VQE_Tutorial_Part3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tutorial on Variational Quantum Eigensolver (Part III)\n",
    "# *Hadamard test* to Estimate Energy\n",
    "\n",
    "---\n",
    "This code was mostly based on Qiskit Variational Quantum Eigensolver Playground, you can find in [Github](https://github.com/JavaFXpert/vqe-playground). Please run all the cells in order.\n",
    "\n",
    "We saw that to estimate the energy in **Part II** we accessed the probabilities of each one of the components of the ansatz wavefunction doing multiple measurements and estimating them.\n",
    "\n",
    "There are several techniques to minimize the number of experiments or to maximize the probability of getting a correct answer but nothing comes for free. The biggest the certainty the more gates and ancilla (auxiliary) qubits we will need. We are going to explore in this Tutorial the [**Hadamard Test**](https://en.wikipedia.org/wiki/Hadamard_test_(quantum_computation)) Circuit to get an estimation of the expected value of the MaxCut Hamiltonian given an Ansatz wavefunction.\n",
    "\n",
    "This step now will be a quantum circuit and a measurement and it will be reproducible in a real quantum computer. In the following figure you can see now the new elements of the algorithm differentiated in Blue (Quantum) and Green(Classical). \n",
    "\n",
    "<img src=\"./img/VQE1.1.png\" >\n",
    "\n",
    "As we can see in the Circuit we will be using an extra quibit as ancilla that will be entangled with the Ansatz wavefuntion through the Hamiltonian. We will be doing the energy estimation in 6 steps one for each sum term of the Hamiltonian that we will call $H_i$.\n",
    "\n",
    "Lets new explore how the Hadamard test module with the one and only ancilla qubit to be measured works.\n",
    "\n",
    "<img src=\"./img/hadamard_test.png\" width=\"300\">\n",
    "\n",
    "When we apply the Hadamard gate and the controlled-U we get the following expresion: \n",
    "\n",
    "$$\\frac {1}{\\sqrt {2}}\\left(\\left|0\\right\\rangle \\otimes \\left|\\psi \\right\\rangle +\\left|1\\right\\rangle \\otimes U\\left|\\psi \\right\\rangle \\right)$$\n",
    "\n",
    "Once we apply another Hadamard we will get:\n",
    "\n",
    "$$\\frac {1}{2}\\left(\\left|0\\right\\rangle \\otimes (I+U)\\left|\\psi \\right\\rangle +\\left|1\\right\\rangle \\otimes (I-U)\\left|\\psi \\right\\rangle \\right)$$\n",
    "\n",
    "Now, the probabilty of getting $|0\\rangle$ after the measurement will be:\n",
    "\n",
    "$$\\frac {1}{4}\\left\\langle \\psi \\mid (I+U^{\\dagger })(I+U)\\mid \\psi \\right\\rangle$$\n",
    "\n",
    "and, the probabilty of getting $|1\\rangle$ after the measurement will be:\n",
    "\n",
    "$$\\frac {1}{4}\\left\\langle \\psi \\mid (I-U^{\\dagger })(I-U)\\mid \\psi \\right\\rangle$$\n",
    "\n",
    "\n",
    "Note now that if we substract both probabilities, we will have:\n",
    "\n",
    "$$P_0-P_1 = \\frac {1}{2}\\left\\langle \\psi \\mid (U^{\\dagger }+U)\\mid \\psi \\right\\rangle ={\\mathcal {Re}}\\left\\langle \\psi \\mid U\\mid \\psi \\right\\rangle$$\n",
    "\n",
    "Which is precisely the expectation value of the Hamiltonian (in this case U) with the Ansatz wavefunction or the Energy of the Ansatz.\n",
    "\n",
    "We will do this process for each and every one of the $H_i$ and will sum them up to get the final total Energy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Import libraries  \n",
    "\n",
    "We import all necessary functions from IBM qiskit and numpy python **libraries**, that we will later use on this Notebook."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Libraries loaded successfully.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit, QuantumRegister, ClassicalRegister, Aer, execute\n",
    "from qiskit.visualization import plot_bloch_multivector, plot_histogram\n",
    "\n",
    "print(\"Libraries loaded successfully.\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definition of the Circuit\n",
    "We already went through the details of classes `CircuitGridNode` and `CircuitGridModel` in PART I "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CircuitGridNode():\n",
    "    def __init__(self, node_type, radians=0.0, ctrl_a=-1):\n",
    "        self.node_type = node_type\n",
    "        self.radians = radians\n",
    "        self.ctrl_a = ctrl_a\n",
    "        self.wire_num = -1\n",
    "        self.column_num = -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the Class: **`CircuitGridModel`** , we are going to add the extra Quantum Circuit necessary to do the Hamiltonian expectation value and the corresponding measurement. \n",
    "\n",
    "We will be adding the extra ancilla quibit, two Hadamard Gates (in the initialization module of the Class) and two control-Z gates for each one of the $H_i$ :\n",
    "\n",
    "$$ H = - \\sum_{i} H_i = - \\left (\\frac{3}{2}Z_{1}Z_{0} + \\frac{1}{2}Z_{2}Z_{0} + \\frac{3}{2}Z_{3}Z_{0} + \\frac{3}{2}Z_{3}Z_{2} + \\frac{2}{2}Z_{4}Z_{1} + \\frac{2}{2}Z_{4}Z_{3}\\right ) $$\n",
    "\n",
    "The function **`Control_Hi`** will be changing these 2 control-Z gates to the corresponding combination of each $H_i$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "class CircuitGridModel():\n",
    "\n",
    "    def __init__(self):\n",
    "        # Define the Quantum Circuit to generate the Ansatz + Other Measurement Circuit\n",
    "        self.max_wires = NUM_QUBITS\n",
    "        self.max_columns = 21           # Columns for the circuit. 21 Columns for the Entanglement/Tuning Circuit\n",
    "                                        # 1 extra wire as ancilla , 4 extra columns for Hadamard and Control Z.\n",
    "        self.nodes = np.empty((self.max_wires+1, self.max_columns+4),\n",
    "                                dtype = CircuitGridNode)\n",
    "        \n",
    "        for column_num in range(self.max_columns):\n",
    "            for wire_num in range(self.max_wires):\n",
