YsECHDx+WJFVWVmratGnasWOHqqqq1NjY6Dq3lhP/db1tvPghh0SoqJfaIl0LKUnqcKQjn0tvu/+TAXHnhxr0Qw7x1tQqVR7rGqpc1BaRnj5okxMQix/qzw85JMKL9dE3U93XAp+0SLtPmaUF9OCHGvRDDvH2ebv0pyNdQ5WL2iLS04eiZ7MA/YXpGSs7d+7U6dOnVVpaKkkKhUIaPny4pk6desVtN23apJycHDmOo4qKCt111106cuSIjh49qsmTJ0uSxo0bp+rqas2dOzfmPlpaWlRXV9d52+kIx/x/ifTuu+8qkJpikkP32F7ac2K8wk5mj/vbwhG9deik0j/mHEDY8LoPWPaAWPG9cqB1gFI1Sh3qGftos7Sv5h3OXIMJ1gLe2XUqXx1OVo/7z4cdvfXeKQ048YlBVoD9sdg6vlfev3C9As4YKcZa4OR5R3tq/q3MYMTzvABJys/PV1ZWz2NUb0wHK9XV1SoqKuq83dTUpOPHj2vixIlX3DYnJ0eSFAgEtGzZMq1evVrHjh1TXl6edu3apdmzZ2v37t0aP358r/uoq6vTlClTOm+nKKANw757Dc+o74qKihS+5LMaL3PoHttLYx/doRu/3vPaOe3nW/Sb8rVa+9ZGg6wA7/uAZQ+IFd8r1426VfmP/0vBjJ4HrHDLZ5paOCXGVkDisRbwzs0P/00Dp8xVIHj5CdSRC+e14bnH9OjW35rkBVgfi63jeyXjq2M0/rf7FUzvOViJXGjVHUWFUsT7YTcgSTU1NZ0nbFwN08FKKBRSZWWlwuGwwuGwHnjgAeXl5Sk9Pf1Lt2ttbVVzc7Oys7MlSa+99ppSUlI0cuRI5ebmatu2bZozZ46GDh2qIUOG9Lqf/Px81dTUdN52OsLa/53H4/PkrlJVVVWPCbVXOXSP7aXa8wP1XFNE7d2+jZaVdZ3+8ugKXferH5nkBXjdByx7QKz4XnEcad2pgE52OHLUdWpKWiCsbw9t0cZLejPgJdYC3jnUeqOebZLau72fy8jM1Ja1y3XjL5aa5AVYH4ut43vpsVNhfdQeUfiS9wRpiuiOmz7Xhuq3TXICpOisoC9MBysLFy7Uli1blJeXp9zcXI0dO1aDB3ddkGndunXasGGDGhsbdeDAAa1YsUJ79+5Venq67r77brW1tSkYDGrQoEHaunWr0tLSJEnr169XJBLR4sWLdfvtt/caPysr67IpVKS9Q/sveXzakz9UqDBPKempyr71Zv3j/ifi/hpMmjRJwbSuP4OXOXSP7aXJksKHpd+/L6UFo2+y0oLSr29LUcHgApOcAMn7PnClHpDoHCz7wHMt0o/3SKdaoxesbg9LM4el6OdThiktOMwkJ4C1gHcmS1K99GxddA0gJ9oLnpga1G2hK5+9DCQKawHvrG+NrgU+bpFSAlJ7RCoKBfXLwiHKSOn9A3LAbwKO45/LAi1dulSzZs3SsmXLXO/j+PHjuu+++xQIBFRaWqp77rnnqreNtHdoU84i17HdWPLR5h6N1Kscuse28OkF6Z0m6fpUqTCbXwCAPa/7gGUPiBXfa44j7f9UOt0q5Q2QRt5glgogibWAhbNtUs1/pMxUqXCwFONbAYCnrI/F1vG95jjSwTPRXwobM0D6GmsB9EPmP7d8qerqaq1ateqa9jFixAht3749Pgkh4QZlSN8abp0FACuBgDTxJussAFgamC59k7UAkLQCAekbg6L/gP7KV4OVQ4cOWacAAAAAAABw1fjiBQAAAAAAgEsMVgAAAAAAAFxisAIAAAAAAOASgxUAAAAAAACXGKxcKhhQ5uABnoXLHDxACgZMcogZG4CnfcCyB/QaH0h2rAUAWB+LreMD6LOA4ziOdRJ+EgmHpYhHL0kwoGBKik0OvcQG4GEfsOwBXxIfSHasBQBYH4ut4wPoGwYrAAAAAAAALvFVIAAAAAAAAJcYrAAAAAAAALjEYAUAAAAAAMAlBisAAAAAAAAuMVgBAAAAAABwicEKAAAAAACASwxWAAAAAAAAXGKwAgAAAAAA4BKDFQAAAAAAAJcYrAAAAAAAALjEYAUAAAAAAMAlBisAAAAAAAAuMVgBAAAAAABwicEKAAAAAACASwxWAAAAAAAAXGKwAgAAAAAA4NL/AHbu9LjM4ifmAAAAAElFTkSuQmCC", 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", 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" + "
" ] }, - "execution_count": 12, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } @@ -516,7 +510,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 10, "metadata": {}, "outputs": [ { @@ -526,7 +520,7 @@ "
" ] }, - "execution_count": 14, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } @@ -553,17 +547,17 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 28, "metadata": {}, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", 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" + "
" ] }, - "execution_count": 15, + "execution_count": 28, "metadata": {}, "output_type": "execute_result" } @@ -602,7 +596,7 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": 30, "metadata": {}, "outputs": [ { @@ -610,7 +604,7 @@ "output_type": "stream", "text": [ "The optimized circuit has 2Q gates depth: 96\n", - "Compared to the unoptimized circuit depth of 78772\n" + "Compared to the unoptimized circuit depth of 96\n" ] } ], @@ -638,20 +632,22 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# Hamiltonian terms to measure\n", "observable_list = []\n", + "for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", + " # print(pauli)\n", + " observable = pauli[::-1].to_label() + 'Z'\n", + " observable_list.append([observable])\n", + "\n", + "# Parameters for the template circuits\n", + "parameters = []\n", "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - " # print(pauli)\n", - " observable = pauli[::-1].to_label() + 'Z'\n", - " observable_list.append(observable)\n", - "\n", - "\n", + " parameters.append(dt_circ*(idx_ket-idx_bra))\n", "\n", "# Real part\n", "# First half hadamard test\n", @@ -671,6 +667,10 @@ "qc_real_2.h(0)\n", "H_real_circ_2 = qc_real_2.decompose().copy()\n", "\n", + "# Compose them\n", + "H_real_circ = H_real_circ_1\n", + "H_real_circ = H_real_circ.compose(H_real_circ_2, list(range(n_qubits+1)))\n", + "\n", "# Imaginary part\n", "# First half hadamard test\n", "qr = QuantumRegister(n_qubits+1)\n", @@ -688,7 +688,11 @@ "qc_imag_2.x(0)\n", "qc_imag_2.sdg(0)\n", "qc_imag_2.h(0)\n", - "H_imag_circ_2 = qc_imag_2.decompose().copy()\n" + "H_imag_circ_2 = qc_imag_2.decompose().copy()\n", + "\n", + "# Compose them\n", + "H_imag_circ = H_imag_circ_1\n", + "H_imag_circ = H_imag_circ.compose(H_imag_circ_2, list(range(n_qubits+1)))\n" ] }, { @@ -702,57 +706,20 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "Generate circuits to calculate all matrix elements of $\\tilde{S}$" + "Instantiate the backend and set runtime parameters" ] }, { "cell_type": "code", - "execution_count": 26, + "execution_count": 13, "metadata": {}, "outputs": [], "source": [ - "S_real_circuits, S_imag_circuits = [], []\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - "\n", - " circuit_real = S_real_circ.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - " circuit_imag = S_imag_circ.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " S_real_circuits.append(circuit_real)\n", - " S_imag_circuits.append(circuit_imag)" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "And $\\tilde{H}$" - ] - }, - { - "cell_type": "code", - "execution_count": 27, - "metadata": {}, - "outputs": [], - "source": [ - "count = 0\n", - "H_real_circuits, H_imag_circuits = [], [] \n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " circuit_real = H_real_circ_1\n", - " circuit_real = circuit_real.compose(H_real_circ_2, list(range(n_qubits+1)))\n", - " circuit_real = circuit_real.