qaoa_inbuilt.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "4accdde3",
   "metadata": {},
   "source": [
    "# Index\n",
    "\n",
    "## Lecture matcut problem using inbuilt QAOA first\n",
    "## A smpler paulis example\n",
    "## The project VQF single iteration \n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fe7ce21",
   "metadata": {},
   "source": [
    "# Lecture matcut problem using inbuilt QAOA first"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "8863e910",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 267.197x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from qiskit.circuit import Parameter\n",
    "from numpy import pi\n",
    "\n",
    "qreg_q = QuantumRegister(5, 'q')\n",
    "qreg_q_mix = QuantumRegister(5, 'q') \n",
    "qreg_q_combined = QuantumRegister(5, 'q') \n",
    " # creg_c = ClassicalRegister(5, 'c')\n",
    "circuit = QuantumCircuit(qreg_q)  #, creg_c)\n",
    "circuit_mix = QuantumCircuit(qreg_q_mix)\n",
    "circuit_combined = QuantumCircuit(qreg_q_combined)\n",
    "\n",
    "beta = Parameter('β')  # pi/4;  \n",
    "gamma = Parameter('γ')  # pi/8; \n",
    "\n",
    "# circuit.h(qreg_q[0])\n",
    "# circuit.h(qreg_q[1])\n",
    "# circuit.h(qreg_q[2])\n",
    "# circuit.h(qreg_q[3])\n",
    "# circuit.h(qreg_q[4])\n",
    "circuit_mix.barrier(qreg_q_mix[4])\n",
    "circuit_mix.barrier(qreg_q_mix[3])\n",
    "circuit_mix.barrier(qreg_q_mix[2])\n",
    "circuit_mix.barrier(qreg_q_mix[0])\n",
    "circuit_mix.barrier(qreg_q_mix[1])\n",
    "circuit_mix.rx(beta, qreg_q_mix[4])\n",
    "circuit_mix.rx(beta, qreg_q_mix[3])\n",
    "circuit_mix.rx(beta, qreg_q_mix[2])\n",
    "circuit_mix.rx(beta, qreg_q_mix[1])\n",
    "circuit_mix.rx(beta, qreg_q_mix[0])\n",
    "circuit_mix.barrier(qreg_q_mix[0])\n",
    "circuit_mix.barrier(qreg_q_mix[1])\n",
    "circuit_mix.barrier(qreg_q_mix[2])\n",
    "circuit_mix.barrier(qreg_q_mix[3])\n",
    "circuit_mix.barrier(qreg_q_mix[4])\n",
    "\n",
    "\n",
    "circuit.barrier(qreg_q_mix[4])\n",
    "circuit.barrier(qreg_q_mix[3])\n",
    "circuit.barrier(qreg_q_mix[2])\n",
    "circuit.barrier(qreg_q_mix[0])\n",
    "circuit.barrier(qreg_q_mix[1])\n",
    "circuit.rz(beta, qreg_q_mix[4])\n",
    "circuit.rz(beta, qreg_q_mix[3])\n",
    "circuit.rz(beta, qreg_q_mix[2])\n",
    "circuit.rz(beta, qreg_q_mix[1])\n",
    "circuit.rz(beta, qreg_q_mix[0])\n",
    "circuit.barrier(qreg_q_mix[0])\n",
    "circuit.barrier(qreg_q_mix[1])\n",
    "circuit.barrier(qreg_q_mix[2])\n",
    "circuit.barrier(qreg_q_mix[3])\n",
    "circuit.barrier(qreg_q_mix[4])\n",
    "\n",
    "circuit.cx(qreg_q[0], qreg_q[1])\n",
    "circuit.rz(gamma, qreg_q[1])\n",
    "circuit.cx(qreg_q[0], qreg_q[1])\n",
    "circuit.cx(qreg_q[0], qreg_q[2])\n",
    "circuit.rz(gamma, qreg_q[2])\n",
    "circuit.cx(qreg_q[0], qreg_q[2])\n",
    "circuit.cx(qreg_q[1], qreg_q[2])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.rz(gamma, qreg_q[2])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[1], qreg_q[2])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[2], qreg_q[3])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "circuit.rz(gamma, qreg_q[3])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[2], qreg_q[3])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[2], qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.rz(gamma, qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[2], qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "circuit.cx(qreg_q[3], qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "# circuit.barrier(qreg_q[2])\n",
    "circuit.rz(gamma, qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "# circuit.barrier(qreg_q[2])\n",
    "circuit.cx(qreg_q[3], qreg_q[4])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "# circuit.barrier(qreg_q[2])\n",
    "# circuit.barrier(qreg_q[4])\n",
    "# circuit.barrier(qreg_q[0])\n",
    "# circuit.barrier(qreg_q[1])\n",
    "# circuit.barrier(qreg_q[2])\n",
    "circuit.barrier(qreg_q)\n",
    "# circuit.measure(qreg_q[0], creg_c[0])\n",
    "# circuit.measure(qreg_q[1], creg_c[0])\n",
    "# circuit.measure(qreg_q[2], creg_c[0])\n",
    "# circuit.measure(qreg_q[3], creg_c[0])\n",
    "# circuit.measure(qreg_q[4], creg_c[0])\n",
    "\n",
    "\n",
    "# binder needed\n",
    "circuit = circuit.bind_parameters({gamma: pi/4, beta: pi/8})\n",
    "circuit_mix = circuit_mix.bind_parameters({beta: pi/8})\n",
    "\n",
    "# circuit_combined = circuit_mix + circuit\n",
    "circuit_combined.compose(circuit_mix)\n",
    "circuit_combined.compose(circuit)\n",
    "# circuit_combined = circuit_combined.bind_parameters({gamma: pi/4, beta: pi/8})\n",
    "\n",
    "\n",
    "circuit_mix.draw('mpl')\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "c99f6fc4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1411x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "a36a43c6",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.5926275470915993+0.12527866582148886j) * IIIII\n",
      "+ (-0.04405536882001815-0.05415650097836969j) * IIIIZ\n",
      "+ (-0.04405536882001815-0.05415650097836969j) * IIIZI\n",
      "+ (-0.07449684520662697-0.24787682587189439j) * IIIZZ\n",
      "+ (-0.1767546610287738-0.05415650097836924j) * IIZII\n",
      "+ (-0.07449684520662692-0.22148129550904577j) * IIZIZ\n",
      "+ (-0.07449684520662692-0.2214812955090458j) * IIZZI\n",
      "+ (-0.11303021364075344+0.0785427912303862j) * IIZZZ\n",
      "+ (-0.04405536882001816-0.054156500978369694j) * IZIII\n",
      "+ (-0.07449684520662589+0.09888313545864247j) * IZIIZ\n",
      "+ (-0.07449684520662589+0.09888313545864247j) * IZIZI\n",
      "+ (0.019669078568002173+0.07854279123038577j) * IZIZZ\n",
      "+ (-0.0744968452066269-0.22148129550904577j) * IZZII\n",
      "+ (-0.04405536882001771+0.07854279123038599j) * IZZIZ\n",
      "+ (-0.04405536882001772+0.07854279123038599j) * IZZZI\n",
      "+ (-0.04810131484377727+0.09888313545864241j) * IZZZZ\n",
      "+ (-0.04405536882001815-0.05415650097836968j) * ZIIII\n",
      "+ (-0.07449684520662589+0.09888313545864247j) * ZIIIZ\n",
      "+ (-0.07449684520662589+0.09888313545864247j) * ZIIZI\n",
      "+ (0.019669078568002207+0.07854279123038577j) * ZIIZZ\n",
      "+ (-0.0744968452066269-0.22148129550904577j) * ZIZII\n",
      "+ (-0.04405536882001773+0.07854279123038597j) * ZIZIZ\n",
      "+ (-0.04405536882001772+0.07854279123038597j) * ZIZZI\n",
      "+ (-0.048101314843777304+0.0988831354586424j) * ZIZZZ\n",
      "+ (-0.07449684520662697-0.2478768258718944j) * ZZIII\n",
      "+ (0.019669078568002183+0.07854279123038577j) * ZZIIZ\n",
      "+ (0.019669078568002176+0.07854279123038578j) * ZZIZI\n",
      "+ (-0.04810131484377739+0.0724876050957938j) * ZZIZZ\n",
      "+ (-0.11303021364075345+0.07854279123038617j) * ZZZII\n",
      "+ (-0.04810131484377729+0.0988831354586424j) * ZZZIZ\n",
      "+ (-0.04810131484377729+0.0988831354586424j) * ZZZZI\n",
      "+ (0.0886439233887379+0.07329239379766973j) * ZZZZZ\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1411x325.08 with 1 Axes>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "\n",
    "circuit_decomposed = circuit.decompose().decompose()\n",
    "circuit_decomposed_paulies = CircuitOp(circuit_decomposed).to_pauli_op().reduce()\n",
    "print(circuit_decomposed_paulies)\n",
    "circuit_decomposed.draw('mpl')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "71284593",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Operator contains complex coefficients, which are not supported.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [8]\u001b[0m, in \u001b[0;36m<cell line: 24>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     20\u001b[0m observable_comb \u001b[38;5;241m=\u001b[39m CircuitOp(circuit_combined); \n\u001b[1;32m     23\u001b[0m qaoa \u001b[38;5;241m=\u001b[39m QAOA(optimizer\u001b[38;5;241m=\u001b[39mCOBYLA(), quantum_instance\u001b[38;5;241m=\u001b[39mqinstance)  \u001b[38;5;66;03m# , mixer=mixed)\u001b[39;00m\n\u001b[0;32m---> 24\u001b[0m result \u001b[38;5;241m=\u001b[39m \u001b[43mqaoa\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcompute_minimum_eigenvalue\u001b[49m\u001b[43m(\u001b[49m\u001b[43mobservable\u001b[49m\u001b[43m)\u001b[49m  \u001b[38;5;66;03m# ValueError: Expectations of Mixed Operators not yet supported.\u001b[39;00m\n\u001b[1;32m     25\u001b[0m \u001b[38;5;66;03m# result = qaoa.compute_minimum_eigenvalue(observable_comb)  #  TypeError: ParameterExpression with unbound parameters ({Parameter(c)}) cannot be cast to a float.\u001b[39;00m\n\u001b[1;32m     27\u001b[0m \u001b[38;5;28mprint\u001b[39m(result)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/algorithms/minimum_eigen_solvers/vqe.py:496\u001b[0m, in \u001b[0;36mVQE.compute_minimum_eigenvalue\u001b[0;34m(self, operator, aux_operators)\u001b[0m\n\u001b[1;32m    492\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mquantum_instance\u001b[38;5;241m.