q_task.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "7a74ea7a",
   "metadata": {},
   "source": [
    "# Introduction"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c7ae54cd",
   "metadata": {},
   "source": [
    "In \"Task 2\" a generative model using a variational circuit is explored. \n",
    "Initially, we start with a set of 4 random 4-qubit quantum states. The goal is then to create and train a variational circuit that transforms input states into the following predefined output states:\n",
    "- If random state 1 is provided, it returns state |0011>\n",
    "- If random state 2 is provided, it returns state |0101>\n",
    "- If random state 3 is provided, it returns state |1010>\n",
    "- If random state 4 is provided, it returns state |1100>\n",
    "\n",
    "I chose this assignment because one of my main interests is in the area of variational quantum algorithms. My goal was to apply my knowledge from previous projects to a new problem and learn something new."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4ad0e571",
   "metadata": {},
   "source": [
    "To solve this problem, I implement a simplified version of the filtering variational quantum eigensolver.https://arxiv.org/pdf/2106.10055.pdf \n",
    "I was interested in learning more about this algorithm and took this as an opportunity to deepen my understanding of its application to a combinatorial optimization problem. Furthermore, I worked with David Amaro and Matthias Rosenkranz, the authors of the F-VQE paper, on an earlier project which helped me understand the algorithm.\n",
    "\n",
    "The main idea here is that applying a filtering operator $f=H^{-\\tau}$ to a quantum state $|\\Psi>$ shifts its probability distribution of eigenvectors in such a way that low energy states dominate. This idea borrows from imaginary time evolution. \n",
    "\n",
    "In general, any arbitrary wavefunction can be written as a superposition of eigenstates:\n",
    "\n",
    "\n",
    "$$\\psi(x,0) = \\sum_i a_i(0) \\psi_i(x) $$\n",
    "and\n",
    "$$ \\psi(x,t) = \\sum_i exp(-it E_n / \\hbar ) a_i(0) \\psi_i(x) $$\n",
    "\n",
    "\n",
    "Eigenstate don't change in their overall magnitude with increasing time evolution but rotate with a frequency proportional to the corresponding energy eigenvalue $En/\\hbar$.\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "With the substitution $(it \\rightarrow{} \\tau )$ \n",
    "\n",
    "\n",
    "$$ \\psi(x,\\tau) = \\sum_i exp(- \\tau E_n / \\hbar ) a_i(0) \\psi_i(x) $$\n",
    "\n",
    "we now see that $\\psi(x,t)$ at imaginary time no longer consists of an \"oscillating\" superposition of energy eigenstates, but of an \"exponentially decaying\" superposition of energy eigenstates. Hereby, the higher energy states are decaying faster, so that with time the state with the lowest energy dominates the wave function.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a15cc06c",
   "metadata": {},
   "source": [
    "The F-VQE algorithm can then be summarized as follows:\n",
    "- Prepare an initial state $|\\psi_0>$ that has finite overlap with the ground state $P(\\lambda_0) > 0$.\n",
    "- Iteratively, the application of the filter operator $F_t$ to $|\\psi_{t-1}>$ is approximated by a state $|\\psi_t>$. \n",
    "For this purpose, a parameterized quantum circuit ansatz $|\\psi(\\theta)>$ is used, which depends on a vector of m parameters\n",
    "$\\theta = (\\theta_1, . . . , \\theta_m)$. \n",
    "At each optimization step t, the parameters that minimize the Euclidean distance between the parameterized quantum state and $|F_t \\psi_{t-1}>$ are sought. For this purpose, a gradient-based approach is chosen, where \n",
    "\n",
    "$$\\theta_t \\propto \\theta_{t-1}-\\sum_i \\frac{\\partial C_t(\\theta)}{\\partial \\theta_i} \\propto \\theta_{t-1}-\\sum_i <\\psi_{t-1}|F_t|\\psi(\\theta \\pm \\frac{\\pi}{2})>$$\n",
    "Simply put, we rotate the parameter values by $\\pm \\frac{\\pi}{2}$, calculate each result, and choose which rotation works best.\n",
    "- Repeat for a given number of optimization steps.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8d92e55",
   "metadata": {},
   "source": [
    "# Generating a random 4-qubit state"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1199dbbc",
   "metadata": {},
   "source": [
    "The first challenge of this task is to generate a random 4-qubit state. For my quantum framework, I'm using Pytket, as I'm the most familiar with it and later computations are simple.\n",
    "As suggested in the problem description, for my random initialization I use $R_x$,$R_y$,$R_z$ and $Cnot$ gates initialized with random values $\\theta$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "0f9b74ec",
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from pytket.circuit import Circuit\n",
    "from pytket.extensions.qiskit import AerStateBackend, AerBackend  \n",
    "from pytket.circuit.display import render_circuit_jupyter\n",
    "from pytket.utils.results import probs_from_state  \n",
    "from qiskit.quantum_info import partial_trace, entropy, Statevector  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "7437a2fa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initial_ansatz(params):\n",
    "    params = params / np.pi  # pytket works in units of pi\n",
    "    param_index = 0\n",
    "    c = Circuit(n_qubits)\n",
    "\n",
    "    for q in range(n_qubits):\n",
    "        c.Rx(params[param_index], q)\n",
    "        param_index += 1\n",
    "    for q in range(n_qubits):\n",
    "        c.Ry(params[param_index], q)\n",
    "        param_index += 1\n",
    "    for q in range(n_qubits):\n",
    "        c.Rz(params[param_index], q)\n",
    "        param_index += 1\n",
    "\n",
    "    # This creates a so called \"Checkerboard\"-Ansatz with the Cnot gates.\n",
    "    # Usually, I get better performance compared to a \"Ladder\"-Ansatz, hence this choice\n",
    "    for q in np.arange(0, n_qubits - 1, 2):\n",
    "        c.CX(q, q + 1)\n",
    "    for q in np.arange(1, n_qubits - 1, 2):\n",
    "        c.CX(q, q + 1)\n",
    "    return c\n",
    "\n",
    "n_qubits = 4\n",
    "n_gates = 3\n",
    "\n",
    "#Initialize #Rx,Ry,Rz gates with normally distributed values of rotations.\n",
    "initial_params = np.random.rand(n_gates*n_qubits)*np.pi/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "cfc979b2",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "\n",
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       "    border-top: none;\n",
       "    border-bottom: none;\n",
       "    height: calc(var(--box-height) + 2px);\n",
       "    z-index: 1;\n",
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       "</style>\n",
       "\n",
       "\n",
       "</head>\n",
       "<body>\n",
       "    <div >\n",
       "        <div class=\"circuit-preview condensed\">\n",
       "    <div class=\"circuit-container nested\">\n",
