challenges/QOSF Monthly/July 2021.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# July 2021 Challenge: Quantum State Tomography\n",
    "\n",
    "[Quantum state tomography](https://en.wikipedia.org/wiki/Quantum_tomography) is the process of reconstructing an unknown quantum state by taking measurements in different bases, and using the result outcomes to estimate its probability amplitides. This is done under the assumption that the same state can be prepared or given to us repeatedly so the process can be performed enough times to build statistical significance. Resource [A] may be helpful as an introduction.\n",
    "\n",
    "For this challenge, your job is to write a program that performs state tomography for an input state, and also returns the [fidelity](https://en.wikipedia.org/wiki/Fidelity_of_quantum_states) of the predicted outcome with respect to the input quantum state. Resource [B] may be helpful to check your work against.\n",
    "\n",
    "**Level 1:** Implement a program to perform quantum state tomography for a 1-qubit state. Report the fidelity of the predicted state as function of the number of samples/shots [2].\n",
    "\n",
    "**Level 2:** Generalize the program to perform quantum state tomography on an n-qubit state. Report the fidelity of the predicted state as function of the number of samples/shots. Keep in mind that you might want to try this for a relatively small number of qubits when you decide to simulate your program. \n",
    "\n",
    "**Level 3:** Instead of trying to reconstructing the state through simple repeated measurements, consider implementing a program that uses variational approach to adjust the parameters of a quantum circuit to reconstruct the unknown state. **Hint**: Consider how using the [SWAP test](https://en.wikipedia.org/wiki/Swap_test) in different measurement bases can help acomplish this [1].\n",
    "\n",
    "**Resources**\n",
    "\n",
    "[A] Quantum state tomography as a numerical optimization problem. \n",
    "Niklas Rohling. https://www.youtube.com/watch?v=Wk6h6NyXkAg  \n",
    "[B] Qiskit Quantum Tomography Tutorial. https://qiskit.org/documentation/tutorials/noise/8_tomography.html  \n",
    "\n",
    "**References**\n",
    "\n",
    "[1] Variational Quantum Circuits for Quantum State Tomograph. Yong Liu, et. al. https://arxiv.org/pdf/1912.07286.pdf  \n",
    "[2] Quantum State Tomography of a Single Qubit: Comparison of Methods. Roman Schmied. https://arxiv.org/pdf/1407.4759.pdf  \n",
    "[3] Quantum State Tomography. J. B. Altepeter, et. al. http://research.physics.illinois.edu/QI/Photonics/tomography-files/tomo_chapter_2004.pdf  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import itertools\n",
    "from qiskit import *\n",
    "from qiskit.visualization import plot_histogram\n",
    "from sympy import Matrix\n",
    "from scipy.optimize import curve_fit, minimize\n",
    "from scipy.linalg import eig as eig_solver\n",
    "from scipy.linalg import sqrtm\n",
    "from IPython.display import clear_output\n",
    "\n",
    "# np.seterr(all=\"ignore\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Level 1\n",
    "We consider each combination of Pauli basis to measure each qubit, generally, this would yield $3^n$ measurements where $n$ is the number of qubits. Since we are working with a single qubit state, we will only perform three measurements. To implement these measurements, we use the circuits given [here](https://quantumcomputing.stackexchange.com/a/13611/16092).\n",
    "\n",
    "To use the measurements to construct the predicted density matrix, we first construct the $\\mu$ matrix detailed in [Maximum Likelihood, Minimum Effort](https://arxiv.org/abs/1106.5458) by John A. Smolin, Jay M. Gambetta, and Graeme Smith, and then perform the *Fast algorithm for Subproblem 1* outlined in the same paper."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [],
   "source": [
    "def one_qubit_tomography(input_state, samples):\n",
    "    \"\"\"\n",
    "    Performs quantum state tomography in a single qubit.\n",
    "    \n",
    "    Parameters:\n",
    "        input_state: np.array\n",
    "            1-qubit state for which we want to perform quantum state tomography\n",
    "        samples: int\n",
    "            Number of samples available of the input state\n",
    "    \n",
    "    Returns:\n",
    "        predicted_state: np.array\n",
    "            Density matrix of state predicted via quantum state tomography\n",
    "        fidelity: float\n",
    "            Fidelity of predicted state in respected to input state\n",
    "    \"\"\"\n",
    "    input_state = np.array(input_state)\n",
    "    \n",
    "    circuits = []\n",
    "    \n",
    "    # Z basis measurement\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.initialize(input_state, 0)\n",
    "    qc.measure_all()\n",
    "    circuits.append(qc)\n",
    "    \n",
    "    # X basis measurement\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.initialize(input_state, 0)\n",
    "    qc.h(0)\n",
    "    qc.measure_all()\n",
    "    circuits.append(qc)\n",
    "    \n",
    "    # Y basis measurement\n",
    "    qc = QuantumCircuit(1)\n",
    "    qc.initialize(input_state, 0)\n",
    "    qc.sdg(0)\n",
    "    qc.h(0)\n",
    "    qc.measure_all()\n",
    "    circuits.append(qc)\n",
    "    \n",
    "    # run circuits\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    job     = execute(circuits, backend, shots=samples)\n",
    "    counts  = job.result().get_counts()\n",
    "    \n",
    "    # get expectation values, ordered the same way as the circuits\n",
    "    expectation_vals = []\n",
    "    for count in counts:\n",
    "        m = (count.get('0', 0) - count.get('1', 0)) / samples\n",
    "        expectation_vals.append(m)\n",
    "    \n",
    "    # calculate µ matrix\n",
    "    Z  = np.array([[1, 0], [0, -1]])\n",
    "    X  = np.array([[0, 1], [1, 0]])\n",
    "    Y  = np.array([[0, -1j], [1j, 0]])\n",
    "    I  = np.array([[1, 0], [0, 1]])\n",
    "    mu = (I + expectation_vals[0] * Z + expectation_vals[1] * X + expectation_vals[2] * Y) / 2\n",
    "\n",
    "    # calculate eigenvalues of µ matrix\n",
