02.QRW_and_localization.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "7152f2bf-5b38-470a-a523-6398a51c2c16",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<frozen importlib._bootstrap>:219: RuntimeWarning: scipy._lib.messagestream.MessageStream size changed, may indicate binary incompatibility. Expected 56 from C header, got 64 from PyObject\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from copy import deepcopy\n",
    "\n",
    "# Importing standard Qiskit libraries\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, transpile, Aer, IBMQ, execute\n",
    "from qiskit.tools.jupyter import *\n",
    "from qiskit.visualization import *\n",
    "from qiskit.providers.aer import QasmSimulator\n",
    "from tqdm.notebook import tqdm\n",
    "\n",
    "from qiskit.providers.aer import QasmSimulator\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit.circuit import Parameter\n",
    "import qiskit.quantum_info as qi\n",
    "\n",
    "from qc_grader.challenges.spring_2022.helpers import generate_XX, generate_YY, generate_disordered_tb_instruction\n",
    "\n",
    "# Suppress warnings\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6d790e43-7e59-40b3-9a3a-806e7df15b70",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = Parameter('t')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "1cd64c4c",
   "metadata": {},
   "outputs": [],
   "source": [
    "XX = generate_XX(t)\n",
    "YY = generate_YY(t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "04b5fd64",
   "metadata": {},
   "source": [
    "# 5 site tight-binding lattice\n",
    "\n",
    "In this exercise we simulate a tight-binding lattice with five sites. First, we look at the tight-binding Hamiltonian with all the site energies at the same value. As a reminder, the Hamiltonian for a 5 site tight-binding lattice is: \n",
    "\n",
    "$$H_{\\rm tb}/\\hbar = J \\sum^{3}_{i=0} (X_i X_{i+1} + Y_i Y_{i+1})$$\n",
    "\n",
    "For this challenge, without loss of generality, we set $\\hbar=1$ and $J=1$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "427ff204",
   "metadata": {},
   "source": [
    "## 1. Particle transport\n",
    "\n",
    "In a tight-binding system the particle propagation can be described by a continuous-time quantum random walk. Quantum random walks are the quantum mechanical analog of classical random walks. A random walk is the process by which a randomly-moving particle moves away from its starting point. Under a classical random walk, the probability of finding the particle at time $t$ at position $r$ from the starting point follows a Gaussian distribution:\n",
    "$$ p_{\\text{classical}}(r,t) \\propto e^{-|r|^2/t} $$\n",
    "\n",
    "The standard deviation of this probability distribution grows as the square-root with time: $\\sigma_{\\text{classical}}= \\sqrt{t}$. Quantum properties such as single-particle superposition and interference result in a qualitative difference between classical and quantum random walks. Under a quantum random walk, the probability of finding the particle at position $r$ from the starting point follows a [Bessel function of the first kind](https://en.wikipedia.org/wiki/Bessel_function):\n",
    "$$ p_{\\text{quantum}}(r,t) \\propto |J_r(2t)|^2 $$\n",
    "\n",
    "The standard deviation of this probability distribution grows linearly with time: $\\sigma_{\\text{quantum}} = t$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "9835208a",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.special import jv\n",
    "\n",
    "t_test = 20\n",
    "r = np.linspace(-50,50,101)\n",
    "gaussian = np.exp(-r**2/t_test) / np.sum(np.exp(-r**2/t_test))\n",
    "bessel = np.abs(jv(r,2*t_test))**2 / np.sum(np.abs(jv(r,2*t_test))**2)\n",
    "\n",
    "plt.figure(facecolor='white')\n",
    "plt.plot(r, gaussian, label=r'Gaussian function')\n",
    "plt.plot(r, bessel, label=r'Bessel function')\n",
    "\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Probability density')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c9ef0341",
   "metadata": {},
   "source": [
    "The spatial propagation of the particle throughout the lattice, relative to its initial location, is quantified by the mean square displacement $⟨x^2⟩= \\sum_i p_i x^2_i$, where $p_i$ is the probability of finding the particle on site $i$. A classical random walk propagates diffusively in time with $⟨x^2⟩ \\propto t$, whereas a QRW exhibits ballistic propagation with a mean-square displacement $⟨x^2⟩ \\propto t^2$. \n",
    "\n",