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       "        \n",
       "            <div class=\"qubit\">q[0]</div>\n",
       "        \n",
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       "        \n",
       "            <div class=\"qubit\">q[2]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[3]</div>\n",
       "        \n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.05725406660477411)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.1902257575569156)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.14408045745888576)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.16611633852137603)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.3560879762022651)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.48672112299254655)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.3622936067652955)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.34022752771690873)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.18776668763313348)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.028330623990913684)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.14710814866265448)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.005031474243580636)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "        <div class=\"circuit-layer qubits\">\n",
       "        \n",
       "            <div class=\"qubit\">q[0]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[1]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[2]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[3]</div>\n",
       "        \n",
       "        \n",
       "    </div>\n",
       "    </div>\n",
       "</div>\n",
       "    </div>\n",
       "</body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "render_circuit_jupyter(initial_ansatz(initial_params))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "844e53ce",
   "metadata": {},
   "source": [
    "To test whether or not our chosen initialization ansatz results in a random \"input\", we can calculate the state vector after applying the circuit and examine the probability distribution of different bitstring configurations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "2104354a",
   "metadata": {},
   "outputs": [],
   "source": [
    "backend = AerBackend()\n",
    "\n",
    "def sample_initial_ansatz(params, state):\n",
    "    c = initial_ansatz(params)\n",
    "    probs = probs_from_state(state)\n",
    "    return probs\n",
    "\n",
    "def get_initial_state(params):\n",
    "    c = initial_ansatz(params)\n",
    "    b = AerStateBackend()\n",
    "    return b.get_state(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cdfb1114",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_probs(probs_dict,title=\"\"):\n",
    "    name = [str(i) for i in probs_dict.keys()]\n",
    "    plt.bar(np.arange(len(probs_dict)), height=probs_dict.values(),edgecolor='b',tick_label=name)\n",
    "    plt.xticks(rotation=90)\n",
    "    plt.xlabel('Bitstring spectrum')\n",
    "    plt.ylabel('Probability')\n",
    "    if title != \"\":\n",
    "        plt.title(title)\n",
    "    plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "10188157",
   "metadata": {},
   "outputs": [],
   "source": [
    "initial_state = get_initial_state(initial_params)\n",
    "initial_probs = sample_initial_ansatz(initial_params,initial_state) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f0f87812",
   "metadata": {
    "scrolled": true
   },
   "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": [
    "plot_probs(initial_probs,\"Probability dist. of random initialization\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91cbfefd",
   "metadata": {},
   "source": [
    "Even though some states are more likely than others here, I would argue that this random overlay is good enough for our purposes. We store 4 random initializations of the first layer for later calculations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "42801127",
   "metadata": {},
   "outputs": [],
   "source": [
    "r_state_1 = np.array([0.87077731, 0.9608887 , 0.65910624, 0.38913493, 0.55916058,\n",
    "       1.19042189, 0.02260924, 0.18232648, 0.07226078, 0.06397665,\n",
    "       1.34375434, 1.10530318])\n",
    "\n",
    "r_state_2 = np.array([0.74483051, 0.15367754, 0.77222841, 0.74372772, 0.27206486,\n",
    "       0.68149258, 0.62596977, 0.96737507, 0.99760277, 0.07116337,\n",
    "       0.58844012, 0.98309846])\n",
    "\n",
    "r_state_3 = np.array([0.79032459, 1.3453711 , 1.03467354, 0.2559368 , 0.11084913,\n",
    "       1.00910984, 0.04164387, 0.92013413, 1.47691021, 0.90395272,\n",
    "       0.60973589, 1.01047477])\n",
    "\n",
    "r_state_4 = np.array([0.11182287, 0.50104575, 1.32712704, 0.03655547, 1.2793641 ,\n",
    "       0.44273644, 0.18561288, 1.09443218, 0.98794111, 1.37832982,\n",
    "       1.1546469 , 1.26210489])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c5e6196d",
   "metadata": {},
   "source": [
    "# Initialize full circuit\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a661bf8",
   "metadata": {},
   "source": [
    "Now that we have a method to initialize a random state with a given set of initial parameters, we can build the rest of the circuit. Here, the structure of the gates $R_x$, $R_y$, $R_z$ and $Cnot$ is repeated in several layers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "061ce290",
   "metadata": {},
   "outputs": [],
   "source": [
    "def ansatz(params):\n",
    "    params = params / np.pi    \n",
    "    param_index = 0\n",
    "    c = Circuit(n_qubits)\n",
    "    \n",
    "    #Initialize one of four 'random' states\n",
    "    for q in range(n_qubits):\n",
    "        c.Rx(params[param_index], q)\n",
    "        param_index += 1\n",
    "    for q in range(n_qubits):\n",
    "        c.Ry(params[param_index], q)\n",
    "        param_index += 1\n",
    "    for q in range(n_qubits):\n",
    "        c.Rz(params[param_index], q)\n",
    "        param_index += 1\n",
    "\n",
    "    for q in np.arange(0, n_qubits - 1, 2):\n",
    "        c.CX(q, q + 1)\n",
    "    for q in np.arange(1, n_qubits - 1, 2):\n",
    "        c.CX(q, q + 1)\n",
    "        \n",
    "    #Initialize rest of circuit used to solve the task\n",
    "        \n",
    "    for l in range(n_layers):\n",
    "        for q in range(n_qubits):\n",
    "            c.Rx(params[param_index], q)\n",
    "            param_index += 1\n",
    "        for q in range(n_qubits):\n",
    "            c.Ry(params[param_index], q)\n",
    "            param_index += 1\n",
    "        for q in range(n_qubits):\n",
    "            c.Rz(params[param_index], q)\n",
    "            param_index += 1\n",
    "            \n",
    "        for q in np.arange(0, n_qubits - 1, 2):\n",
    "            c.CX(q, q + 1)\n",
    "        for q in np.arange(1, n_qubits - 1, 2):\n",
    "            c.CX(q, q + 1)\n",
    "\n",