    "                if column_num % 5 == 0:\n",
    "                    self.nodes[wire_num][column_num] = CircuitGridNode(Ygate, np.pi)              # Ry(pi)\n",
    "                    self.nodes[wire_num][column_num].wire_num = wire_num\n",
    "                    self.nodes[wire_num][column_num].column_num = column_num\n",
    "                else: \n",
    "                    if wire_num != 0 and wire_num == column_num % 5:\n",
    "                        self.nodes[wire_num][column_num] = CircuitGridNode(Xgate, 0, wire_num-1)  # CNOT \n",
    "                        self.nodes[wire_num][column_num].wire_num = wire_num\n",
    "                        self.nodes[wire_num][column_num].column_num = column_num\n",
    "        \n",
    "        # Measurement part of the Circuit : Add the Controlled to the Ancilla and Hadamard.\n",
    "        self.nodes[5][21] = CircuitGridNode(Hgate)                       \n",
    "        self.nodes[5][22] = CircuitGridNode(Zgate, 5, 4)  # CZ4    we initialize with Z3 Z4 as example \n",
    "        self.nodes[5][23] = CircuitGridNode(Zgate, 5, 3)  # CZ3    \n",
    "        self.nodes[5][24] = CircuitGridNode(Hgate)\n",
    "        self.nodes[5][21].wire_num = 5  ;  self.nodes[5][21].column_num = 21\n",
    "        self.nodes[5][22].wire_num = 5  ;  self.nodes[5][22].column_num = 22\n",
    "        self.nodes[5][23].wire_num = 5  ;  self.nodes[5][23].column_num = 23\n",
    "        self.nodes[5][24].wire_num = 5  ;  self.nodes[5][24].column_num = 24\n",
    "    \n",
    "    def Control_Hi(self, index):\n",
    "        # Make the Hadamard Test Circuit different for each and every H sum Term\n",
    "        # H1 = (3/2)Z0Z1   ;   H2 = (1/2)Z0Z2   ;   H3 = (3/2)Z0Z3\n",
    "        # H4 = (3/2)Z2Z3   ;   H5 = (2/2)Z1Z4   ;   H6 = (2/2)Z3Z4 \n",
    "        if index == 0:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 0)  # CZ0\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 1)  # CZ1   \n",
    "        elif index == 1:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 0)  # CZ0\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 2)  # CZ2   \n",
    "        elif index == 2:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 0)  # CZ0\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 3)  # CZ3   \n",
    "        elif index == 3:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 2)  # CZ2\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 3)  # CZ3   \n",
    "        elif index == 4:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 1)  # CZ1\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 4)  # CZ4   \n",
    "        elif index == 5:\n",
    "            self.nodes[5][22] = CircuitGridNode(Zgate, 5, 3)  # CZ3\n",
    "            self.nodes[5][23] = CircuitGridNode(Zgate, 5, 4)  # CZ4   \n",
    "            \n",
    "    def get_rotation_gate_nodes(self):\n",
    "        rot_gate_nodes = []\n",
    "        for column_num in range(self.max_columns):\n",
    "            for wire_num in range(self.max_wires):\n",
    "                node = self.nodes[wire_num][column_num]\n",
    "                if node and node.node_type == Ygate:\n",
    "                    rot_gate_nodes.append(node)\n",
    "        return rot_gate_nodes\n",
    "    \n",
    "    def compute_circuit(self):\n",
    "        qr = QuantumRegister(NUM_QUBITS, 'q')\n",
    "        anc = QuantumRegister(1, 'ancilla')\n",
    "        cr = ClassicalRegister(1, 'c')\n",
    "        qc = QuantumCircuit(qr, anc, cr)\n",
    "    \n",
    "        # Build the Circuit with actual gates based on the Circuit Grid Model\n",
    "        for column_num in range(self.max_columns+4):\n",
    "            qc.barrier(qr) ; qc.barrier (anc)\n",
    "            for wire_num in range(self.max_wires+1):\n",
    "                node = self.nodes[wire_num][column_num]\n",
    "                if node:\n",
    "                    if node.node_type == Xgate:    qc.cx(node.ctrl_a, wire_num)       # Controlled X gate\n",
    "                    elif node.node_type == Ygate:  qc.ry(node.radians, wire_num)      # Rotation around Y axis\n",
    "                    elif node.node_type == Zgate:  qc.cz(node.ctrl_a, wire_num)       # Controlled Z gate\n",
    "                    elif node.node_type == Hgate:  qc.h(wire_num)                     # Hadamard Gate\n",
    "        \n",
    "        # Add Measurement at the end\n",
    "        qc.measure(anc, cr)       \n",
    "        return qc\n",
    "    \n",
    "    def compute_circuit_ansatz(self):\n",
    "        # Function aimed to measure the final Ansatz\n",
    "        qr = QuantumRegister(NUM_QUBITS, 'q')\n",
    "        cr = ClassicalRegister(NUM_QUBITS, 'c')\n",
    "        qc = QuantumCircuit(qr, cr)\n",
    "    \n",
    "        # Build the Circuit with actual gates based on the Circuit Grid Model\n",
    "        for column_num in range(self.max_columns+4):\n",
    "            for wire_num in range(self.max_wires+1):\n",
    "                node = self.nodes[wire_num][column_num]\n",
    "                if node:\n",
    "                    if node.node_type == Xgate:    qc.cx(node.ctrl_a, wire_num)       # Controlled X gate\n",
    "                    elif node.node_type == Ygate:  qc.ry(node.radians, wire_num)      # Rotation around Y axis\n",
    "        \n",
    "        # Add Measurement at the end\n",
    "        qc.measure(qr, cr)       \n",
    "        return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Functions:\n",
    "\n",
    "`ExperimentAndMeasure` Sets up the Qiskit Simulator, Executes the simulation `n_experiments` times and return the results as an histogram (dictionary of results in the format: {'000': n1, '001': n2 ....}). In this case we will be measuring only the ancilla qubit.\n",
    "\n",
    "Also we define an array with all de weights of the $H_i$ and a temporary array `Energies_Hi` that will help us store the partial expectation values as we go calculating each one of the 6 terms of the sum."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# H1 = (3/2)Z0Z1   ;   H2 = (1/2)Z0Z2   ;   H3 = (3/2)Z0Z3\n",
