VQE_Tutorial_Part2.Real.ONCE.ipynb

{
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   "cell_type": "markdown",
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   "source": [
    "# Tutorial on Variational Quantum Eigensolver (Part II)\n",
    "# \"*Brute force*\" Measurement to Estimate Energy\n",
    "# Simulator AND Real Quantum Device\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",
    "In Order to get access to a real device in the cloud it takes around 50 minutes in queue. Clearly it is not something we can afford if we want to implement VQE. The approach we will have in this Notebook is to have a **simulator** running all the VQE iterations and run the latest Ansatz Wavefunction through the **Real Device** only once.\n",
    "\n",
    "We will then measure the Ansatz to see what is the Base State with biggest probability in the Histogram.\n",
    "\n",
    "<img src=\"./img/VQE1.2.png\" >\n"
   ]
  },
  {
   "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": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "configrc.store_credentials:WARNING:2021-02-14 15:26:07,869: Credentials already present. Set overwrite=True to overwrite.\n",
      "c:\\users\\barrient\\appdata\\local\\programs\\python\\python38\\lib\\site-packages\\qiskit\\providers\\ibmq\\ibmqfactory.py:192: UserWarning: Timestamps in IBMQ backend properties, jobs, and job results are all now in local time instead of UTC.\n",
      "  warnings.warn('Timestamps in IBMQ backend properties, jobs, and job results '\n"
     ]
    },
    {
     "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",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "from qiskit import IBMQ\n",
    "IBMQ.save_account('b34d54b460e56752c548f81ff431174ddb290d1572bd92a6e92e5a1a5afd830c2cccc4c806a4312f34f429eb372244dd2bea3e5360608e65584d1a9307938914')\n",
    "IBMQ.load_account()\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": 2,
   "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. In this 'Brute Force' PartII tutorial we will just meassure the 5 qubits. \n",
    "\n",
    "Hence we are not adding extra quibits or Gates in the initialization segment now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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",
    "        self.nodes = np.empty((self.max_wires, self.max_columns),\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 \n",
    "        # Not applicable in Brute Force\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",
    "        cr = ClassicalRegister(NUM_QUBITS, 'c')\n",
    "        qc = QuantumCircuit(qr, cr)\n",
    "        # Build the Circuit with actual gates based on the Circuit Grid Model\n",
    "        for column_num in range(self.max_columns):\n",
    "            qc.barrier(qr)\n",
    "            for wire_num in range(self.max_wires):\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",
    "        \n",
    "        return qc\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Eigenvalues, Quantum State and Expectation Values\n",
    "\n",
    "Now in this section of the code we will calculate the Hamiltonian Matrices for each one of the 6 terms. Note that the resulting 32x32 matrix $(2^5x2^5)$ will be diagonal. This happens because the Hamiltonian has only Z and I matrices (that are in turn diagonal) and stay in the computational basis. We will extract the eigenvalues directly from that diagonal to calculate the expectation value. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Build the each Term of the hamiltonian doing the kronecker product of I and Z \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",
    "I=[[1,0], [0,1]]\n",
    "Z=[[1,0], [0,-1]]\n",
    "II=np.kron(I,I)\n",
    "ZZ=np.kron(Z,Z)\n",
    "ZI=np.kron(Z,I)\n",
    "IZ=np.kron(I,Z)\n",
    "IIIZZ=np.diag(np.kron(I,np.kron(II,ZZ)))\n",
    "IIZIZ=np.diag(np.kron(I,np.kron(IZ,IZ)))\n",
    "IZIIZ=np.diag(np.kron(I,np.kron(ZI,IZ)))\n",
    "IZZII=np.diag(np.kron(I,np.kron(ZZ,II)))\n",
    "ZIIZI=np.diag(np.kron(Z,np.kron(II,ZI)))\n",
    "ZZIII=np.diag(np.kron(ZZ,np.kron(II,I)))\n",
    "    \n",
    "# Extract the Eigenvalues in the Diagonal for each Term and multiply by corresponding factor \n",
    "Eigen_1=[(3/2)*float(i) for i in IIIZZ]\n",
    "Eigen_2=[(1/2)*float(i) for i in IIZIZ]\n",
    "Eigen_3=[(3/2)*float(i) for i in IZIIZ]\n",
    "Eigen_4=[(3/2)*float(i) for i in IZZII]\n",
    "Eigen_5=[(2/2)*float(i) for i in ZIIZI]\n",
    "Eigen_6=[(2/2)*float(i) for i in ZZIII]   \n",
    "Eigen_SUM=[Eigen_1[i]+Eigen_2[i]+Eigen_3[i]+Eigen_4[i]+Eigen_5[i]+Eigen_6[i] for i in range(32)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Global Functions:\n",
    "\n",
    "This list of function will do the following:\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 ....}).\n",
    "* `dict_to_array` translates previous dictionary to an array of probabilities $P_i$\n",
    "* `calc_expectation_value` uses the probability distribution and the eigenvalues to calculate Energy. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ExperimentAndMeasure(circuit):\n",