    "    return c\n",
    "\n",
    "n_qubits = 4\n",
    "n_layers = 2 \n",
    "n_gates = 3\n",
    "n_params = n_qubits * n_layers *n_gates   \n",
    "\n",
    "\n",
    "initial_params = r_state_1\n",
    "circuit_params = np.random.rand(n_params)*np.pi/2\n",
    "params = np.concatenate((initial_params,circuit_params))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "bba11676",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "\n",
       "<!DOCTYPE html>\n",
       "<html lang=\"en\">\n",
       "<head>\n",
       "    <meta charset=\"UTF-8\">\n",
       "    \n",
       "<style>\n",
       "body {\n",
       "    font-family: \"roboto\", system-ui, sans-serif;\n",
       "}\n",
       "\n",
       "/* FOR DISPLAYING CIRCUITS */\n",
       "/* Main preview container */\n",
       ".circuit-preview{\n",
       "    width: 100%;\n",
       "    height: 100%;\n",
       "    padding: 20px;\n",
       "    text-align: center;\n",
       "\n",
       "    /* Define some variables */\n",
       "    --box-height: 40px;\n",
       "    --wire-col: black;\n",
       "    --c-wire-col: grey;\n",
       "}\n",
       ".circuit-preview.condensed{\n",
       "    overflow: auto;\n",
       "}\n",
       "\n",
       ".circuit-container{\n",
       "    max-width: 100%;\n",
       "    display: flex;\n",
       "    flex-flow: row wrap;\n",
       "    justify-content: center;\n",
       "    align-content: flex-start;\n",
       "    margin: auto;\n",
       "    width: fit-content;\n",
       "    background: rgba(255, 255, 255, 1);\n",
       "}\n",
       ".circuit-preview.condensed > .circuit-container{\n",
       "    flex-wrap: nowrap;\n",
       "    min-width: fit-content;\n",
       "}\n",
       ".circuit-container.nested{\n",
       "    position: relative;\n",
       "    flex-wrap: nowrap;\n",
       "    margin: -2px 0;\n",
       "}\n",
       ".nested-circuit-container{\n",
       "    display: flex;\n",
       "    overflow: auto;\n",
       "    max-width: 400px;\n",
       "    background: rgba(130,255,140,0.2);\n",
       "    outline: 1px solid darkseagreen;\n",
       "    outline-offset: -1px;\n",
       "}\n",
       ".nested-circuit-container::-webkit-scrollbar {\n",
       "    height: 0;\n",
       "    width: 0;\n",
       "}\n",
       ".nested-circuit-container > *{\n",
       "    margin: auto;\n",
       "}\n",
       ".circuit-end{\n",
       "    width: 2px;\n",
       "    height: auto;\n",
       "    border: 2px solid black;\n",
       "    margin: calc(var(--box-height)/2) 0 calc(var(--box-height)/2 + 20px);\n",
       "}\n",
       ".circuit-layer{\n",
       "    min-width: 40px;\n",
       "    width: max-content;\n",
       "    display: flex;\n",
       "    flex-flow: column nowrap;\n",
       "    flex-grow: 1;\n",
       "    justify-content: space-between;\n",
       "    align-items: stretch;\n",
       "    margin-bottom: 20px;\n",
       "}\n",
       ".circuit-container:not(.nested) > .circuit-layer:nth-child(2),\n",
       ".circuit-container:not(.nested) > .circuit-layer:nth-last-child(2),\n",
       ".circuit-container.nested > .circuit-layer:nth-child(2),\n",
       ".circuit-container.nested > .circuit-layer:nth-last-child(2),\n",
       ".gate_container.nested > .circuit-layer:first-child,\n",
       ".gate_container.nested > .circuit-layer:last-child{\n",
       "    min-width: 10px;\n",
       "}\n",
       ".nested .circuit-layer{\n",
       "    margin-bottom: 0px;\n",
       "}\n",
       ".circuit-layer.hover-highlight:not(:first-child):not(:last-child):hover{\n",
       "    background: rgba(0, 0, 0, 0.05);\n",
       "}\n",
       ".flex_wire{\n",
       "    flex-grow: 1;\n",
       "}\n",
       "/* Display qubit names at start of circuit */\n",
       ".circuit-layer.qubits{\n",
       "    flex-grow: 0;\n",
       "    color: black;\n",
       "}\n",
       ".qubit{\n",
       "    height: calc(var(--box-height) - 20px);\n",
       "    padding: 10px;\n",
       "    text-align: center;\n",
       "    font-family: monospace;\n",
       "    box-sizing: content-box;\n",
       "}\n",
       ".wire{\n",
       "    height: 0;\n",
       "    border: 1px solid var(--wire-col);\n",
       "    background: var(--wire-col);\n",
       "    margin: calc(var(--box-height)/2) 0;\n",
       "}\n",
       ".wire.transparent-wire{\n",
       "    border-color: transparent;\n",
       "    background: transparent;\n",
       "}\n",
       "\n",
       "/* Generic base for our gates */\n",
       ".gate_container{\n",
       "    position: relative;\n",
       "    min-width: fit-content;\n",
       "}\n",
       ".gate_container.nested{\n",
       "    display: flex;\n",
       "    flex-wrap: nowrap;\n",
       "}\n",
       ".gate_container.nested:after{\n",
       "    display: flex;\n",
       "    flex-wrap: nowrap;\n",
       "}\n",
       ".gate_container .classical{\n",
       "    border-color: var(--c-wire-col);\n",
       "    background: var(--c-wire-col) !important;\n",
       "}\n",
       ".gate{\n",
       "    position: relative;\n",
       "    height: calc(var(--box-height) - 16px);\n",
       "    margin: 0 9px;\n",
       "    padding: 9px 5px;\n",
       "    border: 1px solid darkseagreen;\n",
       "    border-bottom: none;\n",
       "    border-top: none;\n",
       "    text-align: left;\n",
       "    background: darkseagreen;\n",
       "    z-index: 2;\n",
       "    display: flex;\n",
       "    box-sizing: content-box;\n",
       "}\n",
       ".wire-label{\n",
       "    color: green;\n",
       "    padding: 10px 0;\n",
       "    width: fit-content;\n",
       "    height: calc(var(--box-height) - 18px);\n",
       "}\n",
       ".gate_top > .wire-label,\n",
       ".gate_bottom > .wire-label {\n",
       "    padding-top: 0;\n",
       "}\n",
       ".nested-label-layer{\n",
       "    background: darkseagreen;\n",
       "    padding: 0 5px;\n",
       "}\n",
       "\n",
       "/* Multi-qubit gates */\n",
       ".gate_bottom{\n",
       "    height: calc(var(--box-height) - 18px);\n",
       "    margin-bottom: 10px;\n",
       "    padding-bottom: 0;\n",
       "    border-bottom: 1px solid darkseagreen;\n",
       "}\n",
       ".gate_top{\n",
       "    height: calc(var(--box-height) - 18px);\n",
       "    margin-top: 10px;\n",
       "    padding-top: 0;\n",
       "    border-top: 1px solid darkseagreen;\n",
       "}\n",
       ".gate_name{\n",
       "    text-align: center;\n",
       "    flex-grow: 1;\n",
       "    color: black;\n",
       "}\n",
       "/* Single qubit gate*/\n",
       ".gate_box{\n",
       "    height: calc(var(--box-height) - 20px);\n",
       "    margin: 10px;\n",
       "    padding: 0 5px;\n",
       "    border: 1px solid darkseagreen !important;\n",
       "    text-align: center;\n",
       "}\n",
       "\n",
       "/* Special gates */\n",
       ".gate_connection {\n",
       "    position: absolute;\n",