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " circuit_imag = H_imag_circ_1\n", - " circuit_imag = circuit_imag.compose(H_imag_circ_2, list(range(n_qubits+1)))\n", - " circuit_imag = circuit_imag.assign_parameters({t: dt_circ*(idx_ket-idx_bra)})\n", - "\n", - " H_real_circuits.append(circuit_real)\n", - " H_imag_circuits.append(circuit_imag)\n", - "\n", - " count+=1" + "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator\n", + " \n", + "service = QiskitRuntimeService()\n", + "backend = service.least_busy(operational=True, simulator=True)\n", + "shots = 100000\n" ] }, { @@ -764,48 +731,29 @@ }, { "cell_type": "code", - "execution_count": 28, + "execution_count": 15, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "210 circuits to run\n" - ] - } - ], + "outputs": [], "source": [ - "estimator = Estimator()\n", + "estimator = Estimator(backend=backend)\n", "\n", - "jobs = {'S': {'real':[], 'imag':[]},\n", - " 'H': {'real':[], 'imag':[]}\n", - " } # store executed jobs\n", - "\n", - "\n", - "shots = 100000\n", + "# Define a set of observables to measure\n", "observable = 'I'*(n_qubits) + 'Z'\n", + "observables = [observable]\n", "\n", - "job_size_S = 20\n", - "job_idxs_S = [idx for idx in range(0, math.ceil(len(S_real_circuits)/job_size_S)+1)]\n", - "\n", - "\n", - "\n", - "print(len(S_real_circuits), 'circuits to run')\n", - "\n", - "S_real_results_list, S_imag_results_list = [], []\n", - "for i in range(len(job_idxs_S)-1):\n", - "\n", - " job = estimator.run(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_real_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['real'].append(job.job_id())\n", - " S_real_results = job.result()\n", + "# Define a sweep over parameter values\n", + "params = np.vstack(parameters).T\n", "\n", - " job = estimator.run(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S], observables = [observable]*len(S_imag_circuits[job_idxs_S[i]*job_size_S:job_idxs_S[i+1]*job_size_S]), shots=shots)\n", - " jobs['S']['imag'].append(job.job_id())\n", - " S_imag_results = job.result()\n", + "# Estimate the expectation value for all combinations of\n", + "# observables and parameter values, where the pub result will have\n", + "# shape (# observables, # parameter values).\n", + "pub = (S_real_circ, observables, params)\n", + "job = estimator.run([pub], precision=1/np.sqrt(shots))\n", + "S_real_results = job.result()[0]\n", "\n", - "\n", - " S_real_results_list.append(S_real_results); S_imag_results_list.append(S_imag_results)\n" + "pub = (S_imag_circ, observables, params)\n", + "job = estimator.run([pub], precision=1/np.sqrt(shots))\n", + "S_imag_results = job.result()[0]" ] }, { @@ -817,43 +765,28 @@ }, { "cell_type": "code", - "execution_count": 29, + "execution_count": 16, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "5670 circuits to run\n" - ] - } - ], + "outputs": [], "source": [ - "estimator = Estimator()\n", - "\n", - "jobs['H']['real'], jobs['H']['imag'] = [], []\n", - "shots = 100000\n", + "estimator = Estimator(backend=backend)\n", "\n", + "# Define a set of observables to measure\n", + "observables = observable_list\n", "\n", - "job_size = 50\n", - "job_idxs = [idx for idx in range(0, math.ceil(len(H_real_circuits)/job_size)+1)]\n", + "# Define a sweep over parameter values\n", + "params = np.vstack(parameters).T\n", "\n", - "print(len(H_imag_circuits), 'circuits to run')\n", + "# Estimate the expectation value for all combinations of\n", + "# observables and parameter values, where the pub result will have\n", + "# shape (# observables, # parameter values).\n", + "pub = (H_real_circ, observables, params)\n", + "job = estimator.run([pub], precision=1/np.sqrt(shots))\n", + "H_real_results = job.result()[0]\n", "\n", - "H_real_results_list, H_imag_results_list = [], []\n", - "for i in range(len(job_idxs)-1):\n", - "\n", - "\n", - " job_real = estimator.run(H_real_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " jobs['H']['real'].append(job_real.job_id())\n", - " H_real_results = job_real.result()\n", - "\n", - " job_imag = estimator.run(H_imag_circuits[job_idxs[i]*job_size:job_idxs[i+1]*job_size], observables = observable_list[job_idxs[i]*job_size:job_idxs[i+1]*job_size], shots=shots)\n", - " jobs['H']['imag'].append(job_imag.job_id())\n", - " H_imag_results = job_imag.result()\n", - "\n", - "\n", - " H_real_results_list.append(H_real_results); H_imag_results_list.append(H_imag_results)\n" + "pub = (H_imag_circ, observables, params)\n", + "job = estimator.run([pub], precision=1/np.sqrt(shots))\n", + "H_imag_results = job.result()[0]" ] }, { @@ -872,7 +805,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 17, "metadata": {}, "outputs": [], "source": [ @@ -881,15 +814,9 @@ "for idx_ket in range(krylov_dim):\n", " for idx_bra in range(idx_ket + 1):\n", "\n", - " eff_count = count % (job_size_S)\n", - " res_idx = count // (job_size_S)\n", - "\n", - " S_real_results = S_real_results_list[res_idx]\n", - " S_imag_results = S_imag_results_list[res_idx]\n", - "\n", " # Get expectation values from experiment\n", - " expval_real = S_real_results.values[eff_count]\n", - " expval_imag = S_imag_results.values[eff_count]\n", + " expval_real = S_real_results.data.evs[0][count]\n", + " expval_imag = S_imag_results.data.evs[0][count]\n", "\n", " # Get expectation values\n", " expval = expval_real + 1j*expval_imag\n", @@ -898,9 +825,6 @@ " S_circ[idx_bra, idx_ket] = expval\n", " S_circ[idx_ket, idx_bra] = expval.conjugate()\n", "\n", - "\n", - "\n", - "\n", " count+=1" ] }, @@ -913,25 +837,19 @@ }, { "cell_type": "code", - "execution_count": 31, + "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "H_eff_circ = np.zeros((krylov_dim, krylov_dim), dtype=complex)\n", - "count = 0\n", - "for idx_ket in range(krylov_dim):\n", - " for idx_bra in range(idx_ket + 1):\n", - " for pauli, coeff in zip(H_op.paulis, H_op.coeffs):\n", - "\n", - " eff_count = count % (job_size)\n", - " res_idx = count // (job_size)\n", - "\n", - " H_real_results = H_real_results_list[res_idx]\n", - " H_imag_results = H_imag_results_list[res_idx]\n", - "\n", + "for obs_idx, (pauli, coeff) in enumerate(zip(H_op.paulis, H_op.coeffs)):\n", + " count = 0\n", + " for idx_ket in range(krylov_dim):\n", + " for idx_bra in range(idx_ket + 1):\n", " # Get expectation values from experiment\n", - " expval_real = H_real_results.values[eff_count]\n", - " expval_imag = H_imag_results.values[eff_count]\n", + " expval_real = H_real_results.data.evs[obs_idx][count]\n", + " expval_imag = H_imag_results.data.evs[obs_idx][count]\n", + " \n", "\n", " # # Get expectation values\n", " expval = expval_real + 1j*expval_imag\n", @@ -943,7 +861,6 @@ " H_eff_circ[idx_ket, idx_bra] += (coeff*expval).conjugate()\n", "\n", "\n", - "\n", " count+=1" ] }, @@ -960,33 +877,33 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "The estimated ground state energy is: 9.02350357851545\n", - "The estimated ground state energy is: 1.3661212194478773\n", - "The estimated ground state energy is: 1.5519667772645285\n", - "The estimated ground state energy is: -2.433030660377216\n", - "The estimated ground state energy is: -3.8243769047376768\n", - "The estimated ground state energy is: -3.093617946223878\n", - "The estimated ground state energy is: -5.141259443945021\n", - "The estimated ground state energy is: -6.327974564731133\n", - "The estimated ground state energy is: -6.219471601689204\n", - "The estimated ground state energy is: -6.585432430537937\n", - "The estimated ground state energy is: -6.995995439961133\n", - "The estimated ground state energy is: -7.193648275003521\n", - "The estimated ground state energy is: -7.577746195049643\n", - "The estimated ground state energy is: -7.375626245886178\n", - "The estimated ground state energy is: -7.633870979679662\n", - "The estimated ground state energy is: -7.765358735198269\n", - "The estimated ground state energy is: -8.061082731107005\n", - "The estimated ground state energy is: -7.880387217614935\n", - "The estimated ground state energy is: -8.43591065997732\n", - "The estimated ground state energy is: -8.441669993329537\n" + "The estimated ground state energy is: 8.99848\n", + "The estimated ground state energy is: 0.7937378945206248\n", + "The estimated ground state energy is: 1.580148146997832\n", + "The estimated ground state energy is: -2.1358877293150162\n", + "The estimated ground state energy is: -2.868380302510151\n", + "The estimated ground state energy is: -4.308984388844685\n", + "The estimated ground state energy is: -4.908392116269306\n", + "The estimated ground state energy is: -5.049516981337282\n", + "The estimated ground state energy is: -6.7678700851175435\n", + "The estimated ground state energy is: -6.325887605573247\n", + "The estimated ground state energy is: -6.8959604780066766\n", + "The estimated ground state energy is: -8.385726072961965\n", + "The estimated ground state energy is: -8.42929808324567\n", + "The estimated ground state energy is: -6.885616460863645\n", + "The estimated ground state energy is: -9.267911300984151\n", + "The estimated ground state energy is: -9.17835339754369\n", + "The estimated ground state energy is: -8.594949712338924\n", + "The estimated ground state energy is: -8.389182678819786\n", + "The estimated ground state energy is: -8.238216318473675\n", + "The estimated ground state energy is: -8.674016660826856\n" ] } ], @@ -1001,12 +918,12 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 26, "metadata": {}, "outputs": [ { "data": { - "image/png": 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nOH36NBEREbz77rsAOTrU+uDBg2mmnTx5kksvvdR1Pzg4ON1u6927d1+0/ZQv35IlS6Z57PHHH6d169bcf//96S6bkJCQJr/g4GAOHTqUprBK2b2Qk8OSz///nDx5EsD1XgQHB5OUlJTmvdixY0em2n///fc5c+YMa9asYefOnYwcOZLmzZtnOr+crgO1a9emQ4cObsVnREQECxcuBKBChQoXXBac5zw5f/l27dqlWTYmJsa1ay/FyZMnKVu2rFubZcqU4dixY2nadDgcadoMDQ1Nk1dW1s1JkyYRGxvrWt9KlSrF3XffzQ8//JDh606xbNkyqlSpQs2aNWnevDlmxqpVq9wKpFtuuYUVK1bg7LTInvPXQUj7eUxPZoqclMeOHj2a5bwuvfRSPvnkE44cOUJsbCwRERHs3bsXSH/du9hnyZOy8r2alRwef/xx4uPjmTNnDnXq1MlwvvS+pyD761twcDC7du1Ksx6d/x2XlJTElClT6Ny5M0WLFgWga9euFC1aNN8VQhoj5IOOHTtGkyZNaNeuHR06dKBDhw48/PDDjB8/nt69e2e73aSkpCxN9/PzA5y/YBYuXMj27dt5/vnnOXDgAPHx8dx55508//zz+Ptnv96+2HPnVGRkJIcOHaJhw4ZpHksZM5RR8RIXF5ftjUpGy13ovcrt92L79u3UrVuXu+++m/bt23Pvvffyv//9j9dff53XXnvtgst6Yh3w9/dn3rx5fPDBB+k+vnPnzgsuC86xHecf9Qe49XRCxu/l+W2Gh4dnWAinjI1KERMTc9E2L+TUqVP8+uuv3H///bz55pt069aN4sWLu/WIZiSll+bWW2+lRo0arF+/nujoaJYtW8YzzzxDUFAQ11xzDUOGDMlRjtldB7du3UqXLl1o1KgRy5YtS3eeRo0aAc6eNcj4M5K6JzrF5MmTad68OcOGDWPDhg2cOXMGf39/5s6dm+66l5PPUlbyutBz5fTzvHXrVu68804WLlzI/PnzadGiRboFT0bfUzlZ3zJr4sSJPPHEE3To0IHp06dz3333sW3bNjZt2uSx5/AEFUI+KiEhgV9//ZVff/0VPz8/Pv/8c5544gnefPNN9uzZk6NffVnVsWNHihcvTqdOndx+5aS3OyI38tq3bx8NGjRIM71WrVqZWn7WrFk8+uij3HDDDaxZsybHubRu3ZqSJUu69QrVq1fP9Tj8+wu0TJkybsvnpMdo3759FClShJo1a7oVDXXr1s10G9HR0UyePJnJkycTGBjIL7/8wpAhQ3j33XcvWPh5Yh3Ys2cPJUuWdPUAZUVKr8vRo0eztXxGbbZu3ZoVK1Zk+zD4rK6b3377LTNmzOD666/n/vvvZ/369RcchJziwIED7Nu3j1tuuYUaNWq4io2lS5cyfPhwunfvTkBAAEuXLr1gO7n1vTFz5kyGDBnCgw8+mG4h5O/vT8+ePTly5Igrx8x+RsqUKUPr1q159dVX3Q7gyOznPyMZvRcnT55Mk1N6eeWFNWvWcM899zBr1izmz5/PLbfckqan80Kys77t27ePRo0a4efn5/Yenf8dB87179ChQ/To0YPly5dzxx13uA6SyE+0a8wHpe6+B+cHNqXCLlasGABnz54F0n6J5IaUXzapf8mUKlWKPn36pJn37NmzHs9p7ty5XH755XTq1Mk1rVixYjz66KOZWv6DDz7g7NmzjBs3Lt3dL1npcfntt98ICAjg6aefdpv+3HPPce7cOWbPng04dxUcO3YszbiXp556KtPPdb6Utp955hm36c8++2ymlj9/vUpISGDr1q34+fkRGBgIZLxeeWIdSPlV37Zt2zSPlS5dOsNf3OBcB06fPs1LL71EQEDa33fly5fPcNmMTJ48mYCAAF555ZU0j52/a/hCeWVl3Zw9ezbHjh1j4MCBtGzZMku/zpctW8Ydd9zBjTfe6Co2NmzYQGRkJIMGDSI6Ovqi5yfLre+N1atXM3fuXPr06cNdd92V5vG3336bunXr8sEHH7jWpX379pGYmHjRz0h66x5kfr3PSEbr6Z49eyhTpozb2eYrVapEly5dcvR82bVo0SL+85//UKtWLebMmZOlcU7ZWd9+++03Kleu7Db2p0iRIvTt25eoqCi38UVmxs8//0zHjh154IEHCAwMzHe7xUA9QvlShw4dXNV1aitXriQ0NJQxY8ZQtmxZFi1axMGDBwkODqZv37789ddfrv20GzZsIDExkYEDB1K6dGni4uJcg9c8bd68ecTFxTFz5ky++uorSpYs6ToctUqVKm7zrlu3jieffJIhQ4awe/dujh49muPr2Hz11Vc8/fTTTJgwgU8//ZTDhw9z//33u37FX+xX7u7du+nZsycTJkxgx44d/PDDD2zcuBE/Pz+qV69Oz549SUpKSrfb+XwzZ85k0aJFvP3221x55ZVs3LiRtm3bcs899zB8+HBXtz84D3UfPHgwo0ePZu3atdx6660X3Nd/MRs3buTHH3/kf//7H6VLl2blypW0atUq07+M582bx5EjR1ixYgXh4eHUr1+fp59+mlmzZrl6t1I2pG+//TYTJ04kISGBmTNnemQdGDZsGJ06deLXX391HZIdFBTE1VdfTbdu3bjyyis5fvx4urlHRUXx5JNP8t1337F+/XomTpzIsWPHqFatGnfddRcrVqygb9++WXo/ly5dypdffslLL71EkyZNmDdvHgkJCdSuXZvu3bvTr18/pkyZcsE2srpuJiYmMnHiRPr27UtiYqLbgNSLWbZsGb169eLcuXOuXWXnzp1j5cqVtG/fnsWLF1/0ZKq5+b3x4IMPsmjRIqZPn86PP/7IsmXLKFasGF27duX222/nu+++Y/jw4a75IyMj+emnn+jbty9mxp49e7j77rvT/FhJ2fi++OKLBAYGEhYWRtu2balevXqO8l23bh2tW7fmueee49ChQ4SGhvLnn38yceJE3n//faZOncpnn33mOk3Dzp0701z2Iq9MmzaNRx99lJCQEGbMmEH79u0zdYLa7KxvX3/9NY8//jjffPMN1113HXv37qVbt27cfPPN9OvXL834yEmTJvHMM8/w+uuvs2nTJrZv357t15mbvH7omsIZFzp8PvXhol27drU5c+bYkSNHLDY21vbu3WtffPGFVaxY0a29//73v7Z7925LSEhwOyQyo8Pn77333nTzOf8EjymHiaa+5Mfdd99tGzZssOjoaPvnn39swIAB1rt37zSHg1aoUMFmzpxpp0+fNrPMnVDx/PcpvcNXr7zySps5c6adPXvWwsPDbdiwYdalSxczy/yJEmvUqGGjRo2ynTt3WnR0tJ09e9a2bt1qn3/+uTVq1ChNDlFRUem2ExQUZB999JEdPHjQ4uLibMeOHWlOqAjOQ35Hjx5tJ0+etNOnT9vEiROtfPnyZpb+4fPnX2Il5f+T+v0tVqyYffLJJ3bs2DGLiorK0gkVH330UVuyZIkdO3bMYmJibNeuXfb++++bw+Fwm2/IkCF24MABS0xMdHv+nK4DKe/d22+/bTt37rTY2Fg7evSoLV++3J5//nm3UztkFC1btrTZs2fbyZMnLTo62nbt2mXjxo2za6+99qL/u/QOfwbskUcesTVr1tjZs2ft9OnTtnHjRnvvvfesUqVKrnkudPmJrK6b119/vZmZzZkzJ0vfH/Xr1zczsy1btrhNf+mll8zM7PXXX0+zzPmHz1/oeyOj15iVSzAEBQXZK6+8Yps3b7bo6GjXd1t6uQFWrlw5++mnn+zMmTN2/Phx++KLL6xBgwZu34eAValSxaZMmWInTpywkydP2qRJk6xSpUo5+izVqVPHlixZYmfPnjUzc3ufWrdubZs2bbLY2Fjbtm2b9ezZ84InVEw9LeXw//O/EzL6Hj4/LnTi3eeff97MzGbMmGFFihS54PdUZte3jE6oOHbsWDt69KjFxsbaxo0b0z0VSErs27fPzNKeViQfhdcTUChyJfr162dmZlWqVPF6LgpF6rjQuplyPqjU588qqFGlShXbu3evHTx40K644gqv51MYozCtbxcIryegUOQ4zj+hWspJ63bs2OH13BSFO7K6bo4YMcIiIyOtRIkSXs89L6JevXoWERFhf//9d5pLlyhyPwrb+pZeaIyQFAi//PIL+/fvZ8OGDZQuXZpevXpRv359evbs6e3UpJDL7Lp5991306BBAx577DFGjhxZaC6MuX379mwNZpecKazrW0a8Xo0pFDmNfv362ebNmy0qKsqio6Nt7dq1dt9993k9L4Uis+tmaGioRUdH29SpU90uvaBQ5EZoffs3/JJviIiIiBQ6Oo+QiIiIFFoqhERERKTQ0mDpTKhSpcoFr5osIiIi+Y/D4eDQoUMXnEeF0EVUqVKFsLAwb6chIiIi2VC1atULFkMqhC4ipSeoatWq6hUSERHxEQ6Hg7CwsItuu1UIZVJUVJQKIRERkQJGg6VFRESk0FIhJCIiIoWWCiEREREptDRGSEREBAgICKBy5cr4+6uPIL8zMyIiIjxyjTQVQiIiUuhVqFCBt956i+LFi3s7FcmCJUuWEBISgln2rxamQkhERAo1Pz8/HnnkEc6cOcOHH35IXFyct1OSiwgICKBevXrcd999AIwbNy77bXkqKREREV9UpkwZ6tWrx+eff87OnTu9nY5k0p49ewDo0aMHEydOzPZuMu0IFRGRQs3hcABw9OhRL2ciWbV9+3YAypcvn+02VAiJiEih5ufnB0BSUpKXM5GsSkxMBP79H2aHCiEREREptFQIiYiICAAhISFMnTrV22nkKRVCIiIihUxwcDBmRuPGjd2m9+vXj969e+f68+engktHjYmIiAgAkZGR3k4hz6lHyKuqAtkf6S4iIoWbn58fgwYN4p9//iE6OpoNGzZw7733As7TAnz//fccPXqU6Ohodu7c6ert2bt3LwAbNmzAzFi8eDGQtqdm8eLFfPbZZwwfPpwTJ05w5MgRHnnkEUqUKMG4ceOIjIxk165dtG/f3rWMv78/Y8aMceW0fft2nnnmGdfjQ4cOpXfv3txzzz2YGWZGy5YtAbj88suZNGkSJ0+e5Pjx40ybNo3g4ODcfAvVI+Q9Y4GHgUHA+17ORURE0iqRjWXigJSjz4oAxYBzQGwm2s36eXAGDx5Mr169eOKJJ9i1axe33nor33//PceOHaN79+40aNCADh06EBERQa1atbjkkksAuOGGG1izZg2tWrViy5YtxMfHZ/gcDz30EB988AE33ngjPXr04IsvvqBLly5MnTqVd955h+eee47vvvuOatWqERMTg7+/PwcPHqR79+4cP36c5s2b8/XXX3P48GF++uknPvzwQ+rXr0+pUqXo06cPACdOnCAgIIC5c+eyatUqbrnlFhITE3n55ZeZM2cOjRo1IiEhIcvvT2aZIuNwOBxmZuZwODzc9hADMxjv9deoUCgUhTmCg4Pt22+/teDg4PMes2xEt1TLd0uetvi8do9msGzW8i5atKidOXPGmjZt6jZ99OjR9sMPP9j06dNt7NixGb5mM7PGjRu7TQ8JCbGpU6e67i9evNiWLl3quu/v729RUVE2fvy/266KFSuamdlNN92UYa4jRoywn376KcPnAez++++3bdu2uU0LDAy0s2fPWps2bbL4v8v89ls9Ql6zNflvfa9mISIivqlWrVoEBQUxf/58t+lFixblr7/+4rXXXmPKlClce+21zJs3j2nTprFq1aosP8+mTZtct8+dO8fx48fZvHmza1p4eDjgvF5biqeeeoqHH36YatWqcckll1C0aFE2bNhwwedp3LgxtWrVIioqym168eLFqVmzZprX6SkqhLxmW/Lfel7NQkREMhKUjWVSX6dsanIb586b58rsJuSmZMmSANx1112EhYW5ZxEXx8GDBwkODubOO++kTZs2LFy4kFGjRjFgwIAsPc/5u6TMLN3dVP7+zmHHPXr04MMPP6R///6sWrWKqKgoBgwYwE033XTR17Nu3Truv//+NI8dO3YsSzlnhQohr9kNJAAO4HLgoHfTERGR82Tv2lX/SsqgjZy267R161ZiY2OpVq0aS5cuTXeeiIgIvv32W7799luWLVvGsGHDGDBggGtMUJEiRTySS2otWrRg5cqVfPHFF65pNWvWdJsnPj4+zXOvX7+eHj16cPTo0TS9QrlJhZDXJOIshuoDDVAhJCIiWXHmzBk+/PBDhg8fjr+/P8uXL6d06dK0aNGCyMhIatasybp169iyZQvFihXj7rvvZts2596IlCPJ2rdvz8GDB4mNjfXYofO7du3iwQcfpG3btoSGhvLAAw9www03EBoa6ppn7969tGvXjjp16nD8+HFOnz7NDz/8wIABA5g+fTqvvvqqq0era9eufPDBB2l6vTxFh897lcYJiYhI9r3yyiu8+eabDB48mG3btjFnzhzuuusuQkNDiY+P591332XTpk0sXbqUpKQk/u///g9wXlftmWee4fHHH+fQoUNMnz7dYzl99dVX/PLLL0yaNInVq1dTrlw5Pv/8c7d5Ro8ezY4dO1i7di0RERG0aNGCmJgYbr31Vvbv388vv/zCtm3bGDt2LMWLF8/18xt5fcR+fo7cO2oMgzcNzOBLr79OhUKhKKxxoSOPFPk7PHHUmHqEvCplwLR6hERERLxBhZBXpRRCDbyahYiISGGlQsirtuM8rLI8utSGiIhI3lMh5FUxwL7k29o9JiIiktdUCHldyu6x2l7NQkSksDIzIHfOqSO5KyDAeRaglP9hdqgQ8rqncO4WG+ftRERECqWUk/elvkSE+IZ69ZxXZ4iIiMh2Gzqhotftu/gsIiKSa06dOsX27du57777OHHiBHFxcRdfSLwqICCAevXqcd9997FkyRKio7N/tm4/nMfRSwYcDgeRkZGUKlUqT0/5LSIieeeyyy7j7bffpnjx4t5ORbJgyZIlhISEpLtrLLPbbxVCF5H7hZA/8AHOwdL/B6jYEhHxhoCAACpVqqSxQj7AzIiIiLhgT1Bmt9/aNeZ154CeQGWcV6Jf4910REQKqcTERA4e1HUfCxsVQvnC2zivRL/f24mIiIgUKiqE8oVR3k5ARESkUNLh8yIiIlJoqRDKFwKBpsB93k5ERESkUNGusXyhHLAKSAKmAzqHhYiISF5Qj1C+cAQ4CRRBl9oQERHJOyqE8o2Ua47p4qsiIiJ5xWcKodDQUMwsTYwcOTLd+R966KE088bExORx1lmhQkhERCSv+cwYoRtuuMHtbJ8NGzZkwYIF/PTTTxkuc/r0aerWreu6n5Or0+a+lEKogVezEBERKUx8phA6/8qygwYNYvfu3fz+++8ZLmNmhIeH53ZqHrI1+a96hERERPKKz+waSy0wMJBevXoxbty4C85XsmRJ9u7dy/79+5k2bRoNGly8t6Vo0aI4HA63yBspPUJ18NF/i4iIiM/xyS3uPffcQ5kyZfjmm28ynGfHjh08/PDDdO7cmV69euHv78/KlSupWrXqBdsePHgwkZGRrggLC/Nw9hnZB0QDxYHqefScIiIihZtPXn1+zpw5xMfH06lTp0wvExAQwLZt25gwYQKvvvpqhvMVLVqUYsWKue47HA7CwsJy8erzqa0HrgE6ATNz+blEREQKrgJ79flq1arRunVrunbtmqXlEhMT+euvv6hVq9YF54uPjyc+Pj4nKebANpyFUH1UCImIiOQ+n9s11qdPH44ePcqsWbOytJy/vz9XX301hw8fzqXMPEEDpkVERPKSTxVCfn5+9OnTh/Hjx5OUlOT22Pjx43nnnXdc91955RXatGlD9erVueaaa/j+++8JDg5mzJgxeZ12FuhcQiIiInnJp3aNtW7dmuDg4HSPFqtWrRrnzp1z3b/00ksZPXo0lSpV4uTJk6xbt47mzZuzbdu2NMvmH9uAszgHTYuIiEhu88nB0nkps4OtPEf/EhERkZzK7Pbbp3aNFQ4qgkRERPKKCiEREREptFQI5Tv/B2wGPvFyHiIiIgWfTw2WLhyKAA2B495OREREpMBTIZTvLATuBP72diIiIiIFngqhfOcIMNvbSYiIiBQKGiMkIiIihZYKoXzpFuA1oJWX8xARESnYVAjlS/cAQ4G7vJyHiIhIwaZCKF/SxVdFRETyggqhfEkXXxUREckLKoTypZRCKBgI8mYiIiIiBZoKoXzpJBCefLueNxMREREp0FQI5VsaJyQiIpLbVAjlWxonJCIikttUCOVbKYVQA69mISIiUpCpEMq31CMkIiKS21QI5VspY4RqAoHeTERERKTAUiGUbx0GTuO8Lm5tL+ciIiJSMKkQytc0TkhERCQ3BXg7AbmQBTh7ho57OxEREZECSYVQvvaKtxMQEREp0LRrTERERAotFUI+oTLg5+0kREREChwVQvneYeAQUN3biYiIiBQ4KoTyvXAgEbjSy3mIiIgUPBosne/dBRwD4r2diIiISIGjQijfC/N2AiIiIgWWdo2JiIhIoaVCKN+7FBgDzPd2IiIiIgWOdo3le2eBh3D+qyrjPIpMREREPEE9QvlePLAn+XZ9byYiIiJS4KgQ8gkpF19VISQiIuJJKoR8gq5CLyIikhtUCPmErcl/1SMkIiLiSSqEfIJ2jYmIiOQGFUI+YXvy30o4D6cXERERT/CZQmjo0KGYmVts27btgst069aNbdu2ERMTw6ZNm+jQoUMeZetpZ4H9ybfVKyQiIuIpPlMIAfz9999UqlTJFTfffHOG8zZr1owJEyYwduxYrrnmGqZNm8a0adO46qqr8jBjT9I4IREREU/zqUIoMTGR8PBwVxw/fjzDefv168ecOXP48MMP2b59O6+++irr16/n6aefzsOMPUnjhERERDzNpwqh2rVrExYWxp49e/j++++54oorMpy3WbNmLFiwwG3a3Llzadas2QWfo2jRojgcDrfIH1QIiYiIeJrPFEKrV6+md+/etG/fnieffJLq1auzbNkySpYsme78lSpVIjw83G1aeHg4lSpVuuDzDB48mMjISFeEheWXq7/rXEIiIiKe5jPXGpszZ47r9ubNm1m9ejX79u3jvvvuY9y4cR57nnfffZePP/7Ydd/hcOSTYmgL8FnyXxEREfEEnymEznf69Gl27txJrVq10n38yJEjVKxY0W1axYoVOXLkyAXbjY+PJz4+3mN5es5JoJ+3kxARESlQfGbX2PmCgoKoWbMmhw+nfzX2VatW0apVK7dpbdq0YdWqVXmRnoiIiPgI84UYNmyY3XrrrRYcHGzNmjWzefPm2dGjR618+fIG2Pjx4+2dd95xzd+sWTOLj4+3559/3urWrWtDhw61uLg4u+qqq7L0vA6Hw8zMHA6H198DKGlwk8E1+SAXhUKhUCjyb2R2++0zPUKXX345EyZMYMeOHUyePJnjx4/TtGlTIiIiAKhWrRqVK1d2zb9q1Sp69uzJY489xsaNG+nWrRv33HMPW7b48hibPsAfwMveTkRERKRA8MNZEUkGHA4HkZGRlCpViqioKC9n0wYIAeYAj3g5FxERkfwrs9tvnx0sXTjNBy73dhIiIiIFhs/sGhMRERHxNBVCPsvP2wmIiIj4PBVCPmcAcBB4yduJiIiI+DwVQj7HD6iKLrUhIiKScyqEfI4uvioiIuIpKoR8TkohVA/9+0RERHJGW1KfEwrEAZcAwV7ORURExLepEPI5ScCO5NvaPSYiIpITKoR8ksYJiYiIeIIKIZ+kQkhERMQTVAj5JBVCIiIinqBCyCdtTf6rcwmJiIjkhAohn7QT56DpMkAl76YiIiLiw1QI+aR44J/k29o9JiIikl0qhHyWxgmJiIjkVIC3E5Ds+hD4Cljr7URERER8lgohn7XM2wmIiIj4PO0aExERkUJLhZBP6wa8ApTydiIiIiI+SbvGfNrHwBXAfOAPL+ciIiLie1QI+bQpOHuDzng7EREREZ+kQsinPeftBERERHyaxgiJiIhIoaVCyOcFAnW8nYSIiIhP0q4xn3YpcBRnPVsSiPFuOiIiIj5GPUI+7SRwCue/sa53UxEREfFBKoR8Xso1xxp4NQsRERFfpELI5+niqyIiItmlQsjnbU3+q0JIREQkq1QI+Tz1CImIiGSXCiGfl1II1UYHAYqIiGSNCiGfdwDnJTYCgVpezkVERMS3qBAqELR7TEREJDtUCBUIKoRERESyQ4VQgaBzCYmIiGSHCqECQT1CIiIi2eEzhdCgQYP4888/iYyMJDw8nKlTp1KnzoUvNvrQQw9hZm4RE1MQr8eVci4hDZYWERHJCp8phFq2bMmoUaNo2rQpbdq0ITAwkHnz5lGiRIkLLnf69GkqVarkiuDg4DzKOC/tAa4GKng7EREREZ/iMyee6dChg9v93r17c+zYMa677jqWLVuW4XJmRnh4eG6n52XngL+9nYSIiIjP8ZkeofOVLl0agBMnTlxwvpIlS7J3717279/PtGnTaNDgwgOKixYtisPhcAsREREpmHyyEPLz8+OTTz5h+fLlbNmyJcP5duzYwcMPP0znzp3p1asX/v7+rFy5kqpVq2a4zODBg4mMjHRFWFhYbryEXNAMGA0M8HYiIiIiPsV8LT7//HMLDQ21qlWrZmm5gIAA27Vrl73xxhsZzlO0aFFzOByuqFKlipmZORwOr7/uC0cPAzNYng9yUSgUCoXCu+FwODK1/faZMUIpRowYwd13382tt96a5d6axMRE/vrrL2rVyvjoqvj4eOLj43OaphesBl4H1ns7EREREZ/hU7vGRowYQZcuXbjjjjvYu3dvlpf39/fn6quv5vDhw55Pzuv2Aq8BM7ybhoiIiA/xmR6hUaNG0bNnTzp37kxUVBQVK1YEnIfHx8bGAjB+/HjCwsJ46aWXAHjllVf4448/2L17N2XKlGHAgAEEBwczZswYr70OERERyT98phB66qmnAPj999/dpvfu3Zvx48cDUK1aNc6dO+d67NJLL2X06NFUqlSJkydPsm7dOpo3b862bdsomCoBTYBDwCbvpiIiIuID/HAOFpIMOBwOIiMjKVWqFFFRUd5O5yLeB14ERgDPeDkXERER78ns9tunxgjJxeiaYyIiIlmhQqhA0VXoRUREskKFUIGSUghVAUp5MxERERGfoEKoQIkEUs6tpN1jIiIiF6NCqMDROCEREZHMUiFU4GickIiISGapECpwtib/VY+QiIjIxagQKnC0a0xERCSzVAgVOCmFUHWguDcTERERyfdUCBU4R4ETOP+1db2ci4iISP6mQqhAys1xQsWAa4GuOM9XJCIi4rtUCBVI24DDwCXZXD4AqAXcBTwH3JLqsWuBdcBHQJcc5CgiIuJ9PnP1ecmKJ4HHMjFfRaAOzl1oqf/WBAJTzfcxsCz59g6cu98GAxM9lK+IiIh3qBAqkJJS3S4OxKa6/wrQEWfBU/oCbUQDO3EWPutTTT+Bs4ASERHxfdkqhEqUKEF0dLSncxGP8gPeAfoDQUBC8vSawA3Jt88Be3EWOzvP+xsG2EWeIwBohHuhJCIi4juyVQiFh4czefJkxo0bx4oVKzydk3jEF8CdOHdxVcdZ4AB8BUzHWezsAeKy2X6Z5OVL4+whOp6DXEVERLwjW4Ole/XqRdmyZVm0aBE7duxg4MCBVK5c2dO5SY68AnQDyvFvEQSwCpiK88iy7BZBAKeAfUAR4O4ctCMiIuI92SqEpk+fTpcuXahatSpffvklPXv2ZN++fcycOZMuXbpQpEgRT+cpWXYM+BPnmJ7cMj35b+dcfA4REZHcZZ6Ip59+2mJiYiwpKcnCw8Pt9ddft0suucQjbXszHA6HmZk5HA6v55L/oomBGZw18P3/tUKhUCgKTmR2+52j8whVqFCBAQMGsGXLFt577z1+/vlnWrVqRf/+/enatSvTpk3LSfOS723AuXusBNDau6mIiIhkU5arrC5dutiMGTMsLi7O/vrrL/vf//5npUuXdpunRo0aFhcX5/WKMKehHqGLxacGZjAmH+SiUCgUCoUzMrv9ztZRYyEhIUycOJEWLVqwdu3adOc5dOgQb7/9dnaaF58yHXgG57mJ/HEeki8iIuIb/HBWRFlyySWXEBMTkwvp5D8Oh4PIyEhKlSpFVFSUt9PJhwJwnmn6UuBmQKdTEBER78vs9jtbPUIBAQE4HI40082MuLg4EhIS0llKCqZEYBbQC+fRYyqERETEd2RrsPSpU6c4efJkmjh16hQxMTHs3buX1157DT8/P0/nK/mSDqMXERHflK0eod69e/P222/zzTff8OeffwJw44038tBDD/HWW29x2WWX8cILLxAXF8e7777r0YQlP5qD8+SMdYB6wHbvpiMiIpIFWR6JvWDBAuvevXua6d27d7cFCxYYYL169bJt27Z5fdR4TkNHjWU2ZhmYwcB8kItCoVAoCnvk6nmEmjdvzl9//ZVm+l9//UWzZs0AWL58OdWqVctO8+KTpgIrgQPeTkRERCTTslUIHThwgP/+979ppv/3v//lwAHnhrBcuXKcPHkyZ9mJDxkDtAB+9HYiIiIimZatMUIvvPACP/30Ex06dGDNmjUAXH/99dSrV49u3boBcMMNNzBp0iTPZSoiIiLiYdk6jxBAcHAwjz/+OHXr1gVgx44dfPXVV+zbt8+T+XmdziOUVWWAa4DFXs5DREQKs1w7j1BAQABz5szhiSee4KWXXspRklLQVAP24Dy30GXAGe+mIyIichFZHiOUmJhIo0aNciMX8Xn7gVBgF86iSEREJH/L1mDp77//Pt3B0iJwPdAI2OrtRERERC4q25fYePjhh2ndujXr1q3j7Nmzbo/379/fI8mJL4r0dgIiIiKZlq1CqGHDhqxfvx6AOnXquD1mlq2x11LgXAKUAI57OxEREZEMZasQuuOOOzydhxQoTwPvA6OBZ72bioiIyAVka4xQipo1a9K2bVuKFy/uqXwu6qmnniI0NJSYmBj++OMPbrjhhgvO361bN7Zt20ZMTAybNm2iQ4cOeZRpYbYfZ29QZ28nIiIiclFZvn5H2bJlbcGCBZaUlGSJiYlWvXp1A2zs2LH24Ycf5tp1Q+677z6LjY213r17W/369e2rr76yEydO2GWXXZbu/M2aNbOEhAR74YUXrF69evbGG29YXFycXXXVVR6/VokidVxicNbADBrlg3wUCoVCUdgiC9vvrDc+fvx4mz17tlWtWtUiIyNdhVDbtm3t77//zrUX9ccff9iIESNc9/38/OzgwYM2cGD6F/qcOHGizZw5023aqlWr7IsvvsiNN1LhFlMNzOCVfJCLQqFQKApb5OpFV9u2bcvAgQMJCwtzm75r1y6Cg4Oz0+RFBQYGct1117FgwQLXNDNjwYIFrgu9nq9Zs2Zu8wPMnTs3w/nFk6Yn/73Hm0mIiIhcULYGSwcFBREdHZ1metmyZYmLi8txUukpX748AQEBhIeHu00PDw+nXr166S5TqVKldOevVKlShs9TtGhRihUr5rrvcDhykHVh9iuQBFwLXIGuSi8iIvlRtnqEli1bxoMPPui6b2b4+fnx4osvsnjxYo8l5w2DBw8mMjLSFef3eklmRQArk2938mYiIiIiGcpWj9CLL77IwoULuf766ylatCgffPABV111FWXLlqVFixaezhGAiIgIEhMTqVixotv0ihUrcuTIkXSXOXLkSJbmB3j33Xf5+OOPXfcdDoeKoWybDtyCc/fYKO+mIiIiko5s9Qht2bKFOnXqsHz5cqZPn05QUBC//PIL11xzDf/884+ncwQgISGBdevW0apVK9c0Pz8/WrVqxapVq9JdZtWqVW7zA7Rp0ybD+QHi4+OJiopyC8mulHFCLYHS3kxEREQkQ14f2Z3ZuO+++ywmJsYefPBBq1evnn355Zd24sQJq1ChgoHzaLZ33nnHNX+zZs0sPj7enn/+eatbt64NHTpUh8/nefxtYAb/yQe5KBQKhaKwRGa339naNQZQunRpbrzxRipUqIC/v3vH0nfffZfdZi9o8uTJXHbZZbzxxhtUqlSJDRs20L59e44ePQpAtWrVOHfunGv+VatW0bNnT9566y3eeecddu3axT333MOWLVtyJT9Jz3TgKpy7xyZ4NxUREZHz+OGsiLLk7rvv5ocffqBkyZJERka6XV/MzChXrpwnc/Qqh8NBZGQkpUqV0m6ybLkRWA1EAeWBeO+mIyIihUJmt9/ZGiP00UcfMW7cOEqWLMmll15K2bJlXVGQiiDxhDXAXpxHkF3m3VRERETOk61dY1WrVuWzzz4jJibG0/lIgWNAbSDR24mIiIikka0eoblz53L99dd7OhcpsFQEiYhI/pStHqFZs2YxbNgwGjRowObNm0lISHB7fObMmR5JTgqaKjjPNh1+sRlFRETyRLYGSyclJWX4mJkREJDtg9HyHQ2W9pR3gMHA28DLXs5FREQKusxuv7NVsRQpUiTbiUlh9TdwDud1x0RERPKHLI0RmjVrFqVKlXLdHzhwIKVLl3bdL1u2rM7RIxmYhnPX2ENezkNERORfWSqE2rVr53Zl9pdeeomyZcu67gcEBFC3bl3PZScFSDQaGyQiIvlNlgohPz+/C94XyZwgbycgIiICZPPweZHsKQbMByIAnXhTRES8L0uFkJm5XU4jZZpI5sThLICKA3d7ORcREZEsHjXm5+fHN998Q1xcHADFixfnyy+/5OzZswBu44dE0jcNuAboDIz3bioiIlLoZek8QuPGjcvUfA8//HB288l3dB4hT2sMbMA5eLo8oMu0iIiI52V2+52tEyoWJiqEckMocCXQCdBZyEVExPNy9erzIjkzI/lvZ69mISIiokJIvGBa8t+OaBUUERFv0lZIvGAZcBKoADTzci4iIlKYqRASL0gEZiXf1u4xERHxHhVC4iXTk//e480kRESkkFMhJF4yB+cJFmsD9b2ci4iIFFYqhMRLzgALk29r95iIiHiHCiHxouk4C6KS3k5EREQKqSxdYkPEs77DeZmNOG8nIiIihZQKIfEiXV5DRES8S7vGJJ+o5O0ERESkEFIhJF5WFtgK7EVjhUREJK+pEBIvO4FzD60/cJ2XcxERkcJGY4QkH+iO84r0kd5OREREChkVQpIPbPR2AiIiUkhp15jkM37eTkBERAoRFUKST9wJrAY+9nYiIiJSiKgQknwiALgR6OLtREREpBBRIST5xHwgGggGGns5FxERKSxUCEk+EQPMS76ti7CKiEjeUCEk+cj05L8qhEREJG+oEJJ85FcgCbgWqOblXEREpDBQIST5SASwMvl2J28mIiIihYRPFELBwcGMGTOGf/75h+joaHbv3s1rr71GYGDgBZdbvHgxZuYWX3zxRR5lLdkzLfmvdo+