    "The quadratic speed-up of quantum random walks in comparison to classical random walks is analogous to the quadratic speed-up of the Grover search algorithm compared to classical search!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f76797ef",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "<b>Challenge question 2a</b> \n",
    "\n",
    "Append the XX and YY gates to our circuit to create a trotterize time evolution under the tight-binding Hamiltonian.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "85d24eb2-2a44-45cb-b5ab-70c46890a3fd",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 353.94x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_qubits = 5 ## DO NOT EDIT\n",
    "\n",
    "Trot_tb_qr = QuantumRegister(num_qubits)\n",
    "Trot_tb_qc = QuantumCircuit(Trot_tb_qr, name='Trot')\n",
    "\n",
    "###EDIT CODE BELOW\n",
    "\n",
    "for i in range(num_qubits-1):\n",
    "    if(i%2==0):\n",
    "        Trot_tb_qc.append(XX,[Trot_tb_qr[i],Trot_tb_qr[i+1]])\n",
    "        Trot_tb_qc.append(YY,[Trot_tb_qr[i],Trot_tb_qr[i+1]])\n",
    "for i in range(num_qubits-1):\n",
    "    if(i%2==1):\n",
    "        Trot_tb_qc.append(XX,[Trot_tb_qr[i],Trot_tb_qr[i+1]])\n",
    "        Trot_tb_qc.append(YY,[Trot_tb_qr[i],Trot_tb_qr[i+1]])\n",
    "        \n",
    "###DO NOT EDIT BELOW\n",
    "\n",
    "Trot_tb_gate = Trot_tb_qc.to_instruction()\n",
    "\n",
    "Trot_tb_qc.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "id": "c74463db",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "## Grade and submit your solution\n",
    "from qc_grader.challenges.spring_2022 import grade_ex2a\n",
    "\n",
    "grade_ex2a(Trot_tb_qc)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cddeec50",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "<b>Challenge question 2b</b> \n",
    "\n",
    "Next, we want to add a particle in the form of an excitation to **qubit 0**. This can be accomplished by applying an  𝑋  gate to flip the state of the qubit from  |0⟩  to  |1⟩  before time evolution under the Hamiltonian.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "a62b2759-60d6-4929-add2-ad5db47c2ad7",
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_t=0.15 # DO NOT EDIT\n",
    "time_steps=np.arange(1,20,1) # DO NOT EDIT\n",
    "\n",
    "circuits=[]\n",
    "\n",
    "for n_steps in time_steps:\n",
    "    \n",
    "    qr = QuantumRegister(num_qubits)\n",
    "    cr = ClassicalRegister(num_qubits)\n",
    "    qc = QuantumCircuit(qr,cr)\n",
    "\n",
    "    ###EDIT CODE BELOW\n",
    "    qc.x(qr[0])\n",
    "    ###DO NOT EDIT BELOW\n",
    "    \n",
    "    for _ in range(n_steps):\n",
    "        qc.append(Trot_tb_gate, [i for i in range(num_qubits)])\n",
    "        \n",
    "    qc = qc.bind_parameters({t: delta_t})\n",
    "    \n",
    "    circuits.append(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f75b601",
   "metadata": {},
   "source": [
    "We can track the movement of the particle by keeping track of the probability of finding the excitation on each qubit at different time steps. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6781ae1a",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "<b>Challenge question 2c</b> \n",
    "\n",
    "First, extract the probabilities of each qubit being in the $|1\\rangle$ at different times using the output state from the statevector_simulator.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "id": "26c82cf5",
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "ad7d4d913bf2479da86cba9a3371827b",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/19 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import transpile\n",
    "\n",
    "# Use Aer's statevector simulator\n",
    "from qiskit import Aer\n",
    "\n",
    "# Run the quantum circuit on a statevector simulator backend\n",
    "backend_sim = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "probability_density=[]\n",
    "for circ in tqdm(circuits):\n",
    "\n",
    "    transpiled_circ=transpile(circ, backend_sim, optimization_level=3)\n",
    "\n",
    "    job_sim = backend_sim.run(transpiled_circ)\n",
    "\n",
    "    # Grab the results from the job.\n",
    "    result_sim = job_sim.result()\n",
    "    outputstate = result_sim.get_statevector(transpiled_circ, decimals=5)\n",
    "    \n",
    "    ps=[]\n",
    "    \n",
    "    ###EDIT CODE BELOW (Extract the probability of finding the excitation on each qubit)\n",
    "    for i in range(transpiled_circ.num_qubits):\n",
    "        ps.append(outputstate.probabilities([i])[1])\n",
    "    ###DO NOT EDIT BELOW\n",
    "    \n",
    "    probability_density.append(ps)\n",
    "    \n",