    "    backend_sim = Aer.get_backend('qasm_simulator')\n",
    "    job_sim = execute(circuit, backend_sim, shots=n_experiments, optimization_level=3)\n",
    "    result = job_sim.result()\n",
    "    prob_distro = result.get_counts(circuit)\n",
    "    # print(\"Ansatz:\",prob_distro)\n",
    "\n",
    "    # Measure and store in prob_distro in the format: {'000': 524, '111': 500}\n",
    "    return prob_distro\n",
    "\n",
    "def ExperimentAndMeasureREAL(circuit):\n",
    "    provider = IBMQ.get_provider(hub='ibm-q')\n",
    "    backend = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= NUM_QUBITS \n",
    "                                       and not x.configuration().simulator \n",
    "                                       and x.status().operational==True))\n",
    "    print(\"least busy backend: \", backend)\n",
    "    \n",
    "    #backend_sim = Aer.get_backend('qasm_simulator')\n",
    "    #job_sim = execute(circuit, backend_sim, shots=n_experiments, optimization_level=3)\n",
    "    job = execute(circuit, backend, shots=n_experiments, optimization_level=3)\n",
    "    job_monitor(job)\n",
    "    result = job.result()\n",
    "    prob_distro = result.get_counts(circuit)\n",
    "    # print(\"Ansatz:\",prob_distro)\n",
    "\n",
    "    # Measure and store in prob_distro in the format: {'000': 524, '111': 500}\n",
    "    return prob_distro\n",
    "def dict_to_array(prob_distro):\n",
    "    Prob_i=[]\n",
    "    for name in basis_states:\n",
    "        prob_distro.setdefault(name, 0)\n",
    "        Prob_i.append(float(prob_distro.get(name))/n_experiments)\n",
    "    return Prob_i\n",
    "    \n",
    "def calc_expectation_value(prob_distro):\n",
    "    Prob_i = dict_to_array(prob_distro)\n",
    "    new_energy = np.dot(Eigen_SUM,Prob_i)\n",
    "    return new_energy, prob_distro, np.argmax(Prob_i)"
   ]
  },
  {
   "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",
    "    quantumcircuit = circuit_grid_model.compute_circuit()\n",
    "    prob_distro = ExperimentAndMeasure(quantumcircuit)\n",
    "    \n",
    "    return calc_expectation_value(prob_distro)\n",
    "\n",
    "def calc_new_energyREAL(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",
    "    quantumcircuit = circuit_grid_model.compute_circuit()\n",
    "    prob_distro = ExperimentAndMeasureREAL(quantumcircuit)\n",
    "    \n",
    "    return calc_expectation_value(prob_distro)"
   ]
  },
  {
   "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, prob_distro, maxindex, 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]<2):\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, prob_distro, maxindex = 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, prob_distro, maxindex"
   ]
  },
  {
   "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": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "NUM_QUBITS = 5                                        # Qubits to model the problem\n",
    "Xgate = 1 ; Ygate = 2 ; Zgate = 3                     # 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 = 1024\n",
    "maxindex = None\n",
    "proposed_cur_ang_rad = 0\n",
    "cur_ang_rad = 0\n",
    "rot_direction = 1\n",
    "move_radians = np.pi / 9                             # 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:\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=3010x360 at 0x1E85307CF40>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit_grid_model = CircuitGridModel()\n",
    "circuit = circuit_grid_model.compute_circuit()\n",
    "\n",
    "print(\"\\nComplete Quantum Circuit:\")\n",
    "display(circuit.draw(output='latex',scale=0.7,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": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Iteration #1 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.000000 , Best Basis State: 00111\n",
      " Iteration #2 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.025391 , Best Basis State: 00111\n",
      " Iteration #3 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.126953 , Best Basis State: 00111\n",
      " Iteration #4 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.252930 , Best Basis State: 00111\n",
      " Iteration #5 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.383789 , Best Basis State: 00111\n",
      " Iteration #6 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.608398 , Best Basis State: 10110\n",
      " Iteration #7 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.731445 , Best Basis State: 10110\n",
      " Iteration #8 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.871094 , Best Basis State: 10110\n",
      " Iteration #9 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -1.977539 , Best Basis State: 10110\n",