JiEju84kzS9erVw9/f38ef/xxdu/eTcOGDRk9ejRBQUEMGDDggst+/fXXvPrqq6770dHRuZ2u5Mh04COgJVAGOOXNZEREpBAwX4wXXnjB9uzZc8F5Fi9ebMOHD8/R8zgcDjMzczgcXn/NhSf+NjCDB/JBLgqFQqHwxcjs9tsndo2lp3Tp0pw4ceKi891///0cO3aMzZs3884773DJJZfkQXaSMz8n//0YqO3NREREpIDziV1j56tZsyZ9+/blhRdeuOB8P/74I/v27ePQoUM0atSI999/n7p163LvvfdmuEzRokUpVqyY677D4fBY3pJZH+C85MYNOI8kawgkeDUjEREpuLzWbfXuu+/axdStW9dtmSpVqtiuXbts9OjRWX6+22+/3czMatSokeE8Q4cOTTcP7RrL67jMYKPB3fkgF4VCoVD4WmR215hf8g2vKF++POXKlbvgPP/88w8JCc7egMqVK7NkyRL++OMPevfujVnWUi9RogRnz56lXbt2zJs3L9150usRCgsLo1SpUkRFRWXp+SSn/IFz3k5CRER8kMPhIDIy8qLbb6/uGouIiCAiIiJT81apUoXFixezbt06+vTpk+UiCKBJkyYAHD58OMN54uPjiY+Pz3LbkhtSF0FXAg8Br3snFRERKZB8YrB0lSpVWLJkCfv37+eFF17gsssuo2LFilSsWNFtnm3btnHDDTcAUKNGDV5++WWuvfZagoOD6dixI99++y2///47mzdv9tZLkWwpASwHXgOe824qIiJSoPjEYOk2bdpQu3ZtateuTVhYmNtjfn5+AAQGBlKvXj1KlCgBOHt2WrduzbPPPktQUBAHDhxgypQpvPXWW3mev+RUNPAG8CQw0cu5iIhIQeLVMUK+ILP7GCUvBKKjx0REJDMyu/32iV1jIk6pi6AewHXeSkRERAoIFULig+7FuYtsFlDdy7mIiIgvUyEkPmgusB6oCMwByns3HRER8VkqhMQHnQHuAvYCdYCZgC6dIiIiWadCSHzUEaA9cBxoCkwAing1I6e7gc3AEqCod1MREZGLUiEkPmwH0AmIAToDI7yYSy2c10WbifPaaC2B/l7MR0REMkOFkPi4lcD9OM9C/SQwOI+fvwTwNvA3zt118cC05MdeBoLzOB8REckKFUJSAEwF+iXffgd4II+e9z5gO/ASUAyYjbM3qAvOXWMlgOF5lIuIiGSHCiEpIEYCHyTfHgu0yeXnC8R5tusrgH9w7qK7E9iV/Pj/cJ73qAvQIZdzERGR7FIhJAXIIOBHnEXKFKCJh9svxb9XpUkAngZeAa7COTYota3AJ8nz1fNwHiIi4ikqhKQAMaAPsAhwALd7sO3uwE6gb6ppC4C3gNgMlnkDaIx2j4mI5F8qhKSAice5O+o+PFuAOHCewLFHFpY5A2zzYA4iIuJpKoSkAIoEfkp1/xKgeBbbKAfckOp+CNAbuCWbOTUG3szmsiIikltUCEkBVx7nrrIfyNzqXgR4CudusCk4j/wC52638bhf+DWzygGrcB5Of3c2lhcRkdwScPFZRHxZHeAaoDZQA9h9gXlb4Dz6rEny/f1AZWBPDnM4DnyK8wKxf+WwLRER8SQVQlLAreTf8/1kVARVxnnofa/k+yeBIcDXQJKH8ngJZ6+SiIjkJyqEpBCYcd79IOAszsPsnwGG4hwMfQ4Yg7MIivBwDucXQUVxDuwWERFv0hghKWRaAaHA88BG4EOcRdAfwI3A43i+CEqtEs5zHf2Si88hIiKZpR4hKWR6A5cBHyXfDwcGAt+SN7uuSgH34uwR6kTa3ioREclL6hGSQuYRnCdCTMR55ue6OI8Gy6vxOzuBYcm3P8V5aL+IiHiLCiEpZOKAtkAZ4DngtBdyeAfYB1yJcxC1iIh4iwohKYQM52Bpb4kGnk2+PQDnof0iIuINKoREvGIaMBsoBozwbioiIoWYCiERr3kG5666djivjyYiInlNhZCI1+zGeSJHcA7cLpHxrCIikitUCIl41bs4z2tUDee1yEREJC+pEBLxqhigX/Lt/jgP5xcRkbyiQkjE62YCv+I8yaIGTouI5CUVQiL5Qj8gFmcPUZCXcxERKTx0iQ2RfOEfoCGwx9uJiIgUKuoREsk3VASJiOQ1FUIi+c5lwBiggbcTEREp8LRrTCTf+RjohfNaZK29m4qISAGnQkgk33kZZxE0xMt5iIgUfCqERPKdfcAt3k5CRKRQ0BghkXyvtLcTEBEpsFQIieRbfsBrwEHgKu+mIiJSQPlMIRQaGoqZucXAgQMvuEyxYsUYOXIkERERREVF8fPPP1OhQoU8ylgkpwznuYVKAqO8nIuISMHkM4UQwCuvvEKlSpVcMWLEhS9HMHz4cDp27Ej37t1p2bIlVapU4ZdffsmjbEU84TkgGmgJ3O/lXERECibzhQgNDbV+/fplev5SpUpZXFyc3Xvvva5pdevWNTOzm266KdPtOBwOMzNzOBxefw8UhTUGGZjBYYNS+SAfhUKhyP+R2e23T/UIDRo0iIiICNavX88LL7xAkSJFMpz3uuuuo2jRoixYsMA1bceOHezbt49mzZrlRboiHvIxsAOoBLzu5VxERAoWnzl8/rPPPmP9+vWcOHGC5s2b8+6771K5cmX69++f7vyVKlUiLi6O06dPu00PDw+nUqVKGT5P0aJFKVasmOu+w+HwzAsQybZ44GlgPtAXCAE2eTUjEZGCxGvdVu+++65dTN26ddNdtk+fPhYfH29FixZN9/H//Oc/Fhsbm2b66tWr7b333sswp6FDh6abh3aNKbwfkwzMYFk+yEWhUCjyd2R215hf8g2vKF++POXKlbvgPP/88w8JCQlppjdo0IAtW7ZQt25ddu7cmebx22+/nUWLFlGmTBm3XqG9e/fyySef8Mknn6T7fOn1CIWFhVGqVCmioqIy+cpEckNVYDvOo8gextkzJCIi6XE4HERGRl50++3VXWMRERFERERka9kmTZqQlJTE0aNH03183bp1xMfH06pVK9eRYnXq1CE4OJhVq1Zl2G58fDzx8fHZykkkd4XhHCM0DPgSOAlM82ZCIiIFgte7ry4WTZs2tX79+lmjRo2sevXq1rNnTwsPD7dvvvnGNU+VKlVs27ZtdsMNN7imff7557Z371677bbb7Nprr7UVK1bYihUrcqVrTaHImyhiMMHADBIM/pMPclIoFIr8F1nYfns/2YvFNddcY6tWrbKTJ09adHS0bdmyxQYNGuQ2Pig4ONjMzFq2bOmaVqxYMRs5cqQdP37czpw5Y1OmTLGKFSvm1hupUORR+BuEGJjBIYOgfJCTQqFQ5K/wiTFCviCz+xhF8pYf8B7wPbDZy7mIiOQ/PjFGSESyy4DzLzFzBXDAC7mIiPgunzqhoohk5GZgG/CytxMREfEpKoRECoSbgCCgOZDxGddFRMSddo2JFAgfAfuBmUCSl3MREfEd6hESKTB+AmJT3e+Oc1C1iIhkRIWQSIH0FjAZ+AbtKhMRyZgKIZECaTOQCDwITAACvZuOiEg+pUJIpECaBNwLxOHcRTYFKHbBJURECiMVQiIF1gygMxADdMQ5kLqEVzMSEclvVAiJFGhzgTuBM0AbYDbOq9eLiAioEBIpBJYAbYHTwK3AfKCMF/MREck/VAiJFAqrgDuA40BTYBFQ3qsZiYjkByqERAqN9cBtQDhwDc6eokpezEdExPtUCIkUKn/j3D12ELgKWIBOMC8ihZkKIZFCZyfOYmg38BrO8w2JiBRO+ikoUiiF4uwRivd2IiIiXqUeIZFCK3URdDnOAdUNc9BeUaB4qvtXAC8C/c6bbwjwDtAcfQWJiLf5AebtJPIzh8NBZGQkpUqVIioqytvpiOSSScB9OIuh5qmmlwIqAhUy8bcM8CzwafKyNwF/AHuB6snT/HCOT6qSfD8C57mNfsV5zqPTnn1ZIlJoZXb7rV1jIgI8jvM30Quppv2Nc/dZVlRIdXsfMB7Yn2qaf/Jz3A10wHkI/wPJkQgsw1kU/YpzLJOISO5Sj9BFqEdICq/lQAsgEuch90cz8fdUFtovgrP36e7kaHDe47v4tyhaBiRk72WISKGU2e23CqGLUCEkhVc54CwQm0fPVwO4C2dRdBvOMUcpqgEHkm8XAZLyKCcR8VWZ3X5rpKKIZOA4eVcEAfwDjADa4SzCugBjgXn8WwQBTMU5lqlZHuYmIgWVxgiJSD50BpiWHKkVA1oBJXDusktxI3AZsJC8Ld5ExNepR0hEfEgcUBt4ENiSavqzOMcSHcdZPN0POPI4NxHxRSqERMTHHAK+O29aKM6j1EoAnYHvgWPAdKAXztMAiIikpUJIRAqAIcCVQGPgDWAbzt1onXAWTUdRUSQi6VEhJCIFyCZgKM5D8RsCrwNbSVsUzcC5i01ECjsVQiJSQG3BeVHZq5IjdVF0J+7nPKoDlM7b9EQkX1AhJCKFwFbci6JHcI4hSvE1zp6iLnmemYh4lw6fF5FCZmtypCgKXJr8d22q6XfgvBjtdHQNNJGCSz1CIlLIxeMcZF0D9xM3Po/zWmlHgZk4D9nX7jORgkY9QiIigPMQ/NSWA8E4B12nXA8tHmdv0rZUsRXnddF0LTQRX6RrjV2ErjUmUtjVB7onR8MM5kkE9gD9gVnJ0y7BeV20M7mdoIikQ9caExHxiG04z010NVAd6Ai8CIQAf+AcPxQA1MV55usUXYEo4Kfz2msKVMjdlEUk07RrTEQk0/Ymx6/nTa+Ms+co9WDr4OS/EammlQBW4PwNegL3XWzbgM3AQQ/nLCIXol1jF6FdYyKSfWVwnrcoPPl+DWA+zrNgZ9Qhv4V/Lzi7Dn1Fi2RPZrff6hESEck1p867/w9QE+f4oTo4e5FSRz3+PdfRECAM5+H7LwMn8yRjkcJGhZCISJ6LATYmR2plgA7APcl/qwI9gX6p5mmMs6BSD7WIJ/jEYOmWLVtiZunG9ddfn+FyixcvTjP/F198kYeZi4hkxSlgAtADKI+zGOqP86i0FFNxjjtqkdfJpaMSzhNP/g8YAbwJBHo1I5Gs8okeoZUrV1KpUiW3aW+++SatWrVi7dq1GSzl9PXXX/Pqq6+67kdHR+dKjiIinhUPzDlvWvnk6UnAX6mmP4zzSLRpwPZcyOVynBeyPT8uPW++w8Arqe4PTP77I+4nqxTJP3yiEEpISCA8PNx1PyAggM6dOzNixIiLLhsdHe22rIiI74rAOY6oCpD6R10/oBHwLrAD57iiaTgP78/sYGs/nOc9Sul9agW8jbPgcWSwTBLO8ydtxVmAHTrv8Wdx9hot5d9CqAXQBFiDc9dgHCLeZr4WXbt2tcTERKtateoF51u8eLEdPXrUjh07Zps3b7Z33nnHLrnkkgsuU7RoUXM4HK6oUqWKmZk5HA6vv26FQqFIPx41mGUQa2Cp4rDBVwZ3GhRLnreIQY3zlv/S4KxBr1TTbk/VTrzB3waTDV4zuM+gYao204siBv0NJhqk/t4dkardOIM/DUYZPGTQwMA/H7yfioIQDocjs9tv7yeb1Zg1a5bNmjXrovM9+uij1rZtW2vYsKH17NnTDhw4YFOmTLngMkOHDrX0qBBSKBT5P0oadDP43uCk4VYURRlstn+LpaBUy41MnvZOqmmlDboa1DMI8GCODxv8anD0vPxSItJgkcH7BvcaXJEP3leFL4ZPFELvvvtuukVHanXr1nVbpmrVqpaYmGhdu3bN8vPdfvvtZmZWo8b5v4b+DfUIKRSKghGBBq3NWeQcMNyKjTPm7H1JmfdKg1rm7MXJyxyDDbobDDNYkpxXesXRqFTLOAx6GtySD95jRX6OzBZCXj2hYvny5SlXrtwF5/nnn39ISPj3YoYvv/wyffv2pWrVqiQmJl5gybRKlCjB2bNnadeuHfPmzcvUMjqhoogUDNfiHFC9DdiPF7/6L6AIzvMp3QDcmPy3Ec6xRp8nz3MdzjN4H8J5eoEUY3GOnTqI8/xLYefdPp7r2Uv+4hMnVIyIiCAiIuLiM6bSp08fvv322ywXQQBNmjQB4PDhw1leVkTEt633dgKZkAT8nRwhydOK4yyQUpwDFuK8RElqtwK1LtB2LP8WRSlF0kxgWY6zFt/n9e6rzMYdd9yR7u4ywKpUqWLbtm2zG264wQCrUaOGvfzyy3bttddacHCwdezY0Xbv3m1LlizJla41hUKhUHgzbjfobTDE4AuDGQbrDMKNdHe3mcFzqZavaRBqMDofvBaFJyKz22+fOHw+xX//+19WrFjBjh070jwWGBhIvXr1KFGiBADx8fG0bt2aZ599lqCgIA4cOMCUKVN466238jptERHJdYsv8FhRnBfGrYrznEhVk+OPVPPcivMacPXOW/ZDnIf+L8V5uP85z6Qr+YYuunoRGiMkIlIYBAHNkm8vSP5bGucuuJSLMEQCK3EWRctwngvJG+dBKo7zbN41gKf5dzNeHOcuQIHMb79VCF2ECiERkcKqDPA4cAtwM87CKLVY4E+cRdFSnEXSmRw+ZxEgGKidHHWS/24GXkw1TwzOy5lcgXO8E8DXOK9F9xEwBeeYq8JLhZCHqBASERFnr9DVOHeh3ZIclc6bJwnYANwFXOiKBn44j3BLKXJS/62Bc1fe+f7g3x4rgOE4e6g+T36uS3AOAk+57Mle4BOcR9PltDjzTSqEPESFkIiIpK8W7oVRTZwXzi3Hv2OJ3sR52oKByY8BvMe/12FLTyywKzl2Jv/dAqy+SD7lgadw7jarkDztFM6eos9wFkqFhwohD1EhJCIimVMFZ3G0NNW0f4DqOHetrUie9hgwEgjl30In9d+D5GzTXBx4AHiefwd/JwATce4225iDtn2HCiEPUSEkIiLZdzfO3qJf+LdHpxjO3WhZPx9e1vgBdwIvALelmr4AZ0E0J5ef37tUCHmICiEREfF91+HsIbqPf8+lPB7o7a2Ecl1mt9/+GT4iIiIiBcQ64H6cg7E/wjnQelqqxx1A2bxPKx9QISQiIlJoHMC5q+wKYEaq6X2TH+vvjaS8SoWQiIhIoROJ+1mymwMlgCOpphWOEsGnLrEhIiIiueFunKcCWJVqWl/gP8CnwD7+vTzXOdJesitlWjj/FlOBOI+iS8J5NFyKyjjPe5Sy7GG8c4ZuJxVCIiIigvth/wBP4Dz8/scstPEeMDj5djVgKxAFlEo1TwjQLtX91KcWyHsqhERERCQdLXGeoPFenIf8++HcXeaXKvzPux2ZavlzwHHSntk6BmdxlLKsdy8FosPnL0KHz4uIiPgeHT4vIiIichEqhERERKTQUiEkIiIihZYKIRERESm0VAiJiIhIoaVCSERERAotFUIiIiJSaKkQEhERkUJLhZCIiIgUWiqEREREpNBSISQiIiKFlgohERERKbRUCImIiEihpUJIRERECq0AbyfgKxwOh7dTEBERkUzK7HZbhdBFpLyRYWFhXs5EREREssrhcBAVFZXh436A5V06vqlKlSoXfBOzw+FwEBYWRtWqVT3ettr3Xtu+3r4v5+7r7fty7r7evi/n7uvt50Xuhw4duuA86hHKhIu9iTkRFRWVK/98te/dtn29fV/O3dfb9+Xcfb19X87d19vPrbYz06YGS4uIiEihpUJIRERECi0VQl4SFxfHa6+9RlxcnNrP4/Z9Offcbt+Xc/f19n05d19v35dz9/X2czv3zNBgaRERESm01CMkIiIihZYKIRERESm0VAiJiIhIoaVCSERERAotFUJ57JZbbmHGjBmEhYVhZnTu3Nmj7Q8aNIg///yTyMhIwsPDmTp1KnXq1PFI20888QQbN27k9OnTnD59mpUrV9K+fXuPtJ2egQMHYmYMHz7cI+0NHToUM3OLbdu2eaTtFFWqVOG7774jIiKC6OhoNm3axHXXXZfjdkNDQ9PkbmaMHDnSA1mDv78/b7zxBv/88w/R0dHs3r2bl19+2SNtpyhZsiTDhw9n7969REdHs2LFCq6//vpstZWZz9Hrr7/OoUOHiI6OZv78+dSqVcsjbXfp0oW5c+cSERGBmdG4cWOP5R4QEMB7773Hpk2bOHPmDGFhYYwfP57KlSt7pH1wfg62bdvGmTNnOHHiBPPnz+fGG2/0WPupffHFF5gZ/fr180jbISEhaT4Ds2fP9mju9erVY/r06Zw6dYozZ87w559/csUVV3ik/fQ+w2bGCy+8kOO2g4KCGDFiBAcOHCA6OpotW7bw+OOPZyrvzLRfoUIFQkJCCAsL4+zZs8yePTvTn6nMbJeKFSvGyJEjiYiIICoqip9//pkKFSpkOv+cUCGUx4KCgti4cSP/+9//cqX9li1bMmrUKJo2bUqbNm0IDAxk3rx5lChRIsdtHzx4kEGDBnHddddx/fXXs2jRIqZPn06DBg08kLm766+/nscff5yNGzd6tN2///6bSpUqueLmm2/2WNtlypRhxYoVJCQk0KFDBxo0aED//v05efJkjtu+4YYb3PJu3bo1AD/99FOO2wZn0fnkk0/y9NNPU79+fQYOHMiLL75I3759PdI+wJgxY2jTpg0PPPAAV199NfPmzWPBggVUqVIly21d7HP04osv8swzz/DEE09w0003cfbsWebOnUuxYsVy3HZQUBDLly9n4MCBWc77Yu2XKFGCa6+9ljfffJNrr72Wrl27UrduXWbMmOGR9gF27tzJ008/zdVXX83NN9/M3r17mTdvHuXLl/dI+ynuuecemjZtmqXrNGam7dmzZ7t9Fv7zn/94rP0aNWqwfPlytm/fzm233UajRo148803iY2N9Uj7qfOuVKkSffr04dy5c0yZMiXHbX/88ce0b9+eXr16Ub9+fT755BNGjhxJx44dPZL7tGnTqFGjBp07d+aaa65h3759LFiwIFPblsxsl4YPH07Hjh3p3r07LVu2pEqVKvzyyy+Zyt0TTOGdMDPr3Llzrj5H+fLlzczslltuyZX2jx8/bg8//LBH2wwKCrIdO3ZYq1atbPHixTZ8+HCPtDt06FD766+/cu29fvfdd23p0qV5su4MHz7cdu3a5bH2Zs6caWPGjHGb9vPPP9t3333nkfaLFy9uCQkJduedd7pNX7t2rb355ps5aju9z9GhQ4esf//+rvulSpWymJgY69GjR47bTong4GAzM2vcuLFHcz8/rr/+ejMzu+KKK3KlfYfDYWZmd9xxh8far1Klih04cMAaNGhgoaGh1q9fP4+0HRISYlOnTvXIOple+xMmTLBvv/0219o/P6ZOnWoLFizwSNubN2+2l19+2W1adj9f57dfu3ZtMzNr0KCBa5qfn5+Fh4fbf//73yy3f/52qVSpUhYXF2f33nuva566deuamdlNN93kkf/HhUI9QgVc6dKlAThx4oRH2/X396dHjx4EBQWxatUqj7Y9atQoZs2axcKFCz3aLkDt2rUJCwtjz549fP/995nu8s6MTp06sXbtWiZPnkx4eDjr16/nkUce8Vj7KQIDA+nVqxfjxo3zWJsrV66kVatW1K5dG4BGjRpx8803Z2m3w4UEBAQQEBCQ5pd1TEyMR3vlAKpXr07lypVZsGCBa1pkZCSrV6+mWbNmHn2uvFC6dGnOnTvHqVOnPN52YGAgjz32GKdOnfJY76ufnx/fffcdw4YNY+vWrR5pM7XbbruN8PBwtm/fzueff07ZsmU90q6fnx933XUXO3fuZM6cOYSHh/PHH394fPhCigoVKnDXXXcxduxYj7S3cuVKOnXq5Ophve2226hTpw7z5s3LcdspPampP79mRlxcXLY+v+dvl6677jqKFi3q9pndsWMH+/bty7PPbK5XW4r0I7d7hPz8/GzmzJm2bNkyj7XZsGFDi4qKsoSEBDt58qR16NDBozn36NHDNm3aZMWKFTPAoz1C7du3t27dutnVV19tbdu2tRUrVtjevXutZMmSHmk/JibGYmJi7O2337YmTZrYo48+atHR0fbggw969D3q3r27JSQkWOXKlT26rrz77ruWlJRk8fHxlpSUZIMGDfJo3itWrLDFixdb5cqVzd/f3+6//35LTEy07du356jd8z9HzZo1MzOzSpUquc03adIkmzhxYo7aTh150SNUrFgxW7t2rX3//fcebf+uu+6yqKgoS0pKsoMHD9r111/vsfYHDRpkc+fOdd33ZI9Qjx49rGPHjtawYUPr3LmzbdmyxVavXm3+/v45br9ixYpmZnbmzBl79tlnrXHjxjZw4EBLSkqyW2+91eP/2wEDBtjx48dd33U5bbto0aL2zTffmJlZfHy8xcbG2gMPPOCR/2tAQIDt3bvXJk2aZGXKlLHAwEB78cUXzcxszpw5WWo7ve3Sf/7zH4uNjU0z7+rVq+29997L1mvISujq8wXYqFGjaNiwoUd/ce/YsYMmTZpQunRpunXrxvjx42nZsqVHBh1ffvnlfPrpp7Rp0yZXTrc+Z84c1+3NmzezevVq9u3bx3333eeR3hV/f3/Wrl3LkCFDANiwYQMNGzbkiSee4Ntvv81x+yn++9//Mnv2bA4fPuyxNu+77z7uv/9+evbsyZYtW2jSpAmffPIJhw4d8ljuDzzwAOPGjePQoUMkJiayfv16JkyY4JHB5AVRQEAAkydPxs/PjyeffNKjbS9evJgmTZpQvnx5Hn30USZPnsxNN93EsWPHctTutddeS79+/bj22ms9lKm7SZMmuW7//fffbNq0iX/++YfbbruNRYsW5ahtf3/nDpLp06fzySefALBx40aaN2/OE088wdKlS3PU/vkefvhhfvjhB4991/Xt25emTZvSsWNH9u3bx6233sqoUaM4dOhQjnvXExMT6dq1K2PHjuXkyZMkJiayYMECfvvtN/z8/LLUVm5slzwh16stRfqRmz1CI0aMsP3799uVV16Zq69h/vz59uWXX3qkrc6dO5uZWUJCgivMzJKSkiwhISFbv/ouFn/++ae98847Hmlr7969Nnr0aLdpTzzxhB08eNBj+VarVs0SExOtU6dOHn0f9u/fb0899ZTbtCFDhti2bds8/p6XKFHC1VszceJE+/XXX3PU3vmfo+rVq6fbU7NkyRL75JNPctR26sjNHqGAgAD75ZdfbMOGDVa2bFmPt39+7Ny5M1s9gOe3369fP9fnNfVnODEx0UJDQ3Ml96NHj9pjjz2W49wDAwMtPj7ehgwZ4jbfe++9Z8uXL/foe3/zzTebmVmjRo088n8tXry4xcXFpRmDN3r0aJs9e7ZHcy9VqpSVL1/eAPvjjz9s5MiRmW43o+3S7bffbmZmpUuXdpu+d+9ee/bZZ7P1HmUlNEaoABoxYgRdunThjjvuYO/evbn6XP7+/pk6EiczFi5cSMOGDWnSpIkr1qxZww8//ECTJk04d+6cR54nRVBQEDVr1vRYz8qKFSuoW7eu27Q6deqwb98+j7QP0KdPH44ePcqsWbM81iY4j1Y6//1NSkpy/Ur2pOjoaI4cOUKZMmVo164d06dP92j7oaGhHD58mFatWrmmORwObrrpJo+PZ8sNKT1BtWvXpnXr1h4f35ceT32Ov/vuOxo1auT2GQ4LC2PYsGG0a9fOA5m6q1q1KuXKlfPIZzghIYE1a9bk+mcYnL26a9euZdOmTR5pLzAwkKJFi+bJZzgyMpKIiAhq1arF9ddfn+nP74W2S+vWrSM+Pt7tM1unTh2Cg4Pz5DOrXWN5LCgoyO3cC9WrV6dx48acOHGCAwcO5Lj9UaNG0bNnTzp37kxUVBQVK1YE4PTp05k+BDQj77zzDrNnz2b//v04HA569uzJbbfd5rEvuDNnzrBlyxa3aWfPnuX48eNppmfHsGHDmDlzJvv27aNKlSq8/vrrJCUlMWHChBy3Dc7DP1euXMngwYOZPHkyN954I4899hiPPfaYR9r38/OjT58+jB8/nqSkJI+0mWLmzJkMGTKE/fv3s2XLFq655hqef/55jw7Ibtu2LX5+fuzYsYNatWoxbNgwtm/fTkhISJbbutjn6JNPPuHll19m165dhIaG8uabb3Lo0CGmTZuW47YvvfRSqlWr5hqUmrLhPHLkCOHh4Tlq//Dhw/z8889ce+213H333RQpUsT1GT5x4gQJCQk5av/48eMMGTKEGTNmcPjwYcqXL8///vc/qlatmulTMVzs/Tm/cEtISODIkSPs3LkzR22fOHGCoUOHMmXKFI4cOULNmjX54IMP2L17N3PnzvVI7sOGDWPSpEksXbqUxYsX0759ezp27Mhtt93mkfbBWZR3796d/v37Z6rNzLa9ZMkShg