    "probability_density=np.array(probability_density)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "id": "a5fb178e-f077-4d2e-8020-d1520eadbd34",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Time (1/J)')"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAANoAAAE9CAYAAABtK3xVAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAXl0lEQVR4nO3dbVBU590G8GthEVFeHBBSAkyRYCyvrrxEkqBILFV8IUYcIzWxBi3RCY+mtDOdTjqmZp5R244WE5y0m6RxNKl8IONoDOGxjWKiUemKJhUTQ4wYdgUFGytohWX3PB9sN7Xsgijnfy9w/T6555w95xK4vJfjfc4xaJqmgYh05aM6ANFIwKIRCWDRiASwaEQCWDQiASwakQCj6gADZQwYi1HBoapjwMeuOgHg9JLvnl/7DdURAKOv6gQAAL9gJ9rb23st95Jv1Z0bFRyKiUvKVMfA2Fan6gi4EeEdH0jue82iOgJ8wtT/4wsAbZFH3S73ju8U0TDHohEJYNGIBLBoRAJYNCIBLBqRABaNSACLRiSARSMSwKIRCWDRiASwaEQChtykYt8uDeO+6lEdA5pBdQLAPsY7/p10piWojgDD5xdUR+iTd3yniIY5Fo1IAItGJIBFIxLAohEJYNGIBLBoRAJYNCIBLBqRABaNSACLRiSARSMSwKIRCWDRiAQMuctkfLqdGG3tVB0D2mj1Xzr/+wNVRwAAWL8/VnUERB+/pjpCnziiEQlg0YgEsGhEAlg0IgEsGpEAFo1IAItGJEC3ojU3NyM3NxeJiYlISkrC1q1be21TW1uLkJAQmEwmmEwmvPTSS3rFIVJKt/91NRqN2Lx5M9LS0tDR0YH09HTk5eUhMTHxtu2mTZuGffv26RWDyCvoNqJFRkYiLS0NABAUFISEhATYbDa9Dkfk1UR+R2tqasLJkycxderUXuuOHj2KyZMnIz8/Hw0NDRJxiMTpPmGvs7MThYWFKC8vR3Bw8G3r0tLScOHCBQQGBqK6uhoLFixAY2Njr32YzWaYzWYAQHfPDb0jEw06XUc0u92OwsJCLF26FAsXLuy1Pjg4GIGBtybGzpkzB3a7He3t7b22KykpgcVigcViwSjjGD0jE+lCtxFN0zSsWLECCQkJKCsrc7tNa2sr7rvvPhgMBtTV1cHpdCIsLKzvHTsc8LnaoUPiATKqn70/7pyf6ggAAMPj6r8fBl9f1RH6pNtPy5EjR7Bz506kpKTAZDIBADZs2ICvv/4aALBq1SpUVVXh1VdfhdFoREBAACorK2EweMFjWogGmUHTNE11iIEI8b8Pj9y/VHUMrxjRumJDVUcAAPyjTP2IFvb4edURAAB/T/0CFoul13LODCESwKIRCWDRiASwaEQCWDQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEqJ+wN1BOJ9DpBdek+ar/N8r/bLfqCACA74VeVx0BVyZNUB3hX75wu1T9TwvRCMCiEQlg0YgEsGhEAlg0IgEsGpEAFo1IAItGJIBFIxLAohEJYNGIBLBoRAJYNCIBLBqRgCF4mYwG5z//qToFDKNGqY4A59+vqo4AADhh+57qCBg9I0h1BACA8aj75RzRiASwaEQCWDQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgG6Fa25uRm5ublITExEUlIStm7d2msbTdOwZs0axMfHIzU1FfX19XrFIVJKt0nFRqMRmzdvRlpaGjo6OpCeno68vDwkJia6tnn//ffR2NiIxsZGHD9+HKtXr8bx48f1ikSkjG5Fi4yMRGRkJAAgKCgICQkJsNlstxVtz549WLZsGQwGA7KysnD16lW0tLS43ueOpmnQuu16xb5j3jB7X+tR/3UAgFEfqZ85b//+P1RHAKB49n5TUxNOnjyJqVOn3rbcZrMhJibG9To6Oho2m00iEpEo3a9H6+zsRGFhIcrLyxEcHHxX+zCbzTCbzQAAu3ZzMOMRidB1RLPb7SgsLMTSpUuxcOHCXuujoqLQ3Nzsem21WhEVFdVru5KSElgsFlgsFvgZRusZmUgXuhVN0zSsWLECCQkJKCsrc7tNQUEBduzYAU3TcOzYMYSEhPT5+xnRUKXbR8cjR45g586dSElJgclkAgBs2LABX3/9NQBg1apVmDNnDqqrqxEfH48xY8bgzTff1CsOkVK6FS07OxuapvW5jcFgwLZt2/SKQOQ1ODOESACLRiSARSMSwKIRCWDRiASwaEQCWDQiAUPv3vua5hWz1g2+vqojeI3797erjoDn/udd1REAAOvh/qoOjmhEAlg0IgEsGpEAFo1IAItGJIBFIxLAohEJYNGIBLBoRAJYNCIBLBqRABaNSMAdF+369etwOBx6ZiEatjzO3nc6naisrMTbb7+Nv/71r/D390dXVxfGjx+PuXPn4tlnn0V8fLxkVu/iY1CdwGs4PvtCdQTMHeMdd7Ae8Oz93NxcnDt3Dhs3bkRrayuam5tx+fJlHD58GFlZWfj5z3+Ot956S7fARMOJQfNw80W73Q4/P78+33wn2wy2YEMophpmih7THWP4eNUR0NOm/jowb/F/Fz9RHQEA8NC8YFgsll7LPX507Ojo8Lgzf39/jB07VrxkREOVx6Klp6d7fFNPTw8AYNOmTVi6dOngpyIaZjwW7ezZsxjVx8P22trakJOTw6IR3QGPRXvkkUcQHR2N2bNnY/bs2YiNjb1tfXh4OH7961/rnY9oWPBYNIvFgqamJtTU1OD555+HzWZDdnY28vPzkZOTA39/f8yfP18yK9GQ5fGs43+z2+346KOPUFNTg9raWoSHh+O9997TO18vPOv4LZ51/NaQPev43/z8/PDYY4/hscceAwA+a5poAO5qrmN+fr7bR+ASkXseR7T6+nq3yzVNw6lTp/TKQzQseSxaZmYmcnJy3D618+rVq3pmIhp2PBYtISEBf/jDHzBx4sRe62JiYnQNRTTcePwd7Ve/+hWcTqfbda+88opugYiGI48j2qJFizy+acGCBXpkuWPe8IAJzd6jOgJ8/EerjgAAMASoz3Gup1N1hH8JdrvU44j21ltveRzRAODcuXM4fPjwveciGgE8jmhXrlzBlClTkJ6ejvT0dISHh+PmzZv48ssvcejQIYwfPx6bNm2SzEo0ZHkc0dauXYv6+noUFRWhra0NH3zwAerr6xEVFYWdO3finXfecXui5N+Ki4sRERGB5ORkt+tra2sREhICk8kEk8mEl1566d7/NkReqs+ZIb6+vsjLy0NeXt6Ad7x8+XKUlpZi2bJlHreZNm0a9u3bN+B9Ew01ut0Fa/r06QgNDdVr90RDitLbzR09ehSTJ09Gfn4+GhoaVEYh0pWyZ1inpaXhwoULCAwMRHV1NRYsWIDGxka325rNZpjNZgCAHV2SMYkGRb8j2qVLl7BixQrk5+cDAM6cOYM33njjng8cHByMwMBAAMCcOXNgt9vR3u7+so+SkhJYLBZYLBb4wf+ej00krd+iLV++HLNmzcLFixcBAA8++CDKy8vv+cCtra2ueZR1dXVwOp0ICwu75/0SeaN+Pzq2t7dj8eLF2Lhx4603GI3wvYOZGUVFRaitrUV7ezuio6Oxfv162O12AMCqVatQVVWFV199FUajEQEBAaisrITBwJuS0vDUb9HGjh2LK1euuEpw7NgxhISE9LvjXbt29bm+tLQUpaWldxiTaGjrt2hbtmxBQUEBzp07h0cffRRtbW2oqqqSyEY0bPRbtLS0NBw6dAhnz56FpmmYNGkSb5xKNED9Fs3hcKC6uhpNTU3o6enB/v37AQBlZWW6h3PHYDB4xex9Z+d11RHgGx+rOgIAwBESoDoC/vdivuoI/+L+JkH9Fm3+/PkYPXo0UlJS4OPDx6kR3Y1+i2a1WvHpp59KZCEatvodovLz810fF4no7vQ7omVlZeGJJ56A0+mEn58fNE2DwWDAtWvXJPIRDQv9Fq2srAxHjx5FSkoK/0OZ6C71+9ExJiYGycnJLBnRPeh3RIuLi8OMGTOQn58Pf/9vJ/SqOr1PNBT1W7QJEyZgwoQJ6O7uRnd3t0QmomGn36K9+OKLEjmIhjWPRSstLUVFRQXmz5/v9vezvXv36hqMaDjxWLQdO3agoqICP/vZzyTzEA1LHov2wAMPAABycnLEwhANVx6L1tbWhi1btnh8I886Et05j0VzOBzo7Ox0+9gmArQeu+oI+CZN/eN9AcD3pudbx0v56Fii6ggAgNCBzt6PjIzEunXrdAtENJJ4nBnCkYxo8Hgs2gcffCCZg2hY81g03s6baPDwkmkiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgEsGpEAZc+wvluapsFp71EdA77jxqmOgPZU77gFYIRFfY6I46oT3OLpJ5MjGpEAFo1IAItGJIBFIxLAohEJYNGIBLBoRAJ0K1pxcTEiIiKQnJzsdr2maVizZg3i4+ORmpqK+vp6vaIQKadb0ZYvX46amhqP699//300NjaisbERZrMZq1ev1isKkXK6FW369Ol93uBnz549WLZsGQwGA7KysnD16lW0tLToFYdIKWW/o9lsNsTExLheR0dHw2azqYpDpKshMdfRbDbDbDYDAOzoUpyGaOCUjWhRUVFobm52vbZarYiKinK7bUlJCSwWCywWC/zg73YbIm+mbEQrKChARUUFlixZguPHjyMkJASRkZF39mZN/UMVHN/7ruoI6In0jtF99BXVCYBRlztURwAAtHsYB3QrWlFREWpra9He3o7o6GisX78edvutJ7CsWrUKc+bMQXV1NeLj4zFmzBi8+eabekUhUk63ou3atavP9QaDAdu2bdPr8ERehTNDiASwaEQCWDQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgFD4nq0/2Qw+sI4Lkx1DFxKGas6AvBP9c8gAAB/q/rp+9rldtURbnnA/WKOaEQCWDQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgEsGpEAFo1IAItGJIBFIxIw5C6T0QL80ZUaqzoGrrt/8I2ooC+849untV5WHQHOGzdUR+gTRzQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgEsGpEAFo1IgK5Fq6mpwaRJkxAfH49Nmzb1Wr99+3aEh4fDZDLBZDLh9ddf1zMOkTK6zUp1OBx47rnn8Oc//xnR0dHIzMxEQUEBEhMTb9vuySefREVFhV4xiLyCbkWrq6tDfHw84uLiAABLlizBnj17ehVtoLqDDLDN8B+MiPfEp1t1AiD8ZJfqCAC8Y+a85nCojtAn3T462mw2xMTEuF5HR0fDZrP12u6dd95BamoqFi1ahObmZr3iECml9GTI/Pnz0dTUhE8//RR5eXn40Y9+5HY7s9mMjIwMZGRkwHH9unBKonunW9GioqJuG6GsViuiom6/WjIsLAz+/rc+Bq5cuRInTpxwu6+SkhJYLBZYLBb4jvWC55IRDZBuRcvMzERjYyPOnz+P7u5uVFZWoqCg4LZtWlpaXH/eu3cvEhIS9IpDpJRuJ0OMRiMqKiowa9YsOBwOFBcXIykpCevWrUNGRgYKCgrw8ssvY+/evTAajQgNDcX27dv1ikOklEHTNE11iIEYHRWD764qUx3DK846Rn7sHWcdjR+eUh3Ba846fpN2HhaLpddyzgwhEsCiEQlg0YgEsGhEAlg0IgEsGpEAFo1IgHfcvH0AAoK6kDyzUXUMtGx9QHUE+J/xjknYPV7yf1jejCMakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAlg0IgEsGpEAFo1IAItGJIBFIxLAohEJGHKz97/rfxW/j92jOgaWHV+sOgIc7VdUR6A7xBGNSACLRiSARSMSwKIRCWDRiASwaEQCWDQiASwakQAWjUgAi0YkgEUjEsCiEQlg0YgEsGhEAobcw+LHjx+P2NjYe9pHW1sbwsPDByfQEM7gLTm8IcNg5WhqakJ7e3uv5UOuaIMhIyMDFotlxGfwlhzekEHvHPzoSCSARSMSMCKLVlJSojqCV2QAvCOHN2QA9M0xIn9HI5I2Ikc0Imkjqmg1NTWYNGkS4uPjsWnTJiUZiouLERERgeTkZCXHB4Dm5mbk5uYiMTERSUlJ2Lp1q5IcN2/exEMPPYTJkycjKSkJL774opIcAOBwODBlyhTMmzdPnwNoI0RPT48WFxennTt3Tuvq6tJSU1O1hoYG8RyHDh3STpw4oSUlJYkf+98uXryonThxQtM0Tbt27Zo2ceJEJV8Lp9OpdXR0aJqmad3d3dpDDz2kHT16VDyHpmna5s2btaKiIm3u3Lm67H/EjGh1dXWIj49HXFwcRo0ahSVLlmDPHvn7Q06fPh2hoaHix/1PkZGRSEtLAwAEBQUhISEBNptNPIfBYEBgYCAAwG63w263w2AwiOewWq147733sHLlSt2OMWKKZrPZEBMT43odHR2t5IfL2zQ1NeHkyZOYOnWqkuM7HA6YTCZEREQgLy9PSY7nn38ev/nNb+Djo18dRkzRqLfOzk4UFhaivLwcwcHBSjL4+vri1KlTsFqtqKurw+nTp0WPv2/fPkRERCA9PV3X44yYokVFRaG5udn12mq1IioqSmEitex2OwoLC7F06VIsXLhQdRyMGzcOubm5qKmpET3ukSNHsHfvXsTGxmLJkiU4cOAAnnrqqcE/kC6/+Xkhu92uTZgwQfvqq69cJ0NOnz6tJMv58+eVngxxOp3a008/ra1du1ZZBk3TtMuXL2vffPONpmmaduPGDS07O1t79913leU5ePAgT4bcK6PRiIqKCsyaNQsJCQlYvHgxkpKSxHMUFRXh4YcfxtmzZxEdHY033nhDPMORI0ewc+dOHDhwACaTCSaTCdXV1eI5WlpakJubi9TUVGRmZiIvL0+/0+uKcWYIkYARM6IRqcSiEQlg0YgEsGhEAlg0IgEsmpexWq14/PHHMXHiRMTFxaG0tBRdXV39vu/fcwb/27p16/CXv/wFAFBeXo4bN2643W7lypU4c+bMgLJ6Oib1xtP7XkTTNEydOhWrV6/GM888A4fDgZKSEgQGBvZ7KUtgYCA6Ozv73CY2NhYWiwXjx48flLx3cky6hSOaFzlw4ABGjx6NZ555BsCteYC/+93vsGPHDnR2dmL79u0oLS11bT9v3jzU1ta6Xv/kJz9BUlISZs6ciba2NgDA8uXLUVVVhZdffhkXL15Ebm4ucnNzex17xowZrjtABQYG4oUXXsDkyZORlZWFS5cuAQDOnz+Phx9+GCkpKfjlL3952/t/+9vfIjMzE6mpqa7rynbv3o2ZM2dC0zS0tLTgwQcfRGtr6+B9wYYQFs2LNDQ09JrcGhwcjNjYWHz55Zd9vvf69evIyMhAQ0MDcnJysH79+tvWr1mzBvfffz8OHjyIgwcP9ruvrKwsfPLJJ5g+fTpee+01AMDatWuxevVq/O1vf0NkZKRr+/3796OxsRF1dXU4deoUTpw4gQ8//BBPPPEEIiMjsW3bNvz4xz/G+vXr8Z3vfGcgX5Jhg0UbJnx8fPDkk08CAJ566ikcPnz4rvc1atQo11So9PR0NDU1Abg1dauoqAgA8PTTT7u2379/P/bv348pU6YgLS0Nn3/+ORobGwEAr7zyCjZu3Ah/f3/Xe0cio+oA9K3ExERUVVXdtuzatWtobW3FpEmTcPr0aTidTte6mzdvetzXvVxA6efn53q/r68venp6+tyvpmn4xS9+gWeffbbXOqvVCh8fH1y6dAlOp1PXa7682cj8W3upmTNn4saNG9ixYweAWxdF/vSnP0VpaSkCAgIQGxuLU6dOwel0orm5GXV1da73Op1OV0n/9Kc/ITs7u9f+g4KC0NHRcdf5Hn30UVRWVgIA3n77bdfyWbNm4Y9//KPrxIjNZsPly5fR09OD4uJi7Nq1CwkJCdiyZctdH3uoY9G8iMFgwO7du1FVVYWJEyciLCwMPj4+eOGFFwDc+kGfMGECEhMTsWbNGtftCABg7NixqKurQ3JyMg4cOIB169b12n9JSQlmz57t9mTIndi6dSu2bduGlJSU265O/8EPfoAf/vCHrhMlixYtQkdHBzZs2IBp06YhOzsbW7Zsweuvv47PPvvsro491PH0vhf7+OOPUVRUhN27d99WKhp6WDQiAfzoSCSARSMSwKIRCWDRiASwaEQCWDQiASwakYD/B7zevt5pmH4BAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 216x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3,5), facecolor='white')\n",
    "plt.pcolormesh(np.arange(0,num_qubits,1), time_steps*delta_t, probability_density)\n",
    "plt.xlabel('Qubit index')\n",
    "plt.ylabel('Time (1/J)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "id": "96514e41",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "## Grade and submit your solution\n",
    "from qc_grader.challenges.spring_2022 import grade_ex2b\n",
    "\n",
    "grade_ex2b(probability_density)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e1839f4",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "<b>Hardware challenge I</b> \n",
    "    \n",
    "**(This section will not be graded, but take note of the difference between simulation and hardware results.)**\n",
    "\n",
    "Run the circuits for the quantum random walk on real hardware and extract the probability of finding an excitation on each qubit.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "646ef3fe",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit import IBMQ\n",