      " Iteration #10 , Rotating Gate # 1 (Wire, Column) = ( 1 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #11 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #12 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #13 , Rotating Gate # 2 (Wire, Column) = ( 2 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #14 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #15 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #16 , Rotating Gate # 3 (Wire, Column) = ( 3 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #17 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #18 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #19 , Rotating Gate # 4 (Wire, Column) = ( 4 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #20 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #21 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #22 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #23 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #24 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 10110\n",
      " Iteration #25 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #26 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #27 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #28 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #29 , Rotating Gate # 5 (Wire, Column) = ( 5 , 1 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #30 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -2.000000 , Best Basis State: 00110\n",
      " Iteration #31 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -2.128906 , Best Basis State: 00110\n",
      " Iteration #32 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -2.468750 , Best Basis State: 00110\n",
      " Iteration #33 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -3.003906 , Best Basis State: 00110\n",
      " Iteration #34 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -3.683594 , Best Basis State: 00110\n",
      " Iteration #35 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -4.257812 , Best Basis State: 10101\n",
      " Iteration #36 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -4.996094 , Best Basis State: 10101\n",
      " Iteration #37 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -5.449219 , Best Basis State: 10101\n",
      " Iteration #38 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -5.890625 , Best Basis State: 10101\n",
      " Iteration #39 , Rotating Gate # 6 (Wire, Column) = ( 1 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #40 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #41 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #42 , Rotating Gate # 7 (Wire, Column) = ( 2 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #43 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #44 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #45 , Rotating Gate # 8 (Wire, Column) = ( 3 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #46 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #47 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #48 , Rotating Gate # 9 (Wire, Column) = ( 4 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #49 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #50 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #51 , Rotating Gate # 10 (Wire, Column) = ( 5 , 6 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #52 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #53 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #54 , Rotating Gate # 11 (Wire, Column) = ( 1 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #55 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #56 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #57 , Rotating Gate # 12 (Wire, Column) = ( 2 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #58 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #59 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #60 , Rotating Gate # 13 (Wire, Column) = ( 3 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #61 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #62 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #63 , Rotating Gate # 14 (Wire, Column) = ( 4 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #64 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #65 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #66 , Rotating Gate # 15 (Wire, Column) = ( 5 , 11 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #67 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #68 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #69 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #70 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #71 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 10101\n",