    "# H4 = (3/2)Z2Z3   ;   H5 = (2/2)Z1Z4   ;   H6 = (2/2)Z3Z4 \n",
    "Sum_Term_Weights = [3/2,1/2,3/2,3/2,1,1]          # This array will hold the weight of every H_i term.\n",
    "Energies_Hi = [0,0,0,0,0,0]                # This will hold the expectation Values of the terms H_i.\n",
    "\n",
    "def ExperimentAndMeasure(circuit):\n",
    "    backend_sim = Aer.get_backend('qasm_simulator')\n",
    "    job_sim = execute(circuit, backend_sim, shots=n_experiments)\n",
    "    result_sim = job_sim.result()\n",
    "    prob_distro = result_sim.get_counts(circuit)\n",
    "    return prob_distro"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Function to Recalculate Circuit and Recalculate Expectation Value \n",
    "This function will first make use of the array `optimized_rotations` that hold the latest optimal angles for all the Ry Gates. It will assign those angles to the nodes contained in `rotation_gate_nodes` which are the nodes in the circuit subject to rotation (Ry).\n",
    "\n",
    "After that, it will compute the new circuit in the Class `circuit_grid_model` and will obtain the ansatz state and Measure it correspondingly with `ExperimentAndMeasure`. \n",
    "\n",
    "That function will in turn give the probability distribution that will be input in the `calc_expectation_value` function that at last will return the estimated Energy, most probable base state and the actual probability distribution as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_new_energy(circuit_grid_model, rotation_gate_nodes):\n",
    "    \n",
    "    for idx in range(len(rotation_gate_nodes)):\n",
    "        rotation_gate_nodes[idx].radians = optimized_rotations[idx]\n",
    "        \n",
    "    for i in range(6):\n",
    "        circuit_grid_model.Control_Hi(i)\n",
    "        circuit = circuit_grid_model.compute_circuit()\n",
    "        prob_distro = ExperimentAndMeasure(circuit)\n",
    "        Energies_Hi[i] = (prob_distro.setdefault('0', 0) - prob_distro.setdefault('1', 0))\n",
    "        Energies_Hi[i] = Energies_Hi[i] * Sum_Term_Weights[i] / n_experiments \n",
    "   \n",
    "    estimated_Energy = sum(Energies_Hi)\n",
    "    return estimated_Energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Function to Optimize Rotations\n",
    "This function will contain the **classical optimization algorithm** to finetune the angles and make sure that the Energy of the resulting state will be minimal.\n",
    "\n",
    "As input it will gate the, the Class with the Circuit, the Class with the Expectation grid and the array of nodes with Ry Gates. As output it will proyect the latest optimized energy the variable `energy` and the latest *optimal* basis state (basis state with highest probability) \n",
    "\n",
    "`cur_rotation_num` will be the node containing the Ry Gate currently being updated and optimized. Will be a counter 25 times. For each gate, the algorithm will start rotating a fixed angle on one direction, if the Energy stays or decreasis it will continue rotating, if it increases, then it will change direction of rotation unless it already changed direction before. In that case or if the angle is out of the $ [0,2\\pi] $ range, it will move to the next gate.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize_rotations(circuit_grid_model, rotation_gate_nodes):\n",
    "    global energy, move_radians, cur_rotation_num, rot_direction, Fin_optimizacion\n",
    "\n",
    "    if cur_rotation_num < len(optimized_rotations):   # Are we on the last Ry Gate?\n",
    "        cur_ang_rad = optimized_rotations[cur_rotation_num]\n",
    "        proposed_cur_ang_rad = cur_ang_rad\n",
    "        proposed_cur_ang_rad += move_radians * rot_direction\n",
    "        \n",
    "        if (0.0 <= proposed_cur_ang_rad <= np.pi * 2 + 0.01) and (num_times_rot_dir_change[cur_rotation_num]<1):\n",
    "            optimized_rotations[cur_rotation_num] = proposed_cur_ang_rad               \n",
    "            \n",
    "            # Calculate new Energy with the new Circuit, Quantum Qiskit circuit is called here.\n",
    "            temp_energy = calc_new_energy(circuit_grid_model, rotation_gate_nodes)\n",
    "            if temp_energy > energy: \n",
    "                # NOT OPTIMIZED. Distance is increasing so restore the angle and change direction of rot\n",
    "                optimized_rotations[cur_rotation_num] = cur_ang_rad\n",
    "                rot_direction *= -1\n",
    "                num_times_rot_dir_change[cur_rotation_num] += 1\n",
    "            else:\n",
    "                # OPTIMIZED or equal. Distance decreasing, so keep the proposed angle and update Energy\n",
    "                energy = temp_energy\n",
    "        else:                                       \n",
    "            cur_rotation_num += 1       # Out of [0,2pi] range or changed direction twice. Move to next Gate.\n",
    "    else:\n",
    "        Fin_optimizacion = True         # We reached the last Ry, optimization process is over    \n",
    "    \n",
    "    return energy"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Definitions and Initializations\n",
    "In this segment of code we will initialize global variables that will be used in the Main and optimization algorithm. One of the important variables is the Rotation step. Note the Adjacency Matrix does not show up as it is embedded in the Hamiltonian we have manually calculated."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_QUBITS = 5                                                 # Qubits to model the problem\n",
    "Xgate = 1 ; Ygate = 2 ; Zgate = 3 ; Hgate = 4                  # Gate Definitions    \n",
    "basis_states = []                                              # List of Basis states in Text format\n",
    "for idx in range(2**NUM_QUBITS):\n",