    "\n",
    "# Loading your IBM Quantum account\n",
    "IBMQ.load_account()\n",
    "IBMQ.providers() # see a list of providers you have access to"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1bee97c6-012e-4632-b7fb-753bc5ab1ea7",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the special provider assigned to you using information from the output above\n",
    "hub_name = '' # e.g. 'qc-spring-22-1'\n",
    "group_name = '' # e.g. 'group-2'\n",
    "project_name = '' # e.g. 'recPdHH04wfWiNHjG'\n",
    "provider = IBMQ.get_provider(hub=hub_name, group=group_name, project=project_name)\n",
    "\n",
    "# Get `ibm_nairobi` backend from the provider\n",
    "backend_name = 'ibm_nairobi'\n",
    "backend = provider.get_backend(backend_name)\n",
    "backend # See details of the `ibm_nairobi` quantum system"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "id": "b1cd7206",
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_layout=[0 , 1 , 3 , 5 , 4]\n",
    "\n",
    "hardware_transpiled_circuits=[]\n",
    "for circ in circuits:\n",
    "    \n",
    "    hardware_circ=deepcopy(circ)\n",
    "    hardware_circ.barrier()\n",
    "    hardware_circ.measure(range(num_qubits), range(num_qubits))\n",
    "    hardware_transpiled_circuits.append(transpile(hardware_circ, backend, initial_layout=initial_layout, optimization_level=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "b890b98b",
   "metadata": {},
   "outputs": [],
   "source": [
    "shots=1024\n",
    "job = execute(hardware_transpiled_circuits, backend=backend, shots=shots)\n",
    "job_monitor(job)\n",
    "print('Job ID', job.job_id())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "709056a0",
   "metadata": {},
   "outputs": [],
   "source": [
    "experiment_results=job.result()\n",
    "\n",
    "probability_density_exp=[]\n",
    "for output in experiment_results.get_counts():\n",
    "    ps=[]\n",
    "    \n",
    "    ###EDIT CODE BELOW (Extract the probability of finding the excitation on each qubit)\n",
    "\n",
    "    ###DO NOT EDIT BELOW\n",
    "    \n",
    "    probability_density_exp.append(ps)\n",
    "\n",
    "plt.figure(figsize=(3,5), facecolor='white')\n",
    "plt.pcolormesh(np.arange(-.5,num_qubits,1), time_steps*delta_t, probability_density_exp)\n",
    "plt.xlabel('Qubit index')\n",
    "plt.ylabel('Time (1/J)')"
   ]
  },
  {
   "attachments": {
    "Anderson_localization.jpg": {
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    }
   },
   "cell_type": "markdown",
   "id": "64879624",
   "metadata": {},
   "source": [
    "## 2. Anderson localization\n",
    "\n",
    "Particle propagation is significantly impacted by the introduction of disorder in the site energies, leading to Anderson localization. Lattice inhomogeneity causes scattering and leads to quantum interference that tends to inhibit particle propagation, a signature of localization. The wavefunction of a localized particle rapidly decays away from its initial position, effectively confining the particle to a small region of the lattice.\n",
    "\n",
    "Phillip Anderson first proposed that scattering from disorder can bring transport to a complete halt in 1958 [1]. Before Anderson's discovery, scientists modelled crystal disorders as perturbations that scatter electrons randomly, treating electrons as point-like particles. This logic led to the description of transport in such media as Brownian motion, which underlies Ohm's law. However, Anderson revisited the effect of disorder on the evolution of an electron's wavefunction in an otherwise periodic crystal [2]. Anderson analysed the problem in the quantum regime, thus fundamentally accounting for the wave nature of the electron, and found that the classical diffusive motion of the electron breaks down as the electronic wavefunction becomes exponentially localized, under a broad range of conditions. Hence, when the electron is initially placed on one atom, its wavefunction will no longer expand to cover the whole crystal with time, but it will rather remain localized around its initial position. Thus, the material will cease to conduct charge, and eventually become an insulator. This localization phenomenon is a direct consequence of interference between different paths arising from multiple scattering of the electron by lattice defects.\n",
    "\n",
    "<div>\n",
    "<img src=\"attachment:Anderson_localization.jpg\" width=\"600\"/>\n",
    "</div> figure from reference [2]\n",
    "\n",