       "    top: -3px;\n",
       "    left: -1px;\n",
       "    border: none;\n",
       "    margin: calc(var(--box-height)/2) calc(50% - 5px);\n",
       "    padding: 0;\n",
       "}\n",
       ".gate_swap {\n",
       "    height: 20px;\n",
       "    width: 20px;\n",
       "    margin: calc(var(--box-height)/2 - 6px) calc(50% - 9px);\n",
       "    background: url(\n",
       "data:image/svg+xml;utf8,%0A%3C%21--%20Generated%20with%20http%3A//jxnblk.com/paths%20--%3E%0A%3Csvg%0A%20%20xmlns%3D%27http%3A//www.w3.org/2000/svg%27%0A%20%20viewBox%3D%270%200%2064%2064%27%0A%20%20width%3D%2764%27%20height%3D%2764%27%0A%20%20fill%3D%27currentcolor%27%3E%0A%20%20%3Cpath%20d%3D%27M60%200%20L32%2028%20L4%200%20L0%204%20L28%2032%20L0%2060%20L4%2064%20L32%2036%20L60%2064%20L64%2060%20L36%2032%20L64%204%27%20/%3E%0A%3C/svg%3E\n",
       ") center;\n",
       "    background-size: cover;\n",
       "}\n",
       ".gate_measure {\n",
       "    height: 20px;\n",
       "    width: 25px;\n",
       "    margin: calc(var(--box-height)/2 - 10px) calc(50% - 11px);\n",
       "    background: url(\n",
       "data:image/svg+xml;utf8,%0A%3C%21--%20Generated%20with%20http%3A//jxnblk.com/paths%20--%3E%0A%3Csvg%0A%20%20xmlns%3D%27http%3A//www.w3.org/2000/svg%27%0A%20%20viewBox%3D%27-10%20-10%2084%2084%27%0A%20%20width%3D%2764%27%20height%3D%2764%27%0A%20%20fill%3D%27white%27%0A%20%20stroke%3D%22black%22%0A%20%20stroke-width%3D%224px%22%0A%3E%0A%20%20%3Cpath%20d%3D%27M63%2C63%20C63%2C32%2048%2C16%2032%2C16%20C16%2C16%201%2C32%201%2C63%20L63%2C63%27%20/%3E%0A%20%20%3Cpath%20d%3D%22M32%2C63%20L56%2C16%22%20/%3E%0A%3C/svg%3E\n",
       ") center;\n",
       "    background-size: cover;\n",
       "}\n",
       ".gate_control {\n",
       "    position: absolute;\n",
       "    top: 0;\n",
       "    left: 0;\n",
       "    border-radius: 50%;\n",
       "    width: 6px;\n",
       "    height: 6px;\n",
       "    margin: calc(var(--box-height)/2 - 3px) calc(50% - 5px);\n",
       "    padding: 0;\n",
       "    border: 2px solid black;\n",
       "    background: black;\n",
       "}\n",
       ".gate_x {\n",
       "    top: -10px;\n",
       "    left: -6px;\n",
       "    border-radius: 50%;\n",
       "    border-color: black !important;\n",
       "    width: 20px;\n",
       "    background: url(\n",
       "data:image/svg+xml;utf8,%0A%3C%21--%20Generated%20with%20http%3A//jxnblk.com/paths%20--%3E%0A%3Csvg%0A%20%20xmlns%3D%27http%3A//www.w3.org/2000/svg%27%0A%20%20viewBox%3D%270%200%2064%2064%27%0A%20%20width%3D%2764%27%20height%3D%2764%27%0A%20%20fill%3D%27currentcolor%27%3E%0A%20%20%3Cpath%20d%3D%27M36%2064%20L36%2036%20L64%2036%20L64%2028%20L36%2028%20L36%200%20L28%200%20L28%2028%20L0%2028%20L0%2036%20L28%2036%20L28%2064%27%20/%3E%0A%3C/svg%3E\n",
       ") center;\n",
       "    background-size: cover;\n",
       "}\n",
       ".gate_reset{\n",
       "    margin: 11px 10px;\n",
       "    padding: 0 15px;\n",
       "    border: none !important;\n",
       "    border-left: 2px solid black !important;\n",
       "    background: url(\n",
       "data:image/svg+xml;utf8,%0A%3Csvg%0A%20%20xmlns%3D%27http%3A//www.w3.org/2000/svg%27%0A%20%20viewBox%3D%27-30%200%20104%2064%27%0A%20%20width%3D%2764%27%20height%3D%2764%27%0A%20%20fill%3D%22none%22%0A%20%20stroke%3D%22black%22%0A%20%20stroke-width%3D%224px%22%0A%3E%0A%20%20%3Cpath%20fill%3D%22darkseagreen%22%20stroke%3D%22none%22%20d%3D%22M%20-30%2032%20A%201%201%2090%200%201%2074%2032%20A%201%201%2090%200%201%20-30%2032%20Z%22/%3E%0A%20%20%3Cpath%20d%3D%22M%202%200%20L%202%2064%20Z%20M%2024%201%20L%2058%2032%20L%2024%2063%20M%2034%2034%22%20/%3E%0A%20%20%3Cpath%20d%3D%22M%2032%2034%20A%201%201%2090%200%201%2014%2034%20L%2014%2030%20A%201%201%2090%200%201%2032%2030%20Z%22%20/%3E%0A%3C/svg%3E\n",
       ") right no-repeat transparent;\n",
       "    background-size: contain;\n",
       "}\n",
       "\n",
       "/* Add wire sections coming in and out of the gate */\n",
       ".gate_in:before, .gate_in:after{\n",
       "    content: '';\n",
       "    position: absolute;\n",
       "    display: block;\n",
       "    top: calc(50% - 1px);\n",
       "    border: 1px solid var(--wire-col);\n",
       "    width: 9px;\n",
       "    height: 0;\n",
       "    background: var(--wire-col);\n",
       "    box-sizing: content-box;\n",
       "}\n",
       ".gate_in:before.classical,\n",
       ".gate_in:after.classical{\n",
       "    border-color: var(--c-wire-col);\n",
       "}\n",
       "\n",
       ".gate_in:before{\n",
       "    left: -12px;\n",
       "}\n",
       ".gate_out:after{\n",
       "    right: -12px;\n",
       "}\n",
       ".gate_top.gate_in:before, .gate_top.gate_out:after{\n",
       "    top:calc(50% - 6.5px)\n",
       "}\n",
       ".gate_bottom.gate_in:before, .gate_bottom.gate_out:after{\n",
       "    top:calc(50% + 4.5px)\n",
       "}\n",
       "\n",
       "\n",
       ".link-bottom, .link-top {\n",
       "    height: var(--box-height);\n",
       "    width: 0;\n",
       "    border: 1px solid black;\n",
       "    background: black;\n",
       "    position: absolute;\n",
       "    display: block;\n",
       "    left: calc(50% - 1px);\n",
       "    box-sizing: content-box;\n",
       "}\n",
       ".link-top{\n",
       "    top: calc(0px - var(--box-height)/2);\n",
       "}\n",
       ".link-bottom{\n",
       "    top: calc(var(--box-height)/2)\n",
       "}\n",
       ".half-link {\n",
       "    height: calc(var(--box-height) - 9px);\n",
       "}\n",
       ".half-link.link-bottom{\n",
       "    top: calc(var(--box-height)/2 + 11px)\n",
       "}\n",
       ".half-link.link-top{\n",
       "    top: calc(-2px - var(--box-height)/2);\n",
       "}\n",
       ".link-bottom.measurement{\n",
       "    width: 1px;\n",
       "    background: white;\n",
       "    border-top: none;\n",
       "    border-bottom: none;\n",
       "    height: calc(var(--box-height) + 2px);\n",
       "    z-index: 1;\n",
       "}\n",
       "</style>\n",
       "\n",
       "\n",
       "</head>\n",
       "<body>\n",
       "    <div >\n",
       "        <div class=\"circuit-preview condensed\">\n",
       "    <div class=\"circuit-container nested\">\n",
       "        <div class=\"circuit-layer qubits\">\n",
       "        \n",
       "            <div class=\"qubit\">q[0]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[1]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[2]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[3]</div>\n",