    "    eigen = np.linalg.eig(mu)\n",
    "    vals  = eigen[0]\n",
    "    vecs  = eigen[1].transpose()\n",
    "\n",
    "    # order eigenvalues from largest to smallest\n",
    "    eig_vals = sorted(vals, reverse=True)\n",
    "    idx      = []\n",
    "    for val in eig_vals:\n",
    "        idx.append(np.where(vals == val)[0][0])\n",
    "    eig_vecs = []\n",
    "    for i in idx:\n",
    "        eig_vecs.append(vecs[i])\n",
    "        \n",
    "    # calculate eigenvalues of the density matrix\n",
    "    accumulator = 0\n",
    "    lamb_vals   = [None] * len(eig_vals)\n",
    "    for i in range(len(eig_vals) - 1, -1, -1):\n",
    "        if eig_vals[i] + (accumulator / (i + 1)) >= 0:\n",
    "            for j in range(i + 1):\n",
    "                lamb_vals[j] = eig_vals[j] +  (accumulator / (i + 1))\n",
    "            break\n",
    "        else:\n",
    "            lamb_vals[i] = 0\n",
    "            accumulator  += eig_vals[i]\n",
    "\n",
    "    # calculate density matrix\n",
    "    predicted_state = lamb_vals[0] * np.outer(eig_vecs[0], eig_vecs[0].conj()) \\\n",
    "                        + lamb_vals[1] * np.outer(eig_vecs[1], eig_vecs[1].conj())\n",
    "    \n",
    "    # calculate fidelity\n",
    "    fidelity = input_state.conj().dot(predicted_state).dot(input_state)\n",
    "    \n",
    "    return predicted_state, fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 319,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted density matrix:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.5 & 0.49752 + 0.04975 i\\\\0.49752 - 0.04975 i & 0.5\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[                0.5, 0.49752 + 0.04975*I],\n",
       "[0.49752 - 0.04975*I,                 0.5]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With fidelity: (0.99752+0j)\n"
     ]
    }
   ],
   "source": [
    "density, fidelity = one_qubit_tomography(np.array([np.sqrt(1 / 2), np.sqrt(1 / 2)]), 100)\n",
    "print('Predicted density matrix:')\n",
    "display(Matrix(np.round(density, 5)))\n",
    "print(f'With fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To calculate the fidelity based on the number of shots, I ran the function defined above for a wide range of shots. Remember that each measurement circuit is ran this number of shots, so in reality the total number of shots is the number passed to the function times three."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 320,
   "metadata": {},
   "outputs": [],
   "source": [
    "shots      = []\n",
    "fidelities = []\n",
    "\n",
    "initial_state = np.array([np.sqrt(1 / 2), np.sqrt(1 / 2)])\n",
    "\n",
    "for i in range(2, 1500):\n",
    "    shots.append(i)\n",
    "    density, fidelity = one_qubit_tomography(initial_state, i)\n",
    "    fidelities.append(fidelity)\n",
    "    \n",
    "shots = np.array(shots)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 321,
   "metadata": {},
   "outputs": [
    {
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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 6))\n",
    "plt.plot(shots, np.real(fidelities))\n",
    "plt.ylabel('Fidelity')\n",
    "plt.xlabel('Shots per measurement')\n",
    "plt.title('Shots against fidelity for one qubit state tomography');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 322,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def func(t, a, b, c):\n",
    "    return a * np.log(t * b) + c\n",
    "popt, pcov = curve_fit(func, shots, np.real(fidelities), p0=(1, 1, 1))\n",
    "\n",
    "plt.figure(figsize=(14, 6))\n",
    "plt.plot(shots, np.real(fidelities), label=\"Original data\")\n",
    "plt.plot(shots, func(shots, *popt), 'r-', label=\"Fitted Curve\")\n",
    "plt.legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 323,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Peak fidelity found at 917 shots\n"
     ]
    }
   ],
   "source": [
    "for i in range(2, 1500):\n",
    "    if func(i, *popt) >= 1:\n",
    "        print(f'Peak fidelity found at {i} shots')\n",
    "        break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "After running this code for different states assigned to `initial_state`, the logarithm function that fits the fidelities mostly crossed the value 1 after around 900 shots for simple states like $|0\\rangle$ and $|+\\rangle$. However, for more complicated states like $\\begin{pmatrix} 1/\\sqrt{3} & \\sqrt{2/3} \\end{pmatrix}^T$, this fidelity was achieved after around 1100 shots. However, this is because the data in this case is more noise as shown in the graph above. It can easily be seen that fidelities of 1 are already being achieved steadily around the 1000 shots mark. Therefore, 1000 shots should be a good amount for any state.\n",
    "\n",
    "As you can see below, this number of shots produces good results for various types of initial states. In these I've rounded the expected density matrix up to only three decimals to show the closeness to the actual density matrix."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted density matrix:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.001 & -0.023 + 0.017 i\\\\-0.023 - 0.017 i & 0.999\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[           0.001, -0.023 + 0.017*I],\n",
       "[-0.023 - 0.017*I,            0.999]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With fidelity: (0.99918+0j)\n"
     ]
    }
   ],
   "source": [
    "density, fidelity = one_qubit_tomography(np.array([0, 1]), 1000)\n",
    "print('Predicted density matrix:')\n",
    "display(Matrix(np.round(density, 3)))\n",
    "print(f'With fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 263,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted density matrix:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.641 & -0.016 - 0.474 i\\\\-0.016 + 0.474 i & 0.359\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[           0.641, -0.016 - 0.474*I],\n",
       "[-0.016 + 0.474*I,            0.359]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With fidelity: (0.99389+0j)\n"
     ]
    }
   ],
   "source": [
    "density, fidelity = one_qubit_tomography(np.array([np.sqrt(2 / 3), 1j * np.sqrt(1 / 3)]), 1000)\n",