    "    state = format(idx, '0' + str(NUM_QUBITS) + 'b')\n",
    "    basis_states.append(state)\n",
    "    \n",
    "n_experiments = 512\n",
    "proposed_cur_ang_rad = 0\n",
    "cur_ang_rad = 0\n",
    "rot_direction = 1\n",
    "iteration=0\n",
    "Fin_optimizacion = False  \n",
    "cur_rotation_num = 0\n",
    "move_radians = np.pi / 8       # Rotation Step"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Initialization of the Circuit and Visual Output\n",
    "Here we will initialize the circuit for first time and will calculate the Ansatz State of the all the Ry gates with $\\pi$ radians. Also it will create the expectation grid for the first time.\n",
    "\n",
    "When the expectation grid is initialized, it will convert the Adjacency matrix to the Ising Hamiltonian and will print its output in gate format (I and Z gates)\n",
    "\n",
    "On this piece of code we also print the Quantum Optimization Circuit using the Qiskit drawing capabilities as well as the Latex output extensions included in the Qiskit programming language to show the Adjacency Matrix in a readable manner."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Complete Quantum Circuit with Hamiltonian term Z3 Z4 (as example):\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=3054x418 at 0x1616FC12DC0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit_grid_model = CircuitGridModel()\n",
    "circuit = circuit_grid_model.compute_circuit()\n",
    "\n",
    "print(\"\\nComplete Quantum Circuit with Hamiltonian term Z3 Z4 (as example):\")\n",
    "display(circuit.draw(output='latex',scale=0.7,justify='right',plot_barriers=False))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Main Loop and Print Results\n",
    "First extract all nodes with gates suitable for rotation ans intialize first rotation of those with $\\pi$. At the beginning, all Ry Gates will be indeed Pauli Y Gates.\n",
    "\n",
    "After that we will run the first Optimization iteration befor going to the actual main loop.\n",
    "\n",
    "In the main loop showing as a `while` we will **print** the Iteration number, the rotating gate, the position in the 5x21 matrix, the energy of this iteration, and the optimal basis state so far.\n",
    "\n",
    "Then we will try to **optimize** calling `optimize_rotations` function. During the optimization we will also print the simulated Ansatz State that results after the optimization quantum circuit. The output will be a **sum of the basis states and its probability**.\n",
    "\n",
    "Once the optimization comes to an end and we get out of the loop we will print the final Energy and Optimal Base State as a result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Iteration #274 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: 0.103516\n",
      " Iteration #275 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -0.083984\n",
      " Iteration #276 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -0.083984\n",
      " Iteration #277 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -0.083984\n",
      " Iteration #278 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -0.244141\n",
      " Iteration #279 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -0.380859\n",
      " Iteration #280 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -0.380859\n",
      " Iteration #281 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -0.380859\n",
      " Iteration #282 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -0.380859\n",
      " Iteration #283 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -0.380859\n",
      " Iteration #284 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -0.380859\n",
      " Iteration #285 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -0.380859\n",
      " Iteration #286 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -0.380859\n",
      " Iteration #287 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -0.380859\n",
      " Iteration #288 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -0.380859\n",
      " Iteration #289 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -0.380859\n",
      " Iteration #290 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -0.380859\n",
      " Iteration #291 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -0.380859\n",
      " Iteration #292 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -0.380859\n",
      " Iteration #293 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -0.380859\n",
      " Iteration #294 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -0.808594\n",
      " Iteration #295 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.164062\n",
      " Iteration #296 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.611328\n",
      " Iteration #297 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.722656\n",
      " Iteration #298 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.722656\n",
      " Iteration #299 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -1.722656\n",
      " Iteration #300 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -1.896484\n",
      " Iteration #301 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -1.896484\n",
      " Iteration #302 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -1.896484\n",
      " Iteration #303 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -1.896484\n",
      " Iteration #304 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -1.896484\n",
      " Iteration #305 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -1.896484\n",
      " Iteration #306 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -1.896484\n",
      " Iteration #307 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -1.896484\n",
      " Iteration #308 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -1.896484\n",
      " Iteration #309 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -1.896484\n",
      " Iteration #310 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -1.896484\n",