\u001b[39mcircuit_summary \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m    494\u001b[0m \u001b[38;5;66;03m# this sets the size of the ansatz, so it must be called before the initial point\u001b[39;00m\n\u001b[1;32m    495\u001b[0m \u001b[38;5;66;03m# validation\u001b[39;00m\n\u001b[0;32m--> 496\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_check_operator_ansatz\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    498\u001b[0m \u001b[38;5;66;03m# set an expectation for this algorithm run (will be reset to None at the end)\u001b[39;00m\n\u001b[1;32m    499\u001b[0m initial_point \u001b[38;5;241m=\u001b[39m _validate_initial_point(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39minitial_point, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mansatz)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/algorithms/minimum_eigen_solvers/qaoa.py:149\u001b[0m, in \u001b[0;36mQAOA._check_operator_ansatz\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m    147\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m operator \u001b[38;5;241m!=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cost_operator:\n\u001b[1;32m    148\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cost_operator \u001b[38;5;241m=\u001b[39m operator\n\u001b[0;32m--> 149\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mansatz \u001b[38;5;241m=\u001b[39m \u001b[43mQAOAAnsatz\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    150\u001b[0m \u001b[43m        \u001b[49m\u001b[43moperator\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_reps\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minitial_state\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_initial_state\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmixer_operator\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mixer\u001b[49m\n\u001b[1;32m    151\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdecompose\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/blueprintcircuit.py:96\u001b[0m, in \u001b[0;36mBlueprintCircuit.decompose\u001b[0;34m(self, gates_to_decompose, reps)\u001b[0m\n\u001b[1;32m     94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdecompose\u001b[39m(\u001b[38;5;28mself\u001b[39m, gates_to_decompose\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, reps\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m     95\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_built:\n\u001b[0;32m---> 96\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_build\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mdecompose(gates_to_decompose, reps)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/n_local/qaoa_ansatz.py:261\u001b[0m, in \u001b[0;36mQAOAAnsatz._build\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    258\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_built:\n\u001b[1;32m    259\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m\n\u001b[0;32m--> 261\u001b[0m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_build\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    263\u001b[0m \u001b[38;5;66;03m# keep old parameter order: first cost operator, then mixer operators\u001b[39;00m\n\u001b[1;32m    264\u001b[0m num_cost \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m _is_pauli_identity(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcost_operator) \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;241m1\u001b[39m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/evolved_operator_ansatz.py:174\u001b[0m, in \u001b[0;36mEvolvedOperatorAnsatz._build\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    171\u001b[0m         \u001b[38;5;28;01mif\u001b[39;00m _is_pauli_identity(op):\n\u001b[1;32m    172\u001b[0m             \u001b[38;5;28;01mcontinue\u001b[39;00m\n\u001b[0;32m--> 174\u001b[0m         evolved_op \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mevolution\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconvert\u001b[49m\u001b[43m(\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoeff\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mop\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mexp_i\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mreduce()\n\u001b[1;32m    175\u001b[0m         circuits\u001b[38;5;241m.