    "print('Predicted density matrix:')\n",
    "display(Matrix(np.round(density, 3)))\n",
    "print(f'With fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 304,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted density matrix:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.203 & 0.401 - 0.031 i\\\\0.401 + 0.031 i & 0.797\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[          0.203, 0.401 - 0.031*I],\n",
       "[0.401 + 0.031*I,           0.797]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With fidelity: (0.99905-0j)\n"
     ]
    }
   ],
   "source": [
    "density, fidelity = one_qubit_tomography(np.array([np.sqrt(1 / 5), np.sqrt(4 / 5)]), 1000)\n",
    "print('Predicted density matrix:')\n",
    "display(Matrix(np.round(density, 3)))\n",
    "print(f'With fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Level 2\n",
    "For an easier time working on the generalized version of the above, I first breakdown the above function into smaller functions. Starting with adding the measurement gates for each of the single qubit basis. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measure_x_basis(qc, qubit):\n",
    "    \"\"\"\n",
    "    Add a measurement in the X basis to the given qubit\n",
    "    \n",
    "    Parameters:\n",
    "        qc: QuantumCircuit\n",
    "            Quantum circuit with the qubit to which you want to add the measurement\n",
    "        qubit: int\n",
    "            Index of qubit you want to add the measurement to\n",
    "    \"\"\"\n",
    "    qc.h(qubit)\n",
    "    qc.measure(qubit, qubit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measure_y_basis(qc, qubit):\n",
    "    \"\"\"\n",
    "    Add a measurement in the Y basis to the given qubit\n",
    "    \n",
    "    Parameters:\n",
    "        qc: QuantumCircuit\n",
    "            Quantum circuit with the qubit to which you want to add the measurement\n",
    "        qubit: int\n",
    "            Index of qubit you want to add the measurement to\n",
    "    \"\"\"\n",
    "    qc.sdg(qubit)\n",
    "    qc.h(qubit)\n",
    "    qc.measure(qubit, qubit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measure_z_basis(qc, qubit):\n",
    "    \"\"\"\n",
    "    Add a measurement in the Z basis to the given qubit\n",
    "    \n",
    "    Parameters:\n",
    "        qc: QuantumCircuit\n",
    "            Quantum circuit with the qubit to which you want to add the measurement\n",
    "        qubit: int\n",
    "            Index of qubit you want to add the measurement to\n",
    "    \"\"\"\n",
    "    qc.measure(qubit, qubit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now a function that returns all the strings in $\\{X, Y, Z\\}^n$ (or any other set of values), which will help us get all the possible measurement bases for an $n$-qubit system."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def measurements_strings(n, arr=['X', 'Y', 'Z']):\n",
    "    strs  = []\n",
    "    combs = list(itertools.combinations_with_replacement(arr, n))\n",
    "    for comb in combs:\n",
    "        for item in set(list(itertools.permutations(comb))):\n",
    "            strs.append(item)\n",
    "    return strs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "81"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(measurements_strings(4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Also a function that given an array of operators in $\\{I, X, Y, Z\\}$ computes their tensor product."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tensor_operator(arr):\n",
    "    arr = list(arr)[::-1]\n",
    "    \n",
    "    I = np.array([[1, 0], [0, 1]])\n",
    "    X = np.array([[0, 1], [1, 0]])\n",
    "    Y  = np.array([[0, -1j], [1j, 0]])\n",
    "    Z = np.array([[1, 0], [0, -1]])\n",
    "    \n",
    "    first = arr.pop(0)\n",
    "    if first == 'I':\n",
    "        out = I\n",
    "    elif first == 'X':\n",
    "        out = X\n",
    "    elif first == 'Y':\n",
    "        out = Y\n",
    "    else:\n",
    "        out = Z\n",
    "        \n",
    "    for op in arr:\n",
    "        if op == 'I':\n",
    "            out = np.kron(out, I)\n",
    "        elif op == 'X':\n",
    "            out = np.kron(out, X)\n",
    "        elif op == 'Y':\n",
    "            out = np.kron(out, Y)\n",
    "        else:\n",
    "            out = np.kron(out, Z)\n",
    "\n",
    "    return out.astype('complex')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n",
       "       [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n",
       "       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "tensor_operator(['X', 'Z'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a function that is able to get the expectation value of a given operator. This function should also be able to get the expectation value for operators where the identity matrix is present, although this wasn't measured in any circuit. To achieve this, we default all appearances of the identity to $X$ and ignore the correspodning qubit in the counts."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_exp_value(operator_exp, operators_meas, counts, shots):\n",
    "    \"\"\"\n",
    "    Parameters:\n",
    "        operator_exp: tuple\n",
    "        operators_meas: list\n",
    "        counts: list\n",
    "        shots: int\n",
    "    \"\"\"\n",
    "    new_counts = {}\n",
    "    ignore = []\n",
    "    \n",
    "    # if the operator of the expectation value contains the identity in any qubit\n",
    "    if 'I' in operator_exp: \n",
    "        rep_op = []\n",
    "        for idx, x in enumerate(operator_exp):\n",
    "            if x == 'I':\n",
    "                ignore.append(idx)\n",
    "                rep_op.append('X')\n",
    "            else:\n",
    "                rep_op.append(x) \n",
    "    # if there aren't any identities in the expectation operator\n",
    "    else:                   \n",
    "        rep_op = operator_exp\n",
    "        \n",
    "    # get index of operator_exp in experiment operator_meas, which is the same as in counts\n",
    "    for idx, x in enumerate(operators_meas):\n",
    "        if x == tuple(rep_op):\n",