0bRkxMDPv27aNly5Y8+OCDPP/88x5pv1u3bhw7doz9+/dz9dVX8+mnnzJt2jTmz59/0bYvtl2KjIxk7NixfPzxx5w4cYLIyEhGjBjBypUrWb16dZbep+zK9W4nxb/RsmVLS09ISIhH2s/IQw89lOO2x4wZY6GhoRYbG2vh4eE2f/58a926da6+X54cLD1hwgQLCwuz2NhYO3DggE2YMMFq1Kjh0Xzvuusu27Rpk8XExNjWrVvtkUce8Vjbbdq0MTOz2rVre/x9LlmypA0fPtz27t1r0dHRtnv3bnvzzTctMDDQY8/RvXt32717t8XGxtqhQ4dsxIgRVqpUqWy1lZnP0euvv26HDx+2mJgYmz9/fqbft4u1/dBDD6X7+NChQ3PcfsrutvS0bNkyx+0XK1bMpkyZYgcPHrTY2FgLCwuzadOmZWmwdFa/w7IyWPpCbRcvXtzmzJlj4eHhFhcXZ6GhofbVV19ZhQoVPJp7nz59bOfOnRYdHW1//fVXlnZDZ6b9Rx991M6ePZvldf9ibVesWNHGjRtnBw8etOjoaNu2bZs999xzHmu/b9++tn//fouLi7O9e/faG2+8kenvh4yk3i4VK1bMRo4cacePH7czZ87YlClTrGLFitn6fshq+CXfEBERESl0NEZIRERECi0VQiIiIlJoqRASERGRQkuFkIiIiBRaKoRERESk0FIhJCIiIoWWCiEREREptFQIiUgaixcvZvjw4d5OwyeEhIQwdepU131fee/MjM6dO3s7DRGvUyEk4qPO3wAD3HvvvcTExGT6tPrieV27duWVV17xdhoXValSJWbPnu3tNES8TtcaEykg/vvf/zJq1CieeOIJvvnmm3TnCQwMzNT1qiT7Tp486e0UMiUz10UTKQzUIyRSAAwYMIARI0bwf//3f25F0OLFixkxYgTDhw/n2LFjzJ07l7FjxzJz5ky35QMCAggPD+fhhx9Ot/0yZcowfvx4Tpw4wdmzZ/ntt99cF2h0OBxER0fTvn17t2XuueceIiMjueSSS9Jt895772XTpk1ER0cTERHB/PnzKVGiBPBvb9err77K0aNHOX36NF988QWBgYGu5du1a8eyZcs4efIkERERzJw5kxo1arg9R9WqVfnxxx85fvw4Z86cYc2aNdx4442uxzt16sS6deuIiYlhz549vPrqqxQpUiTD99nf35+PPvrI9Zzvv/8+fn5+bvOcv2ssNDSUIUOGMH78eKKioti7dy8dO3akfPnyTJs2jaioKDZu3Mh1113n1k6LFi1YunQp0dHR7N+/n08//dT1/qS0O3jwYMaOHUtkZCT79u3j0UcfdT0eGBjIiBEjOHToEDExMezdu5dBgwa5Hj9/11jDhg1ZuHCh6//x1VdfERQU5Ho85X/Sv39/Dh06REREBCNHjiQgQL+nxfflyUXNFAqFZyMkJMSmTp1q7733nkVGRtodd9yRZp7FixdbZGSkvf/++1anTh2rU6eONWvWzBISEqxSpUqu+e655x6LioqyoKAg13KpL3Y7bdo027Jli918883WqFEjmz17tu3cudMCAgIMsMmTJ9u3337r9tw//fRTmmkpUalSJYuPj7dnn33WgoODrWHDhvbkk0+6nj8kJMQiIyNtwoQJ1qBBA7vzzjstPDzc3nrrLVcbXbt2tS5duljNmjWtcePGNn36dNu4caP5+fkZYEFBQbZ79277/fffrUWLFlazZk3r3r27NW3a1AC7+eab7dSpU/bggw9a9erVrXXr1vbPP//Yq6++muF7PmDAADt+/Lh16dLF6tWrZ6NHj7bTp0/b1KlT3d7z1O9daGioRURE2GOPPWa1atWyUaNG2alTp+y3336zbt26We3ate2XX36xLVu2uJapUaOGRUVFWb9+/axWrVrWrFkzW7dunY0bNy5Nu08++aTVrFnTBg4caImJiVanTh0DrH///rZv3z67+eabrVq1ataiRQv7v//7P9fyZmadO3c2wEqUKGFhYWH2888/21VXXWW333677dmzx+1ioSEhIXbq1Cn7/PPPrW7dunbXXXfZmTNnPHphYYXCS+H1BBQKRTYiJCTEYmNjzczs9ttvT3eexYsX27p169JM//vvv23AgAGu+9OnT3fbyKbemNeqVcvMzJo1a+Z6vGzZsnb27Fnr1q2bAda5c2eLjIy0Sy65xABzOBwWHR1t7dq1Szeva665xszMqlWrluFri4iIcLUH2OOPP26RkZGuQuf8KFeunJmZXXXVVQbOq3yfPn3aLr300nTnnz9/vg0aNMht2v33329hYWEZvudhYWH2wgsvuO4XKVLE9u/ff9FCKHVBWLFiRTMze/31113TbrrpJjMz19W2R48ebV9++aXbc7do0cISExOtWLFi6bYL2JEjR+zxxx83wD799FNbsGBBhq8ldSH0yCOP2PHjx61EiRKuxzt06GCJiYmuq7uHhIRYaGio+fv7u+aZNGmSTZgwweufBYUiJ6FdYyI+bNOmTYSGhvL666+77cZIbd26dWmmjRkzhj59+gBQoUIFOnTowLhx49Jdvn79+iQkJLB69WrXtBMnTrBjxw7q168PwG+//UZCQgKdOnUCnLu9IiMjWbBgQbptbty4kQULFrB582YmT57MI488QpkyZdLMExMT47q/atUqHA4HV1xxBQC1atXixx9/ZM+ePZw+fZq9e/cCUK1aNQCaNGnCX3/9leGYncaNG/Pqq68SFRXlitGjR1OlSpV0d+eVKlWKKlWquL0PSUlJrF27Nt32U9u0aZPrdsrYnM2bN6eZVqFCBVduvXv3dstt7ty5FClShOrVq6fbLsCRI0dcbXzzzTc0adKEHTt28Omnn9KmTZsM86tfvz4bN24kOjraNW3FihUUKVKEunXruqZt2bKFc+fOue4fPnzY9XwivkqFkIgPCwsL47bbbqNq1arMmTOHkiVLppnn7NmzaaZ9++231KhRg6ZNm9KrVy9CQ0NZvnx5tvNISEjg559/pmfPngD07NmTSZMmkZSUlO78586do02bNnTo0IGtW7fSt29fduzYwZVXXpnp55w5cyZly5bl0Ucf5aabbuKmm24CoGjRogBuRVR6SpYsydChQ2nSpIkrrr76amrVqkVsbGym88iM9Aaop55mZoBzDFJKbl999ZVbbo0bN6ZWrVrs2bMnw3bNzNXGX3/9RfXq1XnllVe45JJLmDx5Mj/99JNHX0fq5xPxVVqDRXzc/v37admyJZUqVcqwGDrfiRMnmDZtGn369KF3796EhIRkOO+2bdsIDAx0FRoAZcuWpW7dumzdutU17YcffqB9+/Y0aNCAO+64gx9++OGieaxcuZLXXnuNa665hvj4eLp06eJ6rHHjxhQvXtx1v2nTpkRFRXHgwAHKli1LvXr1eOutt1i0aBHbt2/n0ksvdWt706ZNNGnSJM30FOvXr6du3brs2bMnTaQUJqlFRkZy6NAht/ehSJEiaQY5e8L69etp0KBBurll5ai/qKgoJk+ezGOPPUaPHj3o1q1buu/Htm3baNy4sdtg7BYtWpCUlMSOHTs88ppE8isVQiIFwMGDB7ntttuoUKECc+fOxeFwXHSZMWPG8NBDD1G/fn3Gjx+f4Xy7d+9m2rRpjB49mhYtWtCoUSO+//57wsLCmD59umu+pUuXcuTIEX744QdCQ0P5888/M2zzxhtvZPDgwVx33XVcccUVdO3alcsuu4xt27a55ilatChjx46lfv36dOjQgddff52RI0diZq6jth577DFq1qzJ7bffzscff+z2HBMmTODIkSNMmzaN5s2bU716dbp27UrTpk0BeOONN3jwwQd59dVXadCgAfXq1aNHjx68+eabGeb96aefMmjQIDp37kzdunX5/PPP0+zS84T333+f5s2bM2LECFdPUKdOnRgxYkSm23juuef4v//7P+rWrUvt2rXp3r07hw8f5tSpU2nm/eGHH4iNjWX8+PFcddVV3HbbbYwYMYLvvvuOo0ePevCVieQ/KoRECoiU3WTly5fPVDG0YMECDh8+zNy5czl8+PAF5+3Tpw/r1q3j119/ZdWqVfj5+XHnnXeSmJjoNt+ECRNo0qTJRXuDIiMjufXWW/ntt9/YuXMnb731Fv3792fOnDmueRYuXMiuXbtYunQpkyZNYsaMGbz22muAc5fM//3f/3Hdddfx999/M3z4cAYMGOD2HAkJCbRt25ajR4/y22+/sXnzZgYNGuTaXTdv3jzuvvtu2rZty5o1a/jjjz947rnn2LdvX4Z5f/TRR3z33XeMHz+eVatWERUVleaklp6wefNmWrZsSZ06dVi2bBl//fUXb7zxBocOHcp0G1FRUbz44ousXbuWNWvWcOWVV3LnnXem29sVExNDu3btKFu2LGvWrOHnn39m4cKFPP300558WSL5kh/OUdMiUsgEBQURFhZGnz59cmVjnhMhISGUKVPGbVeZiEhu0JmwRAoZPz8/ypcvT//+/Tl16hQzZszwdkoiIl6jQkikkKlWrRp79+7lwIED9O7dO8Mju0RECgPtGhMREZFCS4OlRUREpNBSISQiIiKFlgohERERKbRUCImIiEihpUJIRERECi0VQiIiIlJoqRASERGRQkuFkIiIiBRaKoRERESk0Pp/YMAZCsjx39sAAAAASUVORK5CYII=", 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", 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" ] From f36cca7a2649e97b2dc64fff303cbcb9d1562951 Mon Sep 17 00:00:00 2001 From: Mirko Amico Date: Thu, 28 Mar 2024 13:44:54 -0600 Subject: [PATCH 22/22] small imports cleanup --- docs/notebooks/krylov.ipynb | 6 ++---- 1 file changed, 2 insertions(+), 4 deletions(-) diff --git a/docs/notebooks/krylov.ipynb b/docs/notebooks/krylov.ipynb index 519933c..3b7133e 100644 --- a/docs/notebooks/krylov.ipynb +++ b/docs/notebooks/krylov.ipynb @@ -78,7 +78,6 @@ "metadata": {}, "outputs": [], "source": [ - "import math\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pylab as plt\n", @@ -92,7 +91,8 @@ "from qiskit.circuit.library import PauliEvolutionGate\n", "from qiskit.synthesis import SuzukiTrotter\n", "from qiskit.providers.fake_provider import Fake20QV1\n", - "from qiskit.primitives import StatevectorEstimator\n", + "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator\n", + "\n", "\n", "def solve_regularized_gen_eig(h: np.ndarray, s:np.ndarray, threshold: float, k: int =1, return_dimn: bool = False) -> Union[float, List[float]]:\n", " \"\"\"\n", @@ -715,8 +715,6 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit_ibm_runtime import QiskitRuntimeService, EstimatorV2 as Estimator\n", - " \n", "service = QiskitRuntimeService()\n", "backend = service.least_busy(operational=True, simulator=True)\n", "shots = 100000\n"