       "        \n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.27717702643752745)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.3058603727322906)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.20980003223742621)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.12386549527843735)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.1779863405782624)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.378923056316593)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.007196744611102007)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.05803632109709119)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.023001320657351935)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.020364400179920212)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.42773029102437476)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.3518289294243819)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.475651484363432)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.1284152247188673)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.16316248974767739)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.22278220494529077)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.3348436544112961)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.4775683202033598)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.15923956351735333)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.02715909459561816)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.33501877320447837)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.09650334327616455)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.19658517739050801)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.3099591864580246)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.1272920452091431)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.3446465992356522)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.2373679349482184)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.49148465230485294)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rx(0.05409217459579829)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.009301211783863061)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.2776318969491586)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.1777092150814934)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Ry(0.02301476868154695)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.4466228956935304)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.09408681567317145)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                <div class=\"gate gate_box gate_in gate_out \">\n",
       "                    <span class=\"gate_name\">Rz(0.1208065470825609)</span>\n",
       "                </div>\n",
       "            \n",
       "\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "                <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_control \"></div>\n",
       "                \n",
       "            </div>\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                        \n",
       "    \n",
       "        \n",
       "        \n",
       "            \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container nested\">\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "        <div class=\"gate_container\">\n",
       "            \n",
       "                    <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "                <div class=\"gate gate_box gate_connection gate_x\"></div>\n",
       "            \n",
       "\n",
       "            \n",
       "                <div class=\"link-top\"></div>\n",
       "            \n",
       "        </div>\n",
       "        <div class=\"flex_wire\">\n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        </div>\n",
       "    </div>\n",
       "        \n",
       "    \n",
       "\n",
       "        \n",
       "    \n",
       "    \n",
       "                    \n",
       "                \n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "            <div class=\"circuit-layer hover-highlight\">\n",
       "            \n",
       "                \n",
       "                \n",
       "                    \n",
       "    \n",
       "    \n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "            <div class=\"gate_container\">\n",
       "        <div class=\"wire \"></div>\n",
       "        \n",
       "    </div>\n",
       "        \n",
       "\n",
       "    \n",
       "    \n",
       "\n",
       "                \n",
       "            \n",
       "        </div>\n",
       "        \n",
       "        <div class=\"circuit-layer qubits\">\n",
       "        \n",
       "            <div class=\"qubit\">q[0]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[1]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[2]</div>\n",
       "        \n",
       "            <div class=\"qubit\">q[3]</div>\n",
       "        \n",
       "        \n",
       "    </div>\n",
       "    </div>\n",
       "</div>\n",
       "    </div>\n",
       "</body>\n",
       "</html>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "render_circuit_jupyter(ansatz(params))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6a5b751",
   "metadata": {},
   "source": [
    "# Defining cost function"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "380dafdb",
   "metadata": {},
   "source": [
    "A key aspect of any VQE algorithm is, of course, the cost function that we wish to minimize.\n",
    "In our case, the structure of $C$ is simple. We want to penalize configurations that have the wrong bitsring value in the wrong place. For example, if the optimal solution is $(0,0,1,1)$, a configuration like $(1,1,0,0)$ should be assigned a high cost. This is realized by the following cost function:   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "e44b1023",
   "metadata": {},
   "outputs": [],
   "source": [
    "def C1(x):\n",
    "    solution = (0,0,1,1)\n",
    "    return np.sum(np.abs(x-np.array(solution)))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e815e141",
   "metadata": {},
   "source": [
    "# Defining F-VQE prerequisites"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ceda2572",
   "metadata": {},
   "source": [
    "This section defines the auxiliary functions of the F-VQE \"protocol\". I have tried to arrange them in descending order of importance.\n",
    "As mentioned earlier, an important component of the F-VQE is the filtering operator $f$. It is defined as a real function $f(c)$, with $c$ as a real parameter, where $f^2(c)$ is strictly decreasing. Furthermore, the $\\tau>0$ function parameter can be varied at each optimization step.\n",
    "Here, an inverse filter was chosen because it showed the best performance in the F-VQE study."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "cf611569",
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(c, t):\n",
    "    if c==0:\n",
    "        return (c+0.0000001) ** (-t)    \n",
    "    return c ** (-t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07c005fd",
   "metadata": {},
   "source": [
    "The $\\tau$ parameter is continuously adjusted to keep the gradient norm as close as possible to a desired large and fixed value to prevent the gradient from disappearing. \n",
    " \n",