    "We can study Anderson localization using the tight-binding Hamiltonian. The Hamltonian in the presence of disorder in site energies takes the following form: \n",
    "$$H_{\\rm tb}/\\hbar = \\sum^{3}_{i=0} (X_i X_{i+1} + Y_i Y_{i+1}) + \\sum_i \\epsilon_i Z_i $$\n",
    "\n",
    "By changing the $\\epsilon_i$ values we can imitate disorder by creating an Aubry-Andre (AA) quasicrystal which leads to Anderson localization. In this lattice model, $\\epsilon_i=W \\rm{cos}(2\\pi\\beta i)$ where $W$ is the disorder strength, and $\\beta$ determines the quasicrystal periodicity.\n",
    "\n",
    "[1] https://physicstoday.scitation.org/doi/10.1063/1.3206091?feed=most-cited\n",
    "\n",
    "[2] https://www.nature.com/articles/nphoton.2013.30"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "id": "f34b668d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "beta=(np.sqrt(5)-1)/2 # DO NOT EDIT\n",
    "AA_patern=np.cos(2*np.pi*beta*np.arange(num_qubits)) # DO NOT EDIT\n",
    "\n",
    "plt.plot(np.linspace(-0.5,4.5,101), np.cos(2*np.pi*beta*np.linspace(-0.5,4.5,101)), '--')\n",
    "plt.plot(np.arange(num_qubits), AA_patern, 'o', label=r'$\\epsilon_i$')\n",
    "plt.xlabel('Position')\n",
    "plt.ylabel('Energy')\n",
    "plt.legend()\n",
    "plt.title('Aubry-Andre potential')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 182,
   "id": "cc27305f-14bc-4926-9979-29799e23b9d5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        , -0.73736888,  0.08742572,  0.60843886, -0.98471349])"
      ]
     },
     "execution_count": 182,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AA_patern"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73c8a13e",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "<b>Challenge question 2d</b> \n",
    "\n",
    "Modify each tight-binding trotter step to include an arbitrary phase used to simulate Anderson localization.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "be5739cf-0f15-4fc9-8183-3d6f618605ec",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 280,
   "id": "9349ca57-b96a-4f4b-ba3e-7701da5a2a4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 333.118x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 280,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Trot_qr_disorder = QuantumRegister(num_qubits)\n",
    "Trot_qc_disorder = QuantumCircuit(Trot_qr_disorder, name='Trot disorder')\n",
    "\n",
    "Trot_qc_disorder.append(Trot_tb_gate,[0,1,2,3,4])\n",
    "deltas=[Parameter('delta_{:d}'.format(idx)) for idx in range(num_qubits)]\n",
    "\n",
    "###EDIT CODE BELOW (add a parametric disorder to each qubit)\n",
    "for i in range(num_qubits):\n",
    "    Trot_qc_disorder.rz(2*deltas[i]*delta_t,Trot_qr_disorder[i])\n",
    "    \n",
    "###DO NOT EDIT BELOW\n",
    "    \n",
    "# Convert custom quantum circuit into a gate\n",
    "Trot_disorder_gate = Trot_qc_disorder.to_instruction()\n",
    "\n",
    "Trot_qc_disorder.draw()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "id": "b13e0211-d494-474a-a56c-7a38cfe365a2",
   "metadata": {},
   "outputs": [],
   "source": [
    "delta_t=0.15\n",
    "time_steps=np.arange(1,20,1)\n",
    "\n",
    "W=2 # DO NOT EDIT\n",
    "\n",
    "disorders=W*AA_patern # DO NOT EDIT\n",
    "\n",
    "disorder_circuits=[]\n",
    "\n",
    "for n_steps in time_steps:\n",
    "\n",
    "    qr = QuantumRegister(num_qubits)\n",
    "    cr = ClassicalRegister(num_qubits)\n",
    "    qc = QuantumCircuit(qr, cr)\n",
    "\n",
    "    qc.x(0)\n",
    "    \n",
    "    for _ in range(n_steps):\n",
    "        qc.append(Trot_disorder_gate, [i for i in range(num_qubits)])\n",
    "\n",
    "    qc = qc.bind_parameters({t: delta_t})\n",
    "    qc = qc.bind_parameters({deltas[idx]: disorders[idx] for idx in range(num_qubits)})\n",
    "\n",
    "    disorder_circuits.append(qc)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "553600c1",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-danger\">\n",
    "    \n",
    "<b>Challenge question 2e</b> \n",
    "\n",
    "Finally, extract the probability of finding an excitation on each qubit.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 282,
   "id": "8c6a37a7-6587-4a9f-8b19-bfd7c7188a9b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "eaa6bb347a0f4c0c9ed563a49b346c12",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "  0%|          | 0/19 [00:00<?, ?it/s]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import transpile\n",
    "\n",
    "# Use Aer's statevector simulator\n",
    "from qiskit import Aer\n",
    "\n",
    "# Run the quantum circuit on a statevector simulator backend\n",
    "backend_sim = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "probability_density_localization=[]\n",