    "            count_idx = idx\n",
    "\n",
    "    # create new counts dictionary\n",
    "    for idx, value in counts[count_idx].items():\n",
    "        w = idx[::-1]\n",
    "        for i in ignore:\n",
    "            w = w[:i] + 'x' + w[i + 1:]\n",
    "        if w in new_counts.keys():\n",
    "            new_counts[w] += value\n",
    "        else:\n",
    "            new_counts[w] = value\n",
    "                \n",
    "    # get expectation value\n",
    "    exp_value = 0\n",
    "    for idx, num_meas in new_counts.items():\n",
    "        meas_val = 1\n",
    "        for x in idx:\n",
    "            if x == '1':\n",
    "                meas_val *= -1\n",
    "            else:\n",
    "                pass        \n",
    "        exp_value += meas_val * num_meas\n",
    "    exp_value /= shots\n",
    "        \n",
    "    return exp_value"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, a function that applies the optimization procedure for the $\\mu$ matrix obtained from the expectation values and operators."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mu_optimize(mu, n):\n",
    "    # calculate eigenvalues of µ matrix\n",
    "    eigen = np.linalg.eig(mu)\n",
    "    vals  = eigen[0]\n",
    "    vecs  = eigen[1].transpose()\n",
    "\n",
    "    # order eigenvalues from largest to smallest\n",
    "    eig_vals = sorted(vals, reverse=True)\n",
    "    idx      = []\n",
    "    for val in eig_vals:\n",
    "        idx.append(np.where(vals == val)[0][0])\n",
    "    eig_vecs = []\n",
    "    for i in idx:\n",
    "        eig_vecs.append(vecs[i])\n",
    "        \n",
    "    # calculate eigenvalues of the density matrix\n",
    "    accumulator = 0\n",
    "    lamb_vals   = [None] * len(eig_vals)\n",
    "    for i in range(len(eig_vals) - 1, -1, -1):\n",
    "        if eig_vals[i] + (accumulator / (i + 1)) >= 0:\n",
    "            for j in range(i + 1):\n",
    "                lamb_vals[j] = eig_vals[j] +  (accumulator / (i + 1))\n",
    "            break\n",
    "        else:\n",
    "            lamb_vals[i] = 0\n",
    "            accumulator  += eig_vals[i]\n",
    "\n",
    "    # calculate density matrix\n",
    "    predicted_state = np.zeros((2 ** n, 2 ** n), 'complex')\n",
    "    for idx, lamb_val in enumerate(lamb_vals):\n",
    "        predicted_state += lamb_vals[idx] * np.outer(eig_vecs[idx], eig_vecs[idx].conj())\n",
    "    \n",
    "    return predicted_state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And now the main function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tomography(input_state, samples):\n",
    "    \"\"\"\n",
    "    Performs quantum state tomography in an n-qubit state.\n",
    "    \n",
    "    Parameters:\n",
    "        input_state: np.array\n",
    "            n-qubit state for which we want to perform quantum state tomography\n",
    "        samples: int\n",
    "            Number of samples available of the input state\n",
    "    \n",
    "    Returns:\n",
    "        predicted_state: np.array\n",
    "            Density matrix of state predicted via quantum state tomography\n",
    "        fidelity: float\n",
    "            Fidelity of predicted state in respected to input state\n",
    "    \"\"\"\n",
    "    # get number of qubits and bases to be measured in\n",
    "    n     = int(np.log(len(input_state)) / np.log(2))\n",
    "    bases = measurements_strings(n)\n",
    "    \n",
    "    # generate 3^n circuits with each measurement operator in {X, Y, Z}^n\n",
    "    circs = []\n",
    "    for base in bases:\n",
    "        qc = QuantumCircuit(n, n)\n",
    "        qc.initialize(input_state)\n",
    "        for idx, b in enumerate(base):\n",
    "            if b == 'X':\n",
    "                measure_x_basis(qc, idx)\n",
    "            elif b == 'Y':\n",
    "                measure_y_basis(qc, idx)\n",
    "            elif b == 'Z':\n",
    "                measure_z_basis(qc, idx)\n",
    "        circs.append(qc)\n",
    "    \n",
    "    # run circuits\n",
    "    backend = Aer.get_backend('qasm_simulator')\n",
    "    job     = execute(circs, backend, shots=samples) # each measurement basis gets a third of the available copies\n",
    "    counts  = job.result().get_counts()\n",
    "    \n",
    "    # get all expectation values\n",
    "    ops      = measurements_strings(n, arr=['I', 'X', 'Y', 'Z'])[1:] # we need to consider identity operator here\n",
    "    exp_vals = []\n",
    "    for op in ops:\n",
    "        exp_vals.append(get_exp_value(op, bases, counts, samples))\n",
    "\n",
    "    # calculate µ matrix \n",
    "    mu = tensor_operator(['I' for _ in range(n)])\n",
    "    for idx, op in enumerate(ops):\n",
    "        mu += exp_vals[idx] * tensor_operator(op)\n",
    "    mu /= (2 ** n)\n",
    "    \n",
    "    # optimize the µ matrix to get the predicted density matrix\n",
    "    predicted_state = mu_optimize(mu, n)\n",
    "    \n",
    "    # calculate fidelity\n",
    "    fidelity = input_state.conj().dot(predicted_state).dot(input_state)\n",
    "    \n",
    "    return predicted_state, fidelity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Predicted density matrix:\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.503 & 0.5 - 0.014 i\\\\0.5 + 0.014 i & 0.497\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([\n",
       "[        0.503, 0.5 - 0.014*I],\n",
       "[0.5 + 0.014*I,         0.497]])"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "With fidelity: (0.9998+0j)\n"
     ]
    }
   ],
   "source": [
    "input_state = np.array([1 / np.sqrt(2), 1 / np.sqrt(2)])\n",
    "\n",
    "density, fidelity = tomography(input_state, 1000)\n",
    "print('Predicted density matrix:')\n",
    "display(Matrix(np.round(density, 3)))\n",
    "print(f'With fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test the fidelity as a function of the number of shots for different number of qubits $n$, I run the tomography function for the equal superposition state of each $n$ qubits and for various number of shots."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 338,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = []\n",