\u001b[39mappend(evolved_op\u001b[38;5;241m.\u001b[39mto_circuit())\n\u001b[1;32m    177\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrotation_blocks \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/opflow/evolutions/pauli_trotter_evolution.py:106\u001b[0m, in \u001b[0;36mPauliTrotterEvolution.convert\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m     92\u001b[0m \u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;124;03mTraverse the operator, replacing ``EvolvedOps`` with ``CircuitOps`` containing\u001b[39;00m\n\u001b[1;32m     94\u001b[0m \u001b[38;5;124;03mTrotterized evolutions equalling the exponentiation of -i * operator.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    100\u001b[0m \u001b[38;5;124;03m    The converted operator.\u001b[39;00m\n\u001b[1;32m    101\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    102\u001b[0m \u001b[38;5;66;03m# TODO uncomment when we implement Abelian grouped evolution.\u001b[39;00m\n\u001b[1;32m    103\u001b[0m \u001b[38;5;66;03m# if self._grouper:\u001b[39;00m\n\u001b[1;32m    104\u001b[0m \u001b[38;5;66;03m#     # Sort into commuting groups\u001b[39;00m\n\u001b[1;32m    105\u001b[0m \u001b[38;5;66;03m#     operator = self._grouper.convert(operator).reduce()\u001b[39;00m\n\u001b[0;32m--> 106\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_recursive_convert\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/opflow/evolutions/pauli_trotter_evolution.py:119\u001b[0m, in \u001b[0;36mPauliTrotterEvolution._recursive_convert\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m    117\u001b[0m pauli \u001b[38;5;241m=\u001b[39m operator\u001b[38;5;241m.\u001b[39mprimitive\u001b[38;5;241m.\u001b[39mprimitive\n\u001b[1;32m    118\u001b[0m time \u001b[38;5;241m=\u001b[39m operator\u001b[38;5;241m.\u001b[39mcoeff \u001b[38;5;241m*\u001b[39m operator\u001b[38;5;241m.\u001b[39mprimitive\u001b[38;5;241m.\u001b[39mcoeff\n\u001b[0;32m--> 119\u001b[0m evo \u001b[38;5;241m=\u001b[39m \u001b[43mPauliEvolutionGate\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    120\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpauli\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtime\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtime\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msynthesis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_evolution_synthesis\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    121\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    122\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m CircuitOp(evo)\n\u001b[1;32m    123\u001b[0m \u001b[38;5;66;03m# operator = EvolvedOp(operator.primitive.to_pauli_op(), coeff=operator.coeff)\u001b[39;00m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/pauli_evolution.py:102\u001b[0m, in \u001b[0;36mPauliEvolutionGate.__init__\u001b[0;34m(self, operator, time, label, synthesis)\u001b[0m\n\u001b[1;32m    100\u001b[0m     operator \u001b[38;5;241m=\u001b[39m [_to_sparse_pauli_op(op) \u001b[38;5;28;01mfor\u001b[39;00m op \u001b[38;5;129;01min\u001b[39;00m operator]\n\u001b[1;32m    101\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 102\u001b[0m     operator \u001b[38;5;241m=\u001b[39m \u001b[43m_to_sparse_pauli_op\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    104\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m synthesis \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    105\u001b[0m     synthesis \u001b[38;5;241m=\u001b[39m LieTrotter()\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/pauli_evolution.py:172\u001b[0m, in \u001b[0;36m_to_sparse_pauli_op\u001b[0;34m(operator)\u001b[0m\n\u001b[1;32m    169\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUnsupported operator type for evolution: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mtype\u001b[39m(operator)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    171\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(np\u001b[38;5;241m.\u001b[39miscomplex(sparse_pauli\u001b[38;5;241m.\u001b[39mcoeffs)):\n\u001b[0;32m--> 172\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mOperator contains complex coefficients, which are not supported.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    174\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m sparse_pauli\n",
      "\u001b[0;31mValueError\u001b[0m: Operator contains complex coefficients, which are not supported."