      " Iteration #311 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -1.896484\n",
      " Iteration #312 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -1.896484\n",
      " Iteration #313 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -1.896484\n",
      " Iteration #314 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -1.896484\n",
      " Iteration #315 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -1.896484\n",
      " Iteration #316 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -1.896484\n",
      " Iteration #317 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -1.896484\n",
      " Iteration #318 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -1.896484\n",
      " Iteration #319 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -1.896484\n",
      " Iteration #320 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -1.896484\n",
      " Iteration #321 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -1.896484\n",
      " Iteration #322 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -1.896484\n",
      " Iteration #323 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -1.896484\n",
      " Iteration #324 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -1.896484\n",
      " Iteration #325 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -1.896484\n",
      " Iteration #326 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -1.896484\n",
      " Iteration #327 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -1.896484\n",
      " Iteration #328 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -1.896484\n",
      " Iteration #329 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -1.896484\n",
      " Iteration #330 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -1.896484\n",
      " Iteration #331 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -1.896484\n",
      " Iteration #333 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.896484\n",
      " Iteration #334 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.896484\n",
      " Iteration #335 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -1.896484\n",
      " Iteration #336 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -1.896484\n",
      " Iteration #337 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -1.896484\n",
      " Iteration #338 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -1.896484\n",
      " Iteration #339 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -1.896484\n",
      " Iteration #340 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -1.896484\n",
      " Iteration #341 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -1.896484\n",
      " Iteration #342 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -1.896484\n",
      " Iteration #343 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -1.896484\n",
      " Iteration #344 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -1.896484\n",
      " Iteration #345 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -1.896484\n",
      " Iteration #346 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -1.896484\n",
      " Iteration #347 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -1.896484\n",
      " Iteration #348 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -1.896484\n",
      " Iteration #349 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.896484\n",
      " Iteration #350 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -1.896484\n",
      " Iteration #351 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -1.896484\n",
      " Iteration #352 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -1.896484\n",
      " Iteration #353 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -1.896484\n",
      " Iteration #354 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -1.896484\n",
      " Iteration #355 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -1.896484\n",
      " Iteration #356 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -2.058594\n",
      " Iteration #357 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -2.058594\n",
      " Iteration #358 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -2.058594\n",
      " Iteration #359 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -2.058594\n",
      " Iteration #360 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -2.058594\n",
      " Iteration #361 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -2.058594\n",
      " Iteration #362 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -2.058594\n",
      " Iteration #363 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -2.058594\n",
      " Iteration #364 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -2.058594\n",
      " Iteration #365 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -2.058594\n",
      " Iteration #366 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -2.058594\n",
      " Iteration #367 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -2.154297\n",
      " Iteration #368 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -2.349609\n",
      " Iteration #369 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -2.410156\n",
      " Iteration #370 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -2.410156\n",
      " Iteration #371 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -2.410156\n",
      " Iteration #372 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -2.410156\n",
      " Iteration #373 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -2.410156\n",
      " Iteration #374 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -2.410156\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Iteration #375 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -2.410156\n",
      " Iteration #376 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -2.410156\n",
      " Iteration #377 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -2.427734\n",