    "\n",
    "for i in range(1, 6):\n",
    "    n              = 2 ** i\n",
    "    input_state    = np.full((n,), 1 / np.sqrt(n))\n",
    "    \n",
    "    fidelities = []    \n",
    "    for j in range(100, 20000, 100):\n",
    "        density, fidelity = tomography(input_state, j)\n",
    "        fidelities.append(fidelity)\n",
    "    results.append(fidelities)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 339,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "domain = np.array(list(range(100, 20000, 100)))\n",
    "plt.figure(figsize=(14, 6))\n",
    "for idx, result in enumerate(results):\n",
    "    plt.plot(domain, np.real(result), label=f'{idx + 1} qubits')\n",
    "    plt.legend()\n",
    "plt.xlabel('Shots per measurement')\n",
    "plt.ylabel('Fidelity of predicted state')\n",
    "plt.title('Fidelity against shots per measurement for states of different dimensions');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, as the number of qubits (dimensions of the state) increases, more shots are needed to achieve a fidelity of 0.99 or higher."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 340,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Parameters for 1 qubits: [2.25662320e-04 3.15624272e-03 9.99144752e-01]\n",
      "Parameters for 2 qubits: [0.00293599 0.02721386 0.98107582]\n",
      "Parameters for 3 qubits: [5.52056358e-03 7.28413656e+00 9.33027179e-01]\n",
      "Parameters for 4 qubits: [0.00876006 3.18059885 0.90072793]\n",
      "Parameters for 5 qubits: [0.0128114  8.60617427 0.84200285]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(14, 6))\n",
    "parameters = []\n",
    "\n",
    "def func(t, a, b, c):\n",
    "    return a * np.log(t * b) + c\n",
    "\n",
    "for idx, result in enumerate(results):\n",
    "    popt, pcov = curve_fit(func, domain, np.real(result), p0=(1, 1, 1))\n",
    "    parameters.append(popt)\n",
    "    print(f'Parameters for {idx + 1} qubits: {popt}')\n",
    "    # plt.plot(domain, np.real(result), label=f'{idx + 1} qubits')\n",
    "    plt.plot(domain, func(domain, *popt), label=f\"Fitted log for {idx+1} qubits\")\n",
    "    plt.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 341,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "From fitted data:\n",
      "Fidelity greater than or equal to 0.99 found at 1 shots for 1 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 768 shots for 2 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 4165 shots for 3 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 8382 shots for 4 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 12083 shots for 5 qubits\n",
      "\n",
      "From experimental data:\n",
      "Fidelity greater than or equal to 0.99 found at 100 shots for 1 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 300 shots for 2 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 1100 shots for 3 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 5000 shots for 4 qubits\n",
      "Fidelity greater than or equal to 0.99 found at 11600 shots for 5 qubits\n"
     ]
    }
   ],
   "source": [
    "print('From fitted data:')\n",
    "for idx, popt in enumerate(parameters):\n",
    "    for i in range(1, 20000):\n",
    "        if func(i, *popt) >= 0.99:\n",
    "            print(f'Fidelity greater than or equal to 0.99 found at {i} shots for {idx + 1} qubits')\n",
    "            break\n",
    "\n",
    "print('\\nFrom experimental data:')\n",
    "for idx, result in enumerate(results):\n",
    "    for i, r in enumerate(result):\n",
    "        if r >= 0.99:\n",
    "            print(f'Fidelity greater than or equal to 0.99 found at {domain[i]} shots for {idx + 1} qubits')\n",
    "            break"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, a fitted logarithmic function isn't a great indicator of the number of shots needed to get a fidelity greater than or equal to 0.99, as it overestimates the actual value. This is due that to the fact that after a certain threshold, the fidelities takes value between 0.98 and 1 (this range gets smaller as the number of qubits decreases) that don't seem to follow any pattern/function. Therefore, a better indicator is to get the said threshold from the experimental data, as shown above.\n",
    "\n",
    "However, when we try to find a pattern in the number of shots needed depending on the number of qubits using the experimental data, no clear pattern arises. To see something, we may need to run the simulations for smaller steps than 100 shots, but that would be too computational intensive for the moment. The table for the experimental data is:\n",
    "\n",
    "| # qubits | # shots | first difference | second difference |\n",
    "|---|---|---|---|\n",
    "|1|100|N/A|N/A|\n",
    "|2|300|200|N/A|\n",
    "|3|1100|800|600|\n",
    "|4|5000|3900|3100|\n",
    "|5|11600|6600|2700|\n",
    "\n",
    "Using the fitted data, we get the following table:\n",
    "\n",
    "| # qubits | # shots | first difference | second difference |\n",
    "|---|---|---|---|\n",
    "|1|100|N/A|N/A|\n",
    "|2|768|668|N/A|\n",
    "|3|4165|3397|2729|\n",
    "|4|8382|4217|820|\n",
    "|5|12083|3701|-516|\n",
    "\n",
    "Again, no particularly interesting pattern arises from this table alone. But using the predicted number of shots for 5 qubits yields good results when trying it out in an equal superposition state, as it is shown below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fidelity: (0.98879-0j)\n"
     ]
    }
   ],
   "source": [
    "n           = 2 ** 5\n",
    "input_state = np.full((n,), 1 / np.sqrt(n))\n",
    "\n",
    "density, fidelity = tomography(input_state, 12100)\n",
    "print(f'Fidelity: {np.round(fidelity, 5)}') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Level 3\n",
    "Here, a viariational algorithm for quantum state tomography is implemented based on the description for pure states given in section 2 of [*Variational Quantum Circuits for Quantum State Tomography*](https://arxiv.org/abs/1912.07286).\n",
    "\n",