    "for circ in tqdm(disorder_circuits):\n",
    "\n",
    "    transpiled_circ=transpile(circ, backend_sim, optimization_level=3)\n",
    "\n",
    "    job_sim = backend_sim.run(transpiled_circ)\n",
    "\n",
    "    # Grab the results from the job.\n",
    "    result_sim = job_sim.result()\n",
    "    outputstate = result_sim.get_statevector(transpiled_circ, decimals=5)\n",
    "    \n",
    "    ps=[]\n",
    "    \n",
    "    ###EDIT CODE BELOW (Extract the probability of finding the excitation on each qubit)\n",
    "    for i in range(transpiled_circ.num_qubits):\n",
    "        ps.append(outputstate.probabilities([i])[1])\n",
    "    ###DO NOT EDIT BELOW\n",
    "    \n",
    "    probability_density_localization.append(ps)\n",
    "    \n",
    "probability_density_localization=np.array(probability_density_localization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 283,
   "id": "d70fdf7d-33f7-4054-84b8-1b53290cc051",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Time (1/J)')"
      ]
     },
     "execution_count": 283,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 216x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(3,5), facecolor='white')\n",
    "plt.pcolormesh(np.arange(0,num_qubits,1), time_steps*delta_t ,probability_density_localization)\n",
    "plt.xlabel('Qubit index')\n",
    "plt.ylabel('Time (1/J)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 284,
   "id": "58b46fd0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Submitting your answer. Please wait...\n",
      "Congratulations 🎉! Your answer is correct and has been submitted.\n"
     ]
    }
   ],
   "source": [
    "## Grade and submit your solution\n",
    "from qc_grader.challenges.spring_2022 import grade_ex2c\n",
    "\n",
    "grade_ex2c(probability_density_localization)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6457aa8",
   "metadata": {},
   "source": [
    "<div class=\"alert alert-block alert-info\">\n",
    "    \n",
    "<b>Hardware challenge II</b> \n",
    "\n",
    "**(This section will not be graded, but take note of the difference between simulation and hardware results.)**    \n",
    "\n",
    "Run the circuits for the quantum random walk with disorder on real hardware and extract the probability of finding an excitation on each qubit.\n",
    "    \n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45cf4789",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.tools.monitor import job_monitor\n",
    "\n",
    "provider = IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(hub='qc-spring-2022', group='group-1', project='project-1')\n",
    "backend = provider.get_backend('ibm_nairobi')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "010cb06b",
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_layout=[0 , 1 , 3 , 5 , 4]\n",
    "\n",
    "hardware_transpiled_circuits_disordered=[]\n",
    "for circ in disorder_circuits:\n",
    "    \n",
    "    hardware_circ=deepcopy(circ)\n",
    "    hardware_circ.barrier()\n",
    "    hardware_circ.measure(range(num_qubits), range(num_qubits))\n",
    "    hardware_transpiled_circuits_disordered.append(transpile(hardware_circ, backend, initial_layout=initial_layout, optimization_level=3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "0ccc52d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "shots=1024\n",
    "job_disorder = execute(hardware_transpiled_circuits_disordered, backend=backend, shots=shots)\n",
    "job_monitor(job_disorder)\n",
    "print('Job ID', job_disorder.job_id())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ad60c532",
   "metadata": {},
   "outputs": [],
   "source": [
    "disorder_experiment_results=job_disorder.result()\n",
    "\n",
    "disorder_probability_density_exp=[]\n",
    "for output in disorder_experiment_results.get_counts():\n",
    "    ps=[]\n",
    "    \n",
    "    ###EDIT CODE BELOW (Extract the probability of finding the excitation on each qubit)\n",
    "    \n",
    "    ###DO NOT EDIT BELOW\n",
    "    \n",
    "    disorder_probability_density_exp.append(ps)\n",
    "    \n",
    "plt.figure(figsize=(3,5), facecolor='white')\n",
    "plt.pcolormesh(np.arange(-.5,num_qubits,1), time_steps*delta_t, disorder_probability_density_exp)\n",
    "plt.xlabel('Qubit index')\n",
    "plt.ylabel('Time (1/J)')"
   ]
  }
 ],