     ]
    }
   ],
   "source": [
    "\n",
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "\n",
    "\n",
    "from qiskit.algorithms import QAOA\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "# from qiskit.opflow\n",
    "from qiskit.utils import QuantumInstance\n",
    "from qiskit import Aer\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "qinstance=QuantumInstance(backend, shots=1, skip_qobj_validation=False)\n",
    "\n",
    "# My assumption: here intial, observable and mixer all in one place\n",
    "# Here it expects pure pauli\n",
    "# have to bring the circuit to pure pauli manually\n",
    "observable = circuit_decomposed_paulies # CircuitOp(circuit.decompose().decompose()).to_pauli_op().reduce()  # Not Implemented => .to_pauli_op()  # PauliOp( equivalent to \"Sum (I - Z^Z)/2\n",
    "mixed = CircuitOp(circuit_mix)  # .to_pauli_op();\n",
    "observable_comb = CircuitOp(circuit_combined); \n",
    "\n",
    "\n",
    "qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qinstance)  # , mixer=mixed)\n",
    "result = qaoa.compute_minimum_eigenvalue(observable)  # ValueError: Expectations of Mixed Operators not yet supported.\n",
    "# result = qaoa.compute_minimum_eigenvalue(observable_comb)  #  TypeError: ParameterExpression with unbound parameters ({Parameter(c)}) cannot be cast to a float.\n",
    " \n",
    "print(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6ecfa889",
   "metadata": {},
   "source": [
    "# A smpler paulis example\n",
    "\n",
    "a bitwise multiplication\n",
    "x*x "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "20908f44",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.75 * III\n",
      "+ 0.25 * IIZ\n",
      "+ 0.25 * IZI\n",
      "- 0.25 * IZZ\n",
      "+ 0.25 * XII\n",
      "- 0.25 * XIZ\n",
      "- 0.25 * XZI\n",
      "+ 0.25 * XZZ\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">          \n",
       "q_0: ──■──\n",
       "       │  \n",
       "q_1: ──■──\n",
       "     ┌─┴─┐\n",
       "q_2: ┤ X ├\n",
       "     └───┘</pre>"
      ],
      "text/plain": [
       "          \n",
       "q_0: ──■──\n",
       "       │  \n",
       "q_1: ──■──\n",
       "     ┌─┴─┐\n",
       "q_2: ┤ X ├\n",
       "     └───┘"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "\n",
    "qreg_q = QuantumRegister(3, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q)  #, creg_c)\n",
    "\n",
    "# bit wise multiplication is an AND operation\n",
    "# in quantum we can use ccx gate\n",
    "# Upon decomposing and reducing\n",
    "#  the ccx gate we get paulies string\n",
    "\n",
    "# circuit.x(qreg_q[0])\n",
    "# circuit.x(qreg_q[1])\n",
    "circuit.ccx(qreg_q[0], qreg_q[1], qreg_q[2])\n",