    "First we define a function that builds a variational circuit (ansatz) using a set of parameters. The variational circuit implemented here consists of alternating $R_y$ and $R_x$ gates with alternating $CNOT$ gates in each layer to enable entanglement. This construction is based on that from section 2 of [*Variational Quantum Circuits for Quantum State Tomography*](https://arxiv.org/abs/1912.07286), but the structure of the $CNOT$ gates in each section is altered."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansatz(n, d, qc, reg, params):\n",
    "    \"\"\"\n",
    "    Build ansatz needed for variational circuit.\n",
    "    \n",
    "    Parameters:\n",
    "        n: int\n",
    "            Size of the ansatz circuit\n",
    "        d: int\n",
    "            Number of layers for the ansatz; depth\n",
    "        qc: QuantumCircuit\n",
    "            Qiskit quantum circuit in which to add the ansatz\n",
    "        reg: QuantumRegister\n",
    "            Register to which you want to add the ansatz\n",
    "        params: np.array\n",
    "            Numpy array with the parameters for the rotation gates in the ansatz\n",
    "    \"\"\"\n",
    "    arr_idx = 0\n",
    "    \n",
    "    for i in range(1, d + 1):\n",
    "        # even layers\n",
    "        if i % 2 == 0:\n",
    "            for j in range(n):\n",
    "                qc.ry(params[arr_idx], reg[j])\n",
    "                arr_idx += 1\n",
    "            for k in range(1, n):\n",
    "                if k + 1 > n:\n",
    "                    break\n",
    "                else:\n",
    "                    qc.cz(reg[0], reg[k])\n",
    "                    \n",
    "        # odd layers\n",
    "        else:\n",
    "            for j in range(n):\n",
    "                qc.ry(params[arr_idx], reg[j])\n",
    "                arr_idx += 1\n",
    "            for k in range(n - 2, -1, -1):\n",
    "                if k + 1 > n - 1:\n",
    "                    break\n",
    "                else:\n",
    "                    qc.cz(reg[-1], reg[k])\n",
    "    \n",
    "    # extra final layer\n",
    "    for i in range(n):\n",
    "        qc.rx(params[arr_idx], reg[i])\n",
    "        arr_idx += 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we define a function that is able to perform the swap test between two registers of equal size in the same circuit. We will use this to calculate the loss function of the algorithm later on. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def swap_test(n, qc, reg_1, reg_2, aux, aux_c, basis=0):\n",
    "    \"\"\"\n",
    "    Add swap test circuit between two registers using an auxilary qubit.\n",
    "    \n",
    "    Paremetrs:\n",
    "        n: int\n",
    "            Size of both registers to which we apply the SWAP test\n",
    "        qc: QuantumCircuit\n",
    "            Quantum circuit containing all the qubits we are going to act on\n",
    "        reg_1: QuantumRegister\n",
    "            First register on the test\n",
    "        reg_2: QuantumRegister\n",
    "            Second register on the test\n",
    "        aux: QuantumRegister\n",
    "            Register with the ancilla qubit used in the SWAP test\n",
    "        aux_c: ClassicalRegister\n",
    "            Register to store measurement value of the aux quantum register\n",
    "        basis: int\n",
    "            Basis in which to perform the SWAP test; 0 for X, 1 for Y and 2 for Z\n",
    "    \"\"\"\n",
    "    # change states in registers to compare to the given basis\n",
    "    if basis == 0:\n",
    "        pass\n",
    "    elif basis == 1:\n",
    "        qc.sdg(reg_1)\n",
    "        qc.h(reg_1)\n",
    "        qc.sdg(reg_2)\n",
    "        qc.h(reg_2)\n",
    "    elif basis == 2:\n",
    "        qc.h(reg_1)\n",
    "        qc.h(reg_2)\n",
    "    \n",
    "    qc.h(aux)\n",
    "    for i in range(n):\n",
    "        qc.cswap(aux, reg_1[i], reg_2[i])\n",
    "    qc.h(aux)\n",
    "    qc.measure(aux, aux_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the two functions above, we can construct a function that calculates the loss function as detailed in the paper already mentioned. This takes the target state and initializes that state into one register of size $n$. Another register of the same size is used to build the variational circuit with some parameters. Once these two steps are done, the SWAP test is performed and the following formula is used to calculate the loss function:\n",
    "\n",
    "$$\n",
    "loss = 1 - \\sqrt{1 - 2 p_1},\n",
    "$$\n",
    "\n",
    "where $p_1$ is the probability of the ancilla qubit used in the SWAP test to be in the state $|1\\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loss_func(params, ansatz, target_state, n, d, shots, backend):\n",
    "    \"\"\"\n",
    "    Calculate loss function of variational circuit used to reconstruct the target state via state tomography.\n",
    "    \n",
    "    Parameters:\n",
    "        params: np.array\n",
    "            Array with the parameters of the variational circuit to try\n",
    "        ansatz: func\n",
    "            Function that takes a circuit of size n and a set of parameters to add a parametrized circuit to it\n",
    "            Must be of the form: ansatz(n, d, qc, reg, params)\n",
    "        target_state: np.array\n",
    "            Statevector of the target state in which we are performing the tomography\n",
    "        n: int\n",
    "            Number of qubits needed to represent the target state\n",
    "        d: int\n",
    "            Desired depth of the variational circuit\n",
    "        shots: int\n",
    "            Number of times to run the quantum circuit\n",
    "        backend: IBMQBackend\n",
    "            Backend to run the quantum circuit in\n",
    "            \n",
    "    Returns:\n",
    "        loss: float\n",
    "            Calculated loss value through the SWAP test\n",
    "    \"\"\"\n",
    "    loss_vals = []\n",
    "    \n",
    "    for i in range(3):\n",
    "        # initialize all registers and quantum circuit\n",
    "        reg_1 = QuantumRegister(n, 'pure')\n",
    "        reg_2 = QuantumRegister(n, 'var')\n",
    "        aux   = QuantumRegister(1, 'aux')\n",
    "        aux_c = ClassicalRegister(1, 'c')\n",