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{'operates': {'qubits': [2]}, 'purpose': 'drive', 'type': 'drive'}, 'd3': {'operates': {'qubits': [3]}, 'purpose': 'drive', 'type': 'drive'}, 'd4': {'operates': {'qubits': [4]}, 'purpose': 'drive', 'type': 'drive'}, 'd5': {'operates': {'qubits': [5]}, 'purpose': 'drive', 'type': 'drive'}, 'd6': {'operates': {'qubits': [6]}, 'purpose': 'drive', 'type': 'drive'}, 'm0': {'operates': {'qubits': [0]}, 'purpose': 'measure', 'type': 'measure'}, 'm1': {'operates': {'qubits': [1]}, 'purpose': 'measure', 'type': 'measure'}, 'm2': {'operates': {'qubits': [2]}, 'purpose': 'measure', 'type': 'measure'}, 'm3': {'operates': {'qubits': [3]}, 'purpose': 'measure', 'type': 'measure'}, 'm4': {'operates': {'qubits': [4]}, 'purpose': 'measure', 'type': 'measure'}, 'm5': {'operates': {'qubits': [5]}, 'purpose': 'measure', 'type': 'measure'}, 'm6': {'operates': {'qubits': [6]}, 'purpose': 'measure', 'type': 'measure'}, 'u0': {'operates': {'qubits': [0, 1]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u1': {'operates': {'qubits': [1, 0]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u10': {'operates': {'qubits': [5, 6]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u11': {'operates': {'qubits': [6, 5]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u2': {'operates': {'qubits': [1, 2]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u3': {'operates': {'qubits': [1, 3]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u4': {'operates': {'qubits': [2, 1]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u5': {'operates': {'qubits': [3, 1]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u6': {'operates': {'qubits': [3, 5]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u7': {'operates': {'qubits': [4, 5]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u8': {'operates': {'qubits': [5, 3]}, 'purpose': 'cross-resonance', 'type': 'control'}, 'u9': {'operates': {'qubits': [5, 4]}, 'purpose': 'cross-resonance', 'type': 'control'}}</td></tr><tr><td>rep_times</td><td>[1000.0]</td></tr><tr><td>conditional</td><td>False</td></tr><tr><td>dynamic_reprate_enabled</td><td>True</td></tr><tr><td>open_pulse</td><td>False</td></tr><tr><td>allow_q_object</td><td>True</td></tr><tr><td>processor_type</td><td>{'family': 'Falcon', 'revision': '5.11', 'segment': 'H'}</td></tr><tr><td>n_uchannels</td><td>12</td></tr><tr><td>sample_name</td><td>family: Falcon, revision: 5.11, segment: H</td></tr><tr><td>live_data</td><td>False</td></tr><tr><td>clops</td><td>2645</td></tr><tr><td>dtm</td><td>0.2222222222222222</td></tr><tr><td>simulator</td><td>False</td></tr><tr><td>memory</td><td>True</td></tr><tr><td>rep_delay_range</td><td>[0.0, 500.0]</td></tr><tr><td>credits_required</td><td>True</td></tr><tr><td>backend_name</td><td>ibm_nairobi</td></tr><tr><td>dt</td><td>0.2222222222222222</td></tr><tr><td>measure_esp_enabled</td><td>False</td></tr><tr><td>meas_levels</td><td>[1, 2]</td></tr><tr><td>timing_constraints</td><td>{'acquire_alignment': 16, 'granularity': 16, 'min_length': 64, 'pulse_alignment': 1}</td></tr><tr><td>default_rep_delay</td><td>250.0</td></tr><tr><td>multi_meas_enabled</td><td>True</td></tr><tr><td>pulse_num_channels</td><td>9</td></tr><tr><td>description</td><td>7 qubit device</td></tr><tr><td>meas_map</td><td>[[0, 1, 2, 3, 4, 5, 6]]</td></tr><tr><td>hamiltonian</td><td>$$\\begin{align} \\mathcal{H}/\\hbar = & \\sum_{i=0}^{6}\\left(\\frac{\\omega_{q,i}}{2}(\\mathbb{I}-\\sigma_i^{z})+\\frac{\\Delta_{i}}{2}(O_i^2-O_i)+\\Omega_{d,i}D_i(t)\\sigma_i^{X}\\right) \\\\ & + J_{0,1}(\\sigma_{0}^{+}\\sigma_{1}^{-}+\\sigma_{0}^{-}\\sigma_{1}^{+}) + J_{1,2}(\\sigma_{1}^{+}\\sigma_{2}^{-}+\\sigma_{1}^{-}\\sigma_{2}^{+}) + J_{4,5}(\\sigma_{4}^{+}\\sigma_{5}^{-}+\\sigma_{4}^{-}\\sigma_{5}^{+}) + J_{5,6}(\\sigma_{5}^{+}\\sigma_{6}^{-}+\\sigma_{5}^{-}\\sigma_{6}^{+}) \\\\ & + J_{1,3}(\\sigma_{1}^{+}\\sigma_{3}^{-}+\\sigma_{1}^{-}\\sigma_{3}^{+}) + J_{3,5}(\\sigma_{3}^{+}\\sigma_{5}^{-}+\\sigma_{3}^{-}\\sigma_{5}^{+}) \\\\ & + \\Omega_{d,0}(U_{0}^{(0,1)}(t))\\sigma_{0}^{X} + \\Omega_{d,1}(U_{1}^{(1,0)}(t)+U_{3}^{(1,3)}(t)+U_{2}^{(1,2)}(t))\\sigma_{1}^{X} \\\\ & + \\Omega_{d,2}(U_{4}^{(2,1)}(t))\\sigma_{2}^{X} + \\Omega_{d,3}(U_{5}^{(3,1)}(t)+U_{6}^{(3,5)}(t))\\sigma_{3}^{X} \\\\ & + \\Omega_{d,4}(U_{7}^{(4,5)}(t))\\sigma_{4}^{X} + \\Omega_{d,5}(U_{8}^{(5,3)}(t)+U_{10}^{(5,6)}(t)+U_{9}^{(5,4)}(t))\\sigma_{5}^{X} \\\\ & + \\Omega_{d,6}(U_{11}^{(6,5)}(t))\\sigma_{6}^{X} \\\\ \\end{align}$$</td></tr><tr><td>conditional_latency</td><td>[]</td></tr><tr><td>parametric_pulses</td><td>['gaussian', 'gaussian_square', 'drag', 'constant']</td></tr><tr><td>discriminators</td><td>['linear_discriminator', 'hw_qmfk', 'quadratic_discriminator']</td></tr><tr><td>coupling_map</td><td>[[0, 1], [1, 0], [1, 2], [1, 3], [2, 1], [3, 1], [3, 5], [4, 5], [5, 3], [5, 4], [5, 6], [6, 5]]</td></tr></table>"
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\n",
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