      " Iteration #378 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -2.427734\n",
      " Iteration #379 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -2.427734\n",
      " Iteration #380 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -2.427734\n",
      " Iteration #381 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -2.427734\n",
      " Iteration #382 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -2.427734\n",
      " Iteration #383 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -2.427734\n",
      " Iteration #384 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -2.427734\n",
      " Iteration #385 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -2.427734\n",
      " Iteration #386 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -2.427734\n",
      " Iteration #388 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -2.427734\n",
      " Iteration #389 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -2.427734\n",
      " Iteration #390 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.427734\n",
      " Iteration #391 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.439453\n",
      " Iteration #392 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.503906\n",
      " Iteration #393 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.503906\n",
      " Iteration #394 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -2.503906\n",
      " Iteration #395 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -2.503906\n",
      " Iteration #396 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -2.503906\n",
      " Iteration #397 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -2.503906\n",
      " Iteration #398 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.503906\n",
      " Iteration #399 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.503906\n",
      " Iteration #400 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -2.503906\n",
      " Iteration #401 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -2.503906\n",
      " Iteration #402 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -2.503906\n",
      " Iteration #403 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -2.826172\n",
      " Iteration #404 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -3.031250\n",
      " Iteration #405 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -3.472656\n",
      " Iteration #406 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -3.472656\n",
      " Iteration #407 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -3.472656\n",
      " Iteration #408 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -3.472656\n",
      " Iteration #409 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -3.472656\n",
      " Iteration #410 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -3.472656\n",
      " Iteration #411 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -3.472656\n",
      " Iteration #412 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -3.472656\n",
      " Iteration #413 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -3.787109\n",
      " Iteration #414 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -4.041016\n",
      " Iteration #415 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -4.326172\n",
      " Iteration #416 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -4.507812\n",
      " Iteration #417 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -4.753906\n",
      " Iteration #418 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -4.753906\n",
      " Iteration #419 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -4.753906\n",
      " Iteration #420 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -4.753906\n",
      " Iteration #421 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -4.753906\n",
      " Iteration #422 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -4.753906\n",
      " Iteration #423 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -4.753906\n",
      " Iteration #424 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -4.753906\n",
      " Iteration #425 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -4.753906\n",
      " Iteration #426 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -4.753906\n",
      " Iteration #427 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -4.753906\n",
      " Iteration #428 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -4.839844\n",
      " Iteration #429 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -4.839844\n",
      " Iteration #430 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -4.839844\n",
      " Iteration #431 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -4.839844\n",
      " Iteration #432 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -4.839844\n",
      " Iteration #433 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -4.839844\n",
      " Iteration #434 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -4.839844\n",
      " Iteration #435 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -4.839844\n",
      " Iteration #436 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -4.839844\n",
      " Iteration #437 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -4.839844\n",
      " Iteration #438 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -4.839844\n",
      " Iteration #439 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -4.839844\n",
      " Iteration #440 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -4.839844\n",
      " Iteration #441 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -4.839844\n",
      " Iteration #442 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -4.839844\n",
      " Iteration #443 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -4.839844\n",
      " Iteration #444 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -4.839844\n",
      " Iteration #445 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -4.839844\n",