    "paulies = CircuitOp(circuit).to_pauli_op().reduce()\n",
    "print(paulies)\n",
    "circuit.draw('text') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3fd30111",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.75 * III\n",
      "+ 0.25 * IIZ\n",
      "+ 0.25 * IZI\n",
      "- 0.25 * IZZ\n",
      "+ 0.25 * XII\n",
      "- 0.25 * XIZ\n",
      "- 0.25 * XZI\n",
      "+ 0.25 * XZZ\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<pre style=\"word-wrap: normal;white-space: pre;background: #fff0;line-height: 1.1;font-family: &quot;Courier New&quot;,Courier,monospace\">          \n",
       "q_0: ──■──\n",
       "       │  \n",
       "q_1: ──■──\n",
       "     ┌─┴─┐\n",
       "q_2: ┤ X ├\n",
       "     └───┘</pre>"
      ],
      "text/plain": [
       "          \n",
       "q_0: ──■──\n",
       "       │  \n",
       "q_1: ──■──\n",
       "     ┌─┴─┐\n",
       "q_2: ┤ X ├\n",
       "     └───┘"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "# from qiskit.optimization.applications.ising import tsp  \n",
    "\n",
    "from qiskit.algorithms import QAOA\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "# from qiskit.opflow\n",
    "from qiskit.utils import QuantumInstance\n",
    "from qiskit import Aer\n",
    "from qiskit.quantum_info.operators import Operator\n",
    " \n",
    "qreg_q = QuantumRegister(3, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q)  #, creg_c)\n",
    "\n",
    "# bit wise multiplication is an AND operation\n",
    "# in quantum we can use ccx gate\n",
    "# Upon decomposing and reducing\n",
    "#  the ccx gate we get paulies string\n",
    "\n",
    "# circuit.x(qreg_q[0])\n",
    "# circuit.x(qreg_q[1])\n",
    "circuit.ccx(qreg_q[0], qreg_q[1], qreg_q[2])\n",
    "paulies = CircuitOp(circuit).to_pauli_op().reduce()\n",
    "print(paulies)\n",
    "circuit.draw('text') "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a73b1c81",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.75 * III\n",
      "+ 0.25 * IIZ\n",
      "+ 0.25 * IZI\n",
      "- 0.25 * IZZ\n",
      "+ 0.25 * XII\n",
      "- 0.25 * XIZ\n",
      "- 0.25 * XZI\n",
      "+ 0.25 * XZZ\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "# from qiskit.optimization.applications.ising import tsp \n",
    "from qiskit_optimization.applications import Maxcut, Tsp\n",
    "\n",
    "from qiskit.algorithms import QAOA\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "# from qiskit.opflow\n",
    "from qiskit.utils import QuantumInstance\n",
    "from qiskit import Aer\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "\n",
    "# multiply 2 bits\n",
    "data = [1, 1]\n",
    "\n",
    "# qubitOps, offset =.get_tsp_qubitops(data)\n",