    "        qc    = QuantumCircuit(reg_1, reg_2, aux, aux_c)\n",
    "\n",
    "        # initialize target state in register 1\n",
    "        init = QuantumCircuit(n) \n",
    "        init.initialize(target_state)\n",
    "        init = transpile(init, basis_gates=['cx', 'u'])\n",
    "        init_gate = init.to_gate(label=' init ')\n",
    "        qc.append(init_gate, reg_1)\n",
    "\n",
    "        # add variational circuit in register 2\n",
    "        ansatz(n, d, qc, reg_2, params)\n",
    "\n",
    "        # perform swap test between registers 1 and 2\n",
    "        swap_test(n, qc, reg_1, reg_2, aux, aux_c, basis=i+1)\n",
    "\n",
    "        # run circuit to calculate the loss function\n",
    "        job     = backend.run(transpile(qc, backend), shots=shots)\n",
    "        counts  = job.result().get_counts()\n",
    "        if 1 - 2 * (counts.get('1', 0) / shots) < 0: # avoid rounding errors\n",
    "            loss = 0\n",
    "        else:\n",
    "            loss = 1 - np.sqrt(1 - 2 * (counts.get('1', 0) / shots))\n",
    "        loss_vals.append(loss)\n",
    "    \n",
    "    clear_output(wait=True)\n",
    "    print(f'X: {loss_vals[0]}. Y: {loss_vals[1]}. Z: {loss_vals[2]}. Avg: {np.average(loss_vals)}')\n",
    "    \n",
    "    return np.average(loss_vals)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To test that this loss function works, I'll use an already built optimizer from [SciPy](https://www.scipy.org) that has many optmization methods available. The target state will be randomly generated. The number of layers and shots is quite arbitrary at this point as well as the initial guess for the parameters, which simply is all $0$s. And we use the QASM simulator to run our circuits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: 0.0004000800320159703. Y: 0.0006001801080810498. Z: 0.0003000450135051125. Avg: 0.00043343505120071085\n",
      "Target state: [0.17874835 0.47691638 0.54261976 0.66795479]\n",
      "Calculated parameters: [ 0.91775659  0.54839631  0.77820996  0.42159966  0.07590215 -0.05597055\n",
      "  0.0806014   1.41798112 -0.29500414  0.1108828   0.1156926   0.04097329]\n",
      "With loss value: 0.00043343505120071085\n"
     ]
    }
   ],
   "source": [
    "n = 2\n",
    "d = 5\n",
    "shots   = 10000\n",
    "target  = np.random.rand(2 ** n)\n",
    "target  = target / np.linalg.norm(target)\n",
    "# target = np.full(2 ** n, 1 / np.sqrt(2 ** n)) # equal superposition of all basis states\n",
    "guess   = [0 for _ in range(n * d + n)]\n",
    "backend = Aer.get_backend('qasm_simulator')    \n",
    "    \n",
    "op_result = minimize(loss_func, guess, args=(ansatz, target, n, d, shots, backend), method='COBYLA')\n",
    "print(f'Target state: {target}')\n",
    "print(f'Calculated parameters: {op_result.x}')\n",
    "print(f'With loss value: {op_result.fun}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the function is able to optimize the parameters really good, as it returns parameters with a small final loss value. We can construct a variational circuit just as the one used in the loss function to check out what state the parameters found by the optimization produce."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 770.141x144.48 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Ansatz has {'ry': 10, 'cz': 5, 'rx': 2}\n"
     ]
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0.18303 - 0.03883 i & 0.47793 - 0.02423 i & 0.54171 - 0.04215 i & 0.66262 - 0.04121 i\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "Matrix([[0.18303 - 0.03883*I, 0.47793 - 0.02423*I, 0.54171 - 0.04215*I, 0.66262 - 0.04121*I]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = QuantumRegister(n, 'reg')\n",
    "qc  = QuantumCircuit(reg)\n",
    "\n",
    "ansatz(n, d, qc, reg, op_result.x)\n",
    "display(qc.draw('mpl'))\n",
    "\n",
    "backend = Aer.get_backend('statevector_simulator')\n",
    "result  = execute(qc, backend).result()\n",
    "vector  = result.get_statevector()[None]\n",
    "print(f'Ansatz has {dict(qc.count_ops())}')\n",
    "Matrix(np.round(vector, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although we see some imaginary values in the statevector above while the target state contians only real values, the amount of the imaginary coefficients can be greatly reduced by factoring out a global phase out of the statevector. This would still leave a small coefficient for $i$ in the statevector, but the similarity of the state got from the circuit and the target state is good as indicated by the loss function. \n",
    "\n",
    "To see the similarity clearly, we can run the circuit using the QASM simulator to get the estimated probability distribution of the predicted and target states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1008x360 with 1 Axes>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg = QuantumRegister(n)\n",
    "qc  = QuantumCircuit(reg)\n",
    "\n",
    "ansatz(n, d, qc, reg, op_result.x)\n",
    "qc.measure_all()\n",
    "\n",
    "qc2 = QuantumCircuit(n)\n",
    "qc2.initialize(target)\n",
    "qc2.measure_all()\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "result  = execute([qc, qc2], backend, shots=10000).result()\n",
    "counts  = result.get_counts()\n",
    "\n",
    "plot_histogram(counts, figsize=(14,5), legend=['Predicted', 'Target'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although visualizing the counts might be a good indicator at first thought, it doesn't reflect the actual state of our quantum system to perfection, since the QASM simulator simulates the randomness of a quantum computer and therefore the counts for the predicted and target states will not be the same even if the states are exactly the same. Therefore, we can introduce another value.\n",
    "\n",
    "This other good indicator of the accuracy of the predicted state is the state fidelity. This is defined as:\n",
    "\n",
    "$$\n",
    "F(\\rho_1, \\rho_2) = Tr\\left[\\sqrt{\\sqrt{\\rho_1} \\rho_2 \\sqrt{\\rho_1}}\\right]^2,\n",
    "$$\n",
    "\n",
    "where $\\rho_1$ and $\\rho_2$ are the density matrices of the states we are comparing. Since we know that we will only be comparing pure states, the expression for fidelity can be simplified to\n",