    "In this case, the implementation is done using a simple heuristic diretly taken from the F-VQE paper.\n",
    "At each iteration step, we want to choose $\\tau$ such that the gradient norm is as close as possible but below a certain threshold $r$, i.e., we solve the implicit equation $\\text{gradient_norm}(\\tau) = r$\n",
    "\n",
    "\n",
    "For this we evaluate the gradient norm for increasing values\n",
    "of $\\tau$ until an upper bound is found such that $\\text{gradient_norm}(t_{up}) >= r$.\n",
    "Then we search for $\\tau$ in the range $[0, \\tau_{up}]$ up to\n",
    "a certain precision. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "218876e6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Gradient where probs_plus/minus represents theta shifted by +- pi/2\n",
    "# The partial derivative of a parameter is the difference \n",
    "# between two circuits that differ in a positive/negative pi/2 \n",
    "# shift of the parameter. \n",
    "def g(probs_plus_all, probs_minus_all, t, spectrum):  \n",
    "    output = np.zeros(n_params)\n",
    "    for i in range(n_params):\n",
    "        filter_exp_plus = evaluate_filter(probs_plus_all[i], t, spectrum)\n",
    "        filter_exp_minus = evaluate_filter(probs_minus_all[i], t, spectrum)\n",
    "        output[i] = filter_exp_minus - filter_exp_plus\n",
    "    return output\n",
    "\n",
    "def t_upper_bound(probs_plus_all, probs_minus_all, spectrum, n_trials=5):\n",
    "    for t in (3**i for i in range(n_trials)):\n",
    "        grad_norm = np.linalg.norm(g(probs_plus_all, probs_minus_all, t, spectrum))\n",
    "        if grad_norm > r:\n",
    "            return t, grad_norm\n",
    "    print('Upper bound of t not found. Returning the largest value tested.' + \\\n",
    "          'Increase the number of trials or reduce the threshold for improvement')\n",
    "    return t, grad_norm\n",
    "\n",
    "# Once the upper bound is found, we look for the value of t in the range[0, t_up] that is closest and below r\n",
    "def update_tau(probs_plus_all, probs_minus_all, spectrum):\n",
    "    precision=r/10\n",
    "    t_low = 0\n",
    "    t_up, grad_norm = t_upper_bound(probs_plus_all, probs_minus_all, spectrum)\n",
    "    while True:\n",
    "        t = (t_up + t_low) / 2\n",
    "        grad = g(probs_plus_all, probs_minus_all, t, spectrum)\n",
    "        grad_norm = np.linalg.norm(grad)\n",
    "        if r < grad_norm:\n",
    "            t_up = t\n",
    "        elif grad_norm < r - precision:\n",
    "            t_low = t\n",
    "        else:\n",
    "            return t, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "595d0ed0",
   "metadata": {},
   "source": [
    "Samples from the two circuits for each parameter (differing in a positive/negative pi/2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "7282286c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_shifted_ansatz(params):  \n",
    "    probs_plus_all = {}\n",
    "    probs_minus_all = {}\n",
    "    for i in range(n_params):\n",
    "        params_plus = params + np.bincount([i], None, n_params) * np.pi / 2\n",
    "        params_minus = params - np.bincount([i], None, n_params) * np.pi / 2\n",
    "        \n",
    "        probs_plus = probs_from_state(get_state(params_plus))\n",
    "        probs_minus = probs_from_state(get_state(params_minus))\n",
    "\n",
    "        probs_plus_all[i] = probs_plus\n",
    "        probs_minus_all[i] = probs_minus\n",
    "    return probs_plus_all, probs_minus_all"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ed3aa8f2",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sample_ansatz(params, state):\n",
    "    c = ansatz(params)\n",
    "    probs = probs_from_state(state)\n",
    "    return probs\n",
    "\n",
    "def get_state(params):\n",
    "    c = ansatz(params)\n",
    "    b = AerStateBackend()\n",
    "    return b.get_state(c)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31adcb77",
   "metadata": {},
   "source": [
    "Function that updates the spectrum dictionary every time we sample a quantum circuit. The best solution will be the bitstring with the smallest cost that we have ever sampled."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "e3c69b6c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_spectrum(probs, spectrum,cost_function):\n",
    "    for bitstring, p in probs.items():\n",
    "        if bitstring in spectrum:\n",
    "            cost = spectrum[bitstring]\n",
    "        else:\n",
    "            cost = cost_function(bitstring)\n",
    "            spectrum[bitstring] = cost\n",
    "    return spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6047f2e",
   "metadata": {},
   "source": [
    "Gradient-based optimiser"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "72a1f2fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_params(params, gradient):\n",
    "    return params - learning_rate * gradient"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "671d0e3a",
   "metadata": {},
   "source": [
    "Evaluate the filter operator from the samples of a quantum circuit.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "6d432cfc",
   "metadata": {},
   "outputs": [],
   "source": [
    "lower_bound = 0 # min cost\n",
    "upper_bound = 4 # max cost\n",
    "def rescale(c, lower_bound=lower_bound, upper_bound=upper_bound):\n",
    "    b = 1 / (upper_bound - lower_bound)\n",
    "    a = - lower_bound / (upper_bound - lower_bound)\n",
    "    return a + b * c\n",
    "\n",
    "def evaluate_filter(probs, t, spectrum):\n",
    "    output = 0\n",
    "    for bitstring, p in probs.items():\n",
    "        cost = spectrum[bitstring]\n",
    "        cost = rescale(cost)\n",
    "        output += f(cost, t) * p\n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec86906",
   "metadata": {},
   "source": [
    "Function evaluating the average of the cost function with a given set of state probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6713f6f1",
   "metadata": {},
   "outputs": [],
   "source": [
    "def evaluate_cost(probs, spectrum):\n",
    "    output = 0\n",
    "    for bitstring, p in probs.items():\n",
    "        cost = spectrum[bitstring]\n",
    "        output += cost * p\n",
    "    return output"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1a49edd6",
   "metadata": {},
   "source": [
    "There are a number of analyses that can be done with VQEs. I have decided to limit myself to one property of interest, namely entaglement. Entaglement plays an important role in the efficiency of our variational algorithms, as described in https://arxiv.org/pdf/2103.14479.pdf.\n",
    "The implementation of this entanglement measure is simply adapted from https://journals.aps.org/pra/abstract/10.1103/PhysRevA.76.022328."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "id": "ae5ef1d6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_entanglement(state):\n",