    "\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "qinstance=QuantumInstance(backend, shots=1, skip_qobj_validation=False)\n",
    "\n",
    "# qaoa = QAOA(qubitOps, qc, 2, 'paulis', quantum_instance=QunatumInstance())\n",
    "qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qinstance)  # , mixer=mixed)\n",
    "qreg_q = QuantumRegister(3, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q)  #, creg_c)\n",
    "\n",
    "\n",
    "# bit wise multiplication is an AND operation\n",
    "# in quantum we can use ccx gate\n",
    "# Upon decomposing and reducing\n",
    "#  the ccx gate we get paulies string\n",
    "\n",
    "# circuit.x(qreg_q[0])\n",
    "# circuit.x(qreg_q[1])\n",
    "circuit.ccx(qreg_q[0], qreg_q[1], qreg_q[2])\n",
    "paulies = CircuitOp(circuit).to_pauli_op().reduce()\n",
    "print(paulies)\n",
    "circuit.draw('text') \n",
    "\n",
    "result = qaoa.compute_minimum_eigenvalue(paulies)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1871f4a8",
   "metadata": {},
   "outputs": [],
   "source": [
    "# from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "\n",
    "# H = b0 * I + b1 * Z "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e5f432b",
   "metadata": {},
   "source": [
    "# The project VQF single iteration "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "f6c2cc20",
   "metadata": {},
   "outputs": [
    {
     "data": {
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uplWjruw7vIPWjbtRs1pdpoz6C1Ur17iwX4w3Dq83xsVIA5s9e7bbIfgVTbkWEREJFdPruYiISDiZWBc1sbyC69xyIO2a9uGZ1DS6tErm7tEvcPrsiWKNje17vyH3RA7NG3R0MdLAUlNT3Q7Br2jKtYiISKiYXs9FRETCycS6qEZSBZd9eDuN6rYCICd3N0fzcmjVuOuFnx87eZjn3p3C/WNfdStE29LS0twOwa9oyrWIiEiomF7PRUREwsnEuqhGUgX3/b5NNG+YREFhAR6Pl3VbltCz7VAACgry+cOcn3L7DTOpW6uhy5FGPuVaREREREREIp0aSRXczv2baNEgiXP5Zziad4B1W5aSmNALgPRv5pG5ezUvf/Ab7p+dwrc7V7gcbWRTrkVERERERCTSabHtCu7Wa3934fuX799A+vq5eL1Wf3Fw9/EM7j7erdCClpGR4XYIfkVTrkVERELF9HouIiISTibWRc1IkmKSu45zO4Qymzt3rtshBCWScy0iIhIqkVbPRUREQsnEuqgZSQE0qROZv7tmfefiiITfC/DII48wblz4mzMVMdciIiKh4lY9FxERMZGJdVGNpABG93I7grJpN9jtCCoO5VpEREREREQqCl3aJiIiIiIiIiIitqiRJFHjhRdecDsEERERKSfVcxERkSIm1kU1kiRqJCUluR2CiIiIlJPquYiISBET66IaSRI1kpOT3Q5BREREykn1XEREpIiJdVGNJBERERERERERsUWNJBERERERERERsUWNJIkavXv3djsEERERKSfVcxERkSIm1kU1kiRqrF692u0QREREpJxUz0VERIqYWBfVSBIREREREREREVvUSBIREREREREREVvUSJKoMX/+fLdDEBERkXJSPRcRESliYl1UI0lERERERERERGxRI0mixpgxY9wOQURERMpJ9VxERKSIiXUx1u0ATPfOGthzxJ3f3aQOjO5Vtsd+9wkcP+BsPHbUrA/tBof/97pJuQ4f5VpERERERMRdaiQFsOcIbHPhjWt5HT8AR7PcjqJiUK7DR7kWERERERFxly5tk6gxefJkt0MQERGRclI9FxERKWJiXVQjSaLGlClT3A5BREREykn1XEREpIiJdVGNJIkaAwcOdDuEqOTzwa5DkLYZ3lxetH3Bali1DY6edC+2aFPosy6l/eRbeOOLou3/WgtrdkDeafdiExEJF9VzERGRIibWRa2RVIHdPzuFjO9XEBMTh9cbQ8M6Lbn12mkkdx3rdmhlkpOT43YIpYrEXPt8sHoHpGXA3qOX//yzTOu/HqBzUxiaBE2vDGeEJYvEXBcUwvIt8Ol3kHP88p+nb7b+G