      " Iteration #72 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #73 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #74 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #75 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #76 , Rotating Gate # 16 (Wire, Column) = ( 1 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #77 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #78 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #79 , Rotating Gate # 17 (Wire, Column) = ( 2 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #80 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Iteration #81 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #82 , Rotating Gate # 18 (Wire, Column) = ( 3 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #83 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #84 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #85 , Rotating Gate # 19 (Wire, Column) = ( 4 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #86 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #87 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #88 , Rotating Gate # 20 (Wire, Column) = ( 5 , 16 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #89 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #90 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #91 , Rotating Gate # 21 (Wire, Column) = ( 1 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #92 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #93 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #94 , Rotating Gate # 22 (Wire, Column) = ( 2 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #95 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #96 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #97 , Rotating Gate # 23 (Wire, Column) = ( 3 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #98 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #99 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #100 , Rotating Gate # 24 (Wire, Column) = ( 4 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #101 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #102 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      " Iteration #103 , Rotating Gate # 25 (Wire, Column) = ( 5 , 21 ). Energy: -6.000000 , Best Basis State: 01010\n",
      "least busy backend:  ibmq_quito\n",
      "Job Status: job has successfully run\n",
      "\n",
      "-------------------------------------------------------- \n",
      "\n",
      "Final Energy:  -1.041992 , Optimal Basis State: 01010\n",
      "\n",
      "-------------------------------------------------------- \n",
      "\n",
      "Ansatz: {'00000': 29, '00001': 20, '10000': 9, '10001': 9, '10010': 29, '10011': 5, '10100': 19, '10101': 29, '10110': 28, '10111': 10, '11000': 37, '11001': 19, '11010': 153, '11011': 23, '11100': 26, '11101': 29, '11110': 30, '11111': 28, '00010': 68, '00011': 16, '00100': 21, '00101': 21, '00110': 34, '00111': 19, '01000': 25, '01001': 19, '01010': 177, '01011': 18, '01100': 25, '01101': 15, '01110': 19, '01111': 15}\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",
    "rotation_gate_nodes = circuit_grid_model.get_rotation_gate_nodes()\n",
    "optimized_rotations = np.full(len(rotation_gate_nodes), np.pi)\n",
    "\n",
    "energy, prob_distro, maxindex = calc_new_energy(circuit_grid_model, rotation_gate_nodes)\n",
    "\n",
    "Fin_optimizacion = False \n",
    "iteration=0\n",
    "cur_rotation_num = 0\n",
    "num_times_rot_dir_change = np.zeros(len(optimized_rotations))\n",
    "\n",
    "# MAIN OPTIMIZATION LOOP \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",
    "        ', Best Basis State:', basis_states[maxindex])\n",
    "        #print(' Ansatz:',prob_distro,\"\\n\")\n",
    "    energy, prob_distro, maxindex = optimize_rotations(circuit_grid_model, rotation_gate_nodes)\n",
    "    iteration +=  1\n",
    "    #print (optimized_rotations)\n",
    "\n",
    "# REAL COMPUTER SIMULATION\n",
    "energy, prob_distro, maxindex = calc_new_energyREAL(circuit_grid_model, rotation_gate_nodes)\n",
    "\n",
    "# PRINT FINAL RESULT        \n",
    "print(\"\\n-------------------------------------------------------- \\n\")\n",
    "print('Final Energy: ', \"{:.6f}\".format(np.real(energy)), ', Optimal Basis State:', basis_states[maxindex])\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": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Histogram: \n"
     ]
    },
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       "    </g>\r\n",
       "    <g id=\"xtick_12\">\r\n",
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       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n",
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       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n",
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       "    <g id=\"xtick_16\">\r\n",
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       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-49\"/>\r\n",
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       "    <g id=\"xtick_17\">\r\n",
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       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n",
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       "       <use x=\"63.623047\" xlink:href=\"#DejaVuSans-48\"/>\r\n",
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      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 15,
     "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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