    "    Q = 0\n",
    "    for i in range(n_qubits):\n",
    "        trace_over = [q for q in range(n_qubits) if q != i]  \n",
    "        reduced_density_matrix = partial_trace(state, trace_over).data  \n",
    "        #raise matrix to power 2 and trace it\n",
    "        Q += np.real((np.linalg.matrix_power(reduced_density_matrix, 2)).trace())\n",
    "    Q = 2 - (2 / n_qubits) * Q\n",
    "    return Q"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "89719cd5",
   "metadata": {},
   "source": [
    "Function that keeps track of the relevant quantities during evolution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "ef3feb8d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_print_evolution(probs, t, spectrum, evolution, state):  \n",
    "    best_cost = min(spectrum.values())\n",
    "    best_solutions = {bitstring for bitstring, cost in spectrum.items() if cost==best_cost}\n",
    "    solution = next(iter(best_solutions))\n",
    "    try: \n",
    "        overlap_ground = probs.get(solution, 0)\n",
    "    except:\n",
    "        overlap_ground = None\n",
    "    average_cost = evaluate_cost(probs, spectrum)\n",
    "    most_likely_solution = max(probs, key=probs.get)\n",
    "    overlap_most_lik_sol = probs[most_likely_solution]\n",
    "    evolution['overlap ground state'].append(overlap_ground)\n",
    "    evolution['best cost'].append(best_cost)\n",
    "    evolution['average cost'].append(average_cost)\n",
    "    evolution['overlap most likely solution'].append(overlap_most_lik_sol)\n",
    "    evolution['tau'].append(t)\n",
    "\n",
    "    entanglement = get_entanglement(state)\n",
    "    evolution['entanglement'].append(entanglement)\n",
    "        \n",
    "    string_to_print = 'ov gr = ' + '{:.1e}'.format(overlap_ground) +  ', av cost = ' + '{:.1e}'.format(average_cost) + ', best cost = ' + '{:.1e}'.format(best_cost) + ', ent = ' + '{:.1e}'.format(entanglement) \n",
    "                           \n",
    "    return evolution, string_to_print    "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c92e82db",
   "metadata": {},
   "source": [
    "Function plotting the evolution of the relevant quantities of a F_VQE instance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "1f96f244",
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot_evolution(evolution):\n",
    "    instructions_l_axis = {'overlap ground state': {'color': 'green'},\n",
    "                           'overlap most likely solution': {'color': 'blue', 'linestyle': '--'}}\n",
    "\n",
    "    instructions_l_axis['entanglement'] = {'color': 'gray'}\n",
    "        \n",
    "    instructions_r_axis = {'best cost': {'color': 'red', 'linestyle': '--'},\n",
    "                           'average cost': {'color': 'red'}}\n",
    "    fig, ax = plt.subplots()\n",
    "    fig.patch.set_facecolor('white')  \n",
    "    plt.title(f'{n_qubits} qubits')\n",
    "    X = np.arange(n_steps + 1)\n",
    "    plt.xlim(0, n_steps)\n",
    "    plt.xlabel('optimisation step')\n",
    "    \n",
    "    ax.set_ylabel('overlap and entanglement')\n",
    "    ax.set_ylim([0, 1])\n",
    "    for label, style in instructions_l_axis.items():\n",
    "        Y = np.array(evolution[label])\n",
    "        if style.get('rescale', False): \n",
    "            rescale_factor = max([y for y in Y if not np.isnan(y)]) / ax.get_ylim()[1]\n",
    "            if rescale_factor > 1:\n",
    "                rescale_factor = 10 ** np.ceil(np.log10(rescale_factor))\n",
    "                Y /= rescale_factor\n",
    "                label += ' x ~' + '{:.0e}'.format(rescale_factor)\n",
    "            del style['rescale']\n",
    "        ax.plot(X, Y, **style, label=label)\n",
    "    \n",
    "    ax2 = ax.twinx()\n",
    "    ax.plot([], [], color='red', linewidth=3)\n",
    "    ax2.set_ylabel('cost', color='tab:' + 'red')\n",
    "    ax2.tick_params(axis='y', labelcolor='tab:' + 'red')\n",
    "    for label, style in instructions_r_axis.items():\n",
    "        ax2.plot(X, np.array(evolution[label]), **style, label=label)\n",
    "    \n",
    "    ax.legend(bbox_to_anchor=(1.1, 1), loc='upper left')\n",
    "    ax2.legend(bbox_to_anchor=(1.1, 0.7), loc='upper left')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c9477eb",
   "metadata": {},
   "source": [
    "# F-VQE algorithm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31841d15",
   "metadata": {},
   "source": [
    "This is the core of this notebook. The algorithm takes an initial set of parameters and a cost function, iterates n times, and optimizes the circuit so that parameters are returned that give the desired solution with high probability."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "26d67570",
   "metadata": {},
   "outputs": [],
   "source": [
    "def fvqe(params, t, n_steps, spectrum, cost_function,allowPrint=True):\n",
    "    evolution = {'overlap ground state': [], 'best cost': [], 'average cost': [], \n",
    "                 'overlap most likely solution': [], 'tau': [], 'entanglement':[]}    \n",
    "    for step in range(n_steps):   \n",
    "        state = get_state(params)\n",
    "        probs = sample_ansatz(params, state) \n",
    "        spectrum = update_spectrum(probs, spectrum,cost_function)\n",
    "        evolution, string_to_print = update_print_evolution(probs, t, spectrum, evolution, state)  \n",
    "        if allowPrint:\n",
    "            print(f\"step {step}: \" + string_to_print)   \n",
    "        probs_plus_all, probs_minus_all = sample_shifted_ansatz(params)    \n",
    "        for i in range(n_params):\n",
    "            spectrum = update_spectrum(probs_plus_all[i], spectrum,cost_function)\n",
    "            spectrum = update_spectrum(probs_minus_all[i], spectrum,cost_function)\n",
    "        \n",
    "        t, gradient = update_tau(probs_plus_all, probs_minus_all, spectrum)\n",
    "        params = update_params(params, gradient)\n",
    "        \n",
    "    step = n_steps  \n",
    "    probs = sample_ansatz(params,state)  \n",
    "    spectrum = update_spectrum(probs, spectrum,cost_function)\n",
    "    evolution, string_to_print = update_print_evolution(probs, t, spectrum, evolution, state)  \n",
    "    if allowPrint:\n",
    "        print(f\"step {step}: \" + string_to_print)  \n",
    "    return evolution, params, spectrum"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "322da489",
   "metadata": {},
   "source": [
    "# First experiment \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "13bb0b3d",
   "metadata": {},
   "source": [
    "Before we perform our first experiment, we need to set some constants to prepare $\\tau$ and initialize the spectrum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "a46df168",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 1  # initial value of tau.\n",
    "r = 0.1  # threshold for tau scheduling.\n",
    "learning_rate = 1\n",