      " Iteration #446 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -4.839844\n",
      " Iteration #447 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -4.839844\n",
      " Iteration #449 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -4.839844\n",
      " Iteration #450 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -4.917969\n",
      " Iteration #451 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -4.917969\n",
      " Iteration #452 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -4.917969\n",
      " Iteration #453 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -4.917969\n",
      " Iteration #454 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -4.917969\n",
      " Iteration #455 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -4.917969\n",
      " Iteration #456 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -4.917969\n",
      " Iteration #457 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -4.917969\n",
      " Iteration #458 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -4.917969\n",
      " Iteration #459 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -4.917969\n",
      " Iteration #460 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -4.917969\n",
      " Iteration #461 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -4.917969\n",
      " Iteration #462 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -4.917969\n",
      " Iteration #463 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -4.917969\n",
      " Iteration #464 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -4.917969\n",
      " Iteration #465 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -4.917969\n",
      " Iteration #466 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -4.917969\n",
      " Iteration #467 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -4.917969\n",
      " Iteration #468 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -5.300781\n",
      " Iteration #469 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -5.550781\n",
      " Iteration #470 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -5.550781\n",
      " Iteration #471 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -5.550781\n",
      " Iteration #472 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -5.550781\n",
      " Iteration #473 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -5.550781\n",
      " Iteration #474 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -5.550781\n",
      " Iteration #475 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -5.550781\n",
      " Iteration #476 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -5.550781\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Iteration #477 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -5.550781\n",
      " Iteration #478 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -5.550781\n",
      " Iteration #479 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -5.550781\n",
      " Iteration #480 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -5.550781\n",
      " Iteration #481 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -5.550781\n",
      " Iteration #482 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -5.550781\n",
      " Iteration #483 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -5.550781\n",
      " Iteration #484 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -5.550781\n",
      " Iteration #485 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -5.550781\n",
      " Iteration #486 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -5.550781\n",
      " Iteration #487 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -5.550781\n",
      " Iteration #488 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -5.550781\n",
      " Iteration #489 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -5.550781\n",
      " Iteration #490 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -5.550781\n",
      " Iteration #491 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -5.550781\n",
      " Iteration #492 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -5.550781\n",
      " Iteration #493 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -5.550781\n",
      " Iteration #494 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -5.550781\n",
      " Iteration #495 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -5.550781\n",
      " Iteration #496 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -5.550781\n",
      " Iteration #497 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -5.550781\n",
      " Iteration #498 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -5.550781\n",
      " Iteration #500 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -5.550781\n",
      " Iteration #501 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -5.550781\n",
      " Iteration #502 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -5.550781\n",
      " Iteration #503 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -5.550781\n",
      " Iteration #504 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -5.550781\n",
      " Iteration #505 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -5.550781\n",
      " Iteration #506 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -5.550781\n",
      " Iteration #507 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -5.550781\n",
      " Iteration #508 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -5.550781\n",
      " Iteration #509 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -5.550781\n",
      " Iteration #510 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -5.550781\n",
      " Iteration #511 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -5.550781\n",
      " Iteration #512 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -5.550781\n",
      " Iteration #513 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -5.550781\n",
      " Iteration #514 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -5.550781\n",