    "\n",
    "$$\n",
    "F(\\rho_1, \\rho_2) = \\langle\\psi_1|\\psi_2\\rangle\\langle\\psi_2|\\psi_1\\rangle = |\\langle\\psi_2|\\psi_1\\rangle|^2,\n",
    "$$\n",
    "\n",
    "where $\\rho_i = |\\psi_i\\rangle\\langle\\psi_i|$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fidelity of predicted state compared to target state: 0.9991361000514039\n"
     ]
    }
   ],
   "source": [
    "fidelity = np.abs(target.conj().dot(vector[0])) ** 2\n",
    "print(f'Fidelity of predicted state compared to target state: {fidelity}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determining the number of layers $d$ optimal for each number of qubits $n$ is an interesting task. Through testing, the following roughly optimal values (optimal considering both runtime and fidelity of predicted state against target state) are found:\n",
    "\n",
    "|$n$|$d$|\n",
    "|---|---|\n",
    "|1|2|\n",
    "|2|3|\n",
    "|3|4|\n",
    "|4|5|\n",
    "\n",
    "However, although this values for $d$ work really well for most states, there are some target states for which this number of layers isn't sufficient. To account for this, we can add more layers to our variational circuit, or repeat the optimizing process while the loss function gives a value greater than or equal to $0.01$. There is no right or wrong choice for that, as the effectiveness of the algorithm depends on the ansatz choice which in turn depends on the target state and might need further experimentation to get right.\n",
    "\n",
    "To account for this flexibility, we can go ahead and already implement the general tomography function that only takes in a target state and tries to reproduce it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "def tomography(ansatz, layers, num_params, loss_func, target, shots, method='COBYLA', repeat=False):\n",
    "    \"\"\"\n",
    "    Performs state tomography on the target state using a variational algorithm.\n",
    "    \n",
    "    Parameters:\n",
    "        ansatz: func\n",
    "            Function that takes a circuit of size n and a set of parameters to add a parametrized circuit to it\n",
    "            Must be of the form: ansatz(n, layers, qc, reg, params)\n",
    "        layers: int\n",
    "            Number of layers of the ansatz to add to the variational circuit\n",
    "        num_params: int\n",
    "            Number of parameters the specified ansatz needs\n",
    "        loss_func: func\n",
    "            Function that adds the cost function to the circuit, which uses the SWAP test\n",
    "            Must be of the form: loss_func(params, ansatz, target_state, n, layers, shots, backend)\n",
    "        target: np.array\n",
    "            2^n normalized array with the target statevector\n",
    "        shots: int\n",
    "            Number of available shots for each measurement of the variational circuit\n",
    "        method: str\n",
    "            String with name of SciPy optimizer to use to optimize the parameters; defaults to COBYLA\n",
    "        repeat: bool\n",
    "            If True, it will repeat the optimization procedure until the final loss value is less than 0.01\n",
    "            \n",
    "    Returns:\n",
    "        op_result.x: np.array\n",
    "            Array with the optimized parameters\n",
    "        op_result.fun: float\n",
    "            Value of the given loss function with the found optimal parameters\n",
    "    \"\"\"\n",
    "    n = int(np.log(len(target)) / np.log(2))\n",
    "    \n",
    "    guess   = [0 for _ in range(num_params)]\n",
    "    backend = Aer.get_backend('qasm_simulator')    \n",
    "    \n",
    "    op_result = minimize(loss_func, guess, args=(ansatz, target, n, layers, shots, backend), method=method)\n",
    "    \n",
    "    if repeat:\n",
    "        loss_val  = op_result.fun\n",
    "        while loss_val >= 0.01:\n",
    "            params    = op_result.x            \n",
    "            op_result = minimize(loss_func, params, args=(ansatz, target, n, layers, shots, backend), method=method)\n",
    "            loss_val  = op_result.fun\n",
    "    \n",
    "    return op_result.x, op_result.fun"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X: 0.0011006056664164543. Y: 0.0015011266906707066. Z: 0.0017014474617325082. Avg: 0.0014343932729398896\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(array([ 1.85334458,  1.11375543,  1.01091467,  0.55874179,  0.16858715,\n",
       "        -0.13331855, -0.24708919, -0.51150903, -0.31604596,  0.13370372,\n",
       "        -0.25932827, -1.16169993,  0.13753899, -0.12170018, -0.02577196]),\n",
       " 0.0014343932729398896)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_qubits = 3\n",
    "layers     = 4\n",
    "num_params = num_qubits * (layers + 1)\n",
    "target     = np.random.rand(2 ** num_qubits)\n",
    "target     = target / np.linalg.norm(target)\n",
    "shots      = 10000\n",
    "\n",
    "tomography(ansatz, layers, num_params, loss_func, target, shots, 'COBYLA', repeat=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As you can see, the general tomography function that we have created has a lot of flexibility. It is done this way because variational algorithms heavily depend on the choice of ansatz and loss function, which can be chosen carefully if previous knowledge about the target state is given. This previous knowledge can help make the ansatz circuit smaller in depth and therefore improve the runtime and use of resources of the whole algorithm. \n",
    "\n",
    "Further work with this algorithm can be done to implement a specific optimization method for this problem, as now the COBYLA method we are using isn't the perfevt choice for what we want to achieve. Also, research in the ansatz design is an active field within variational algorithms and can have applications to our algorithm, given that we know something about the target state we can use an optimal ansatz and if no knowledge is known, at least we can use a somewhat efficient ansatz that is able to reach all states in $\\mathcal{H}^n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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