    "n_steps = 40 # number of F-VQE iterations\n",
    "\n",
    "spectrum = dict()\n",
    "\n",
    "n_qubits = 4\n",
    "n_layers = 2  # number of ansatz circuit layers\n",
    "n_gates = 3\n",
    "n_para = n_qubits * n_layers *n_gates  # number of parameters for the ansatz below\n",
    "\n",
    "initial_params = r_state_1\n",
    "circuit_params = np.random.rand(n_para)*np.pi/2\n",
    "\n",
    "params = np.concatenate((initial_params,circuit_params))\n",
    "n_params = len(params)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5ff5cf10",
   "metadata": {},
   "source": [
    "Finally, we run the experiment and plot the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "f000792d",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "evolution, final_param, spectrum = fvqe(params, t, n_steps,spectrum,cost_function = C1,allowPrint=False)\n",
    "plot_evolution(evolution)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0bd7ca4f",
   "metadata": {},
   "source": [
    "This diagram is full of interesting information. I will discuss all the curves listed in the legend step by step. \n",
    "- Starting from the bottom, the best cost is just the cost of the optimal solution. If we use our random state 1, these would be $|0011>$. Logically, it remains constant as we do not vary our cost function.\n",
    "- The average cost is calculated by taking the cost average of the bit strings, weighted by their probability distribution. For example, if the sample $(0,0,1,1)$ has a probability of $1$ and $C((0,0,1,1))=0$, the average cost is $0$. \n",
    "- The entanglement curve shows the evolution of, well, entanglement in the circuit. We see that in the random superposition we start with, we have a strongly entangled state. This is not surprising, since when a state is randomly generated, the probability of generating an entangled state is higher than vice versa. Entanglement decreases over time as our state evolves from a superposition to a particular single state.\n",
    "- Lastly, overlap most likely solution/ground state give us a measure of $|<\\psi|\\lambda_0>|^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "id": "94cdcd89",
   "metadata": {
    "scrolled": false
   },
   "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": [
    "final_state = get_state(final_param)\n",
    "final_probs = sample_ansatz(final_param,final_state) \n",
    "plot_probs(final_probs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6c10ec2",
   "metadata": {},
   "source": [
    "Plotting the probability distribution of the states confirms that we have successfully accomplished our task of taking a random input state and returning the state $(0,0,1,1)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1ffc65a3",
   "metadata": {},
   "source": [
    "# Solving for 4 different initial parameters with "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12c1b1b6",
   "metadata": {},
   "source": [
    "We now extend our code to handle multiple cost functions/ input states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "d965011b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def C2(x):\n",
    "    solution = (0,1,0,1)\n",
    "    return np.sum(np.abs(x-np.array(solution)))\n",
    "def C3(x):\n",
    "    solution = (1,0,1,0)\n",
    "    return np.sum(np.abs(x-np.array(solution)))\n",
    "def C4(x):\n",
    "    solution = (1,1,0,0)\n",
    "    return np.sum(np.abs(x-np.array(solution)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "id": "7182b9c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "problem 1\n",
      "problem 2\n",
      "problem 3\n",
      "problem 4\n"
     ]
    }
   ],
   "source": [
    "problem_set = [C1,C2,C3,C4]\n",
    "initial_param_arr = [r_state_1,r_state_2,r_state_3,r_state_4]\n",
    "\n",
    "def fvqe_on_set(t, n_steps,spectrum,allowPrint=False):\n",
    "    output_evo = []\n",
    "    output_params = []\n",
    "    for i, cost_function in enumerate(problem_set):\n",
    "        print(f'problem {i+1}')\n",
    "                \n",
    "        params = np.concatenate((initial_param_arr[i],np.random.rand(n_para)*np.pi/2))\n",
    "        spectrum = dict()\n",
    "        \n",
    "        evolution, final_params, spectrum = fvqe(params, t, n_steps,spectrum,cost_function=cost_function,allowPrint=False)\n",
    "        output_evo.append(evolution)\n",
    "        output_params.append(final_params)\n",
    "        \n",
    "    return output_evo,output_params\n",
    "\n",
    "evo_4, params_4 = fvqe_on_set( t, n_steps,spectrum,allowPrint=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "6377e38c",
   "metadata": {
    "scrolled": true
   },
   "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": [
    "for final_params in params_4:\n",
    "    final_state = get_state(final_params)\n",
    "    final_probs = sample_ansatz(final_params,final_state)\n",
    "    plot_probs(final_probs)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1936d51d",
   "metadata": {},
   "source": [
    "This completes the main task. The array params_4 contains the information about how the circuit should be initialized so that we immediately get the right result when choosing the appropriate cost function/output state."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "128deb9f",
   "metadata": {},
   "source": [
    "# Applying a new state to trained circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fd66960f",
   "metadata": {},
   "source": [
    "An additional question in the task was to investigate what happens when we apply a new state to a trained circuit. This will be investigated in the following:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "id": "db34e20b",
   "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": [
    "r_state_5 = np.array([0.72837575, 0.55504438, 0.91680488, 0.12210528, 1.53057578,\n",
    "       1.54913621, 1.09666986, 0.8420982 , 0.48620484, 1.27830623,\n",
    "       1.07557321, 0.25543809])\n",
    "\n",
    "initial_state = get_initial_state(r_state_5)\n",
    "initial_probs = sample_initial_ansatz(r_state_5,initial_state) \n",
    "plot_probs(initial_probs,\"Initial State\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "id": "251a77de",
   "metadata": {
    "scrolled": true
   },
   "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": [
    "final_params_test = np.concatenate((r_state_5, final_params[len(r_state_5):]))\n",
    "final_state = get_state(final_params_test)\n",
    "final_probs = sample_ansatz(final_params_test,final_state)\n",
    "plot_probs(final_probs,\"State after Trained Circuit\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a4b169a",
   "metadata": {},
   "source": [
    "We see that our trained circuit is not able to reproduce the results with a different input. For this to work, we would simply have to train the circuit for the new input as well!"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}