      " Iteration #515 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -5.550781\n",
      " Iteration #516 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -5.550781\n",
      " Iteration #517 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -5.550781\n",
      " Iteration #518 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -5.550781\n",
      " Iteration #519 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -5.550781\n",
      " Iteration #520 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -5.550781\n",
      " Iteration #521 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -5.550781\n",
      " Iteration #522 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -5.550781\n",
      " Iteration #523 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -5.550781\n",
      " Iteration #524 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -5.550781\n",
      " Iteration #525 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -5.550781\n",
      " Iteration #526 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -5.550781\n",
      " Iteration #527 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -5.550781\n",
      " Iteration #528 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -5.550781\n",
      " Iteration #529 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -5.550781\n",
      " Iteration #530 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -5.550781\n",
      " Iteration #531 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -5.550781\n",
      " Iteration #532 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -5.550781\n",
      " Iteration #533 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -5.550781\n",
      " Iteration #534 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -5.550781\n",
      " Iteration #535 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -5.550781\n",
      " Iteration #536 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -5.550781\n",
      " Iteration #537 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -5.550781\n",
      " Iteration #538 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -5.550781\n",
      " Iteration #539 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -5.550781\n",
      " Iteration #540 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -5.550781\n",
      " Iteration #541 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -5.550781\n",
      " Iteration #542 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -5.550781\n",
      " Iteration #543 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -5.550781\n",
      " Iteration #544 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -5.550781\n",
      " Iteration #545 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -5.550781\n",
      " Iteration #546 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -5.550781\n",
      "\n",
      "-------------------------------------------------------- \n",
      "\n",
      "Final Energy:  -5.550781\n",
      "\n",
      "-------------------------------------------------------- \n",
      "\n",
      "Ansatz: {'00000': 3, '10000': 2, '10010': 5, '11000': 8, '11001': 5, '11010': 23, '11100': 1, '11110': 1, '00010': 3, '00110': 2, '01000': 2, '01001': 3, '01010': 443, '01011': 4, '01100': 5, '01110': 1, '01111': 1}\n",
      "\n",
      "-------------------------------------------------------- \n",
      "\n"
     ]
    }
   ],
   "source": [
    "circuit_grid_model = CircuitGridModel()\n",
    "circuit = circuit_grid_model.compute_circuit()\n",
    "\n",
    "# INITIALIZATION OF FIRST CIRCUIT AND FIRST ENERGY\n",
    "# Random angles at the beginning\n",
    "rotation_gate_nodes = circuit_grid_model.get_rotation_gate_nodes()\n",
    "optimized_rotations = np.full(len(rotation_gate_nodes), 2 * np.pi * np.random.default_rng().random())\n",
    "\n",
    "energy = calc_new_energy(circuit_grid_model, rotation_gate_nodes)\n",
    "\n",
    "# MAIN OPTIMIZATION LOOP    \n",
    "nloops = 5\n",
    "for i in range(nloops):\n",
    "    Fin_optimizacion = False  \n",
    "    cur_rotation_num = 0\n",
    "    num_times_rot_dir_change = np.zeros(len(optimized_rotations))\n",
    "    while not Fin_optimizacion:\n",
    "        if cur_rotation_num != len(optimized_rotations):\n",
    "            print(' Iteration #' + str(iteration+1) , ', Rotating Gate #' , str(cur_rotation_num+1) , \n",
    "            '(Wire, Column) = (', rotation_gate_nodes[cur_rotation_num].wire_num+1, ',' , \n",
    "            rotation_gate_nodes[cur_rotation_num].column_num+1, '). Energy:', \"{:.6f}\".format(energy))\n",
    "        energy = optimize_rotations(circuit_grid_model, rotation_gate_nodes)\n",
    "        iteration +=  1\n",
    "\n",
    "# Extract the latest Ansatz (near EigenState) for the Histogram given the latest optimization circuit\n",
    "circuit = circuit_grid_model.compute_circuit_ansatz()\n",
    "backend_sim = Aer.get_backend('qasm_simulator')\n",
    "job_sim = execute(circuit, backend_sim, shots=n_experiments)\n",
    "result_sim = job_sim.result()\n",
    "prob_distro = result_sim.get_counts(circuit)\n",
    "\n",
    "# PRINT FINAL RESULT        \n",
    "print(\"\\n-------------------------------------------------------- \\n\")\n",
    "print('Final Energy: ', \"{:.6f}\".format(np.real(energy)))\n",
    "print(\"\\n-------------------------------------------------------- \\n\")\n",
    "print('Ansatz:',prob_distro)\n",
    "print(\"\\n-------------------------------------------------------- \\n\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Histogram of Ansatz Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram: \n"
     ]
    },
    {
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     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Histogram: ')\n",
    "plot_histogram(prob_distro, title=\"Ansatz Measurement\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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