+OFbs3guk7Q4IrwxigiEi4m13MREZFwM7EuqpFUwU0Y8hAThjxIQUE+7y1/jiffupU2TbrTJL6N26FFnUjK9ZET8NYK2LI/8L4+4JvdsDELBneE4Z0hNibkIfoVSbnel2vletehwPsWFMLanbB+F4zsCikdwOsJeYgiIiIiIiIX6NI2ASAmJpYRfX9JQWE+2/Z+7XY4ZdKxY0e3Q7DF9Fzvy4VZ/7HXRLpYoQ+WboLXPoX8gtDEFizTc73zIDz7H3tNpIvlF8LCr2DOSigsDE1sIiJuiZR6LiIiEg4m1kU1kgSAc/lneX/5bAAS4hNdjqZsFixY4HYItpic6+OnYfbHcOxU2Y/x7V74xwrr0ji3mZzrnOPw0idw+lzZj7F6u9VQEhGJJpFSz0VERMLBxLqoS9squLc+fpx56TM5deY4MTFx3Df2FVo17gLAnoNbefzNH/OnKSuIi63E3LSnOXnmOLcNe8zlqEv28MMP89hjZsYG/nO9+MtXWbr2jQv7Zh/eTueW1/DbW/8R1hjnr4bcAE2kZydY/53qJ7SvvofOCdCjhWOhBcX0XBf6YM4KOBWgiWQn12mbISkB2jZwLj4RETeZXs9FRETCycS6aPSMpMLCQmbOnEnbtm2pUqUKXbt2JT09nXbt2nH77be7HV5UuPXaabw74yjzHz1In/YjWb912YWfNYlvw9Wdb+HtT54k+/AO0r5+m1uvneZitP7NmzfP7RD88pfrEX0m8UxqGs+kpjFtwttUqVSdicMfD2t832Vba+845Z01cDbfueMFw/Rcr9kB2x1cM2/el1ZzSkQkGphezy+2Lxc+2gAL18Fn38GJM25HFL12H4LF31gzcVduhTPlmNEbLqfOwhdbrOfHhxtg7xG3I4peeaetm5MsXAdLNkLOMbcjEnGOiXXR6BlJkyZN4p133uGhhx6iZ8+eLF++nPHjx5OTk8N9993ndnglmv/7FJp1GkKfUQ/a2m6KmtXqcN/YV/ivP7Rm+cb36N/pJgDGpfyae57rz5ffLSb1xmepFFvZ5UgjX2m5Bqt5+uScCUwa8SQN67YIa1zn78LmlLwz8PUu6NPK2eMGw9Rcf+5wrg8cgy37oF0jZ48rIiIlO3UW3lwOm/YU3/7uOhjW2bqTqUc3Q3DEsVPw+meXfwDzzlq4qQcMaOtOXIGkZcD764uvG/nhN5DYEP7raqiul9SOKPTB4vXw8bfFP1T7YL11p9vxV0HlOPfiE4lWxs5ImjNnDq+//joLFy7kgQceYNCgQUybNo1+/fqRn59Pjx493A4x6tSqVpdbrrmP1z78HYU/rOAbGxNH51YDyTt1hE4tr3Y5wuhRUq4B3lgynZYNOzOg06iwxnPizOUvhp2wZofzxwyWabnenxv84tp2rDYg1yIiFUFBIfx1Wcl1s6AQFq23bj4h5XfmHDy/FHaUMIv3bL41I3fVtvDHFchn31lNxZJuPrJlH7zwMZwz5MYkkW7xeliyqeSZ2V/vglc/1axtkVAwtpH0xBNPMHz4cJKTk4ttb9OmDXFxcXTpYq138vDDD5OYmIjX62X+/PluhBpVbr7mHg4fy2bJ2r8DsHPfJjbt/ILubYawaNXLLkfnX3p6utshBOXSXK/b8jFrMz/il9c/FfZYsg6HZnHsXYfMWHTbpFx/H4ImEoSmOSUi4gbT6/nGLNhx0P8+/9lozVqS8vlyO+w/Bv5eSvz7a6uBZ4qz+dZsmNL4gD1HrPUkpXyOnbJmIvmTuc9q3olEMhPropGXtmVlZbFx40buvffey362a9cukpKSqFzZmg86fPhwbrvtNn7+85+HO8yI90xq2mXbqlepxTuPHQasS3/+9M6vuOvm50mIT+Se5/vTP+km6tQ0c1XfTZs2Ub9+fbfDKFGgXB8+to/n3p3CE5MWExdbKczRwd6joTnu6XNw5ATUrRGa45fE9FxnHw3NcXOOWZ9uxsWE5vgiIuFicj0HWLnNumzN3wcl+QVWo6C/oZddRYoVW8GD/0ZS3mnI2AudEsIVlX8bdge+I6sHa50nNy//jwZrdwaebeTxWOesLv+XSGZiXTS2kQTQsGHDYttPnTpFeno6I0aMuLCtf//+ZfodHpsXrt8ybRkJHVKCOvaX7z3O2kUzi207dzqPZp2GBHWc9PQ07r5uUFCPOW/mr5bRtXVKmR573r9XzKZtk54kJvQE4LZhM3hh4VSmTZhT6mPS09PoPb5sMftTUlPxUrNmzQq436xZs5wK6QIncv3m0hmcOJ3L0/+87cK2pvXaMXXMS6U+xslc9735Ya66ZXqxbefvGFaa0n5+6R3GEjt04lCWM3P8oyHXgyfOpvO1vyq2zYlc+4Bata/kdN7h8gVYTve8ab2iszvGStlFaq4jNe5IY2qeTa7ndv30Dxu5MiHJ7z4+n48Hfvc4K+Y/FKaootMdLx6iSo26AfebMHEy3yx9IQwRBdbzht9w9U/+1+8+PuDrjO/xDGsRlpii1cCfzqLrdXfh9Zb+KZrPBx8sWc5t1wwIY2QiwbFT88JVF302LycxspEUHx8PQGZmJiNHjryw/amnniI7O5uePXu6FZotfW6aVuJi25HmpgGTi/17QKdRYV9PpqK4e/Tz3D36edd+f0F+6ObfF5wz6xY2yrWIiJTHmRNH8BUW4PHz5tXj8XDmVG4Yo4pOZ07mUrl6nYANUZNyffZk4Fh8vkLOnDwa+mCi3NlTx/B4/K/UUlhYwFnlWsRxHp/dllMYFRYW0r17d7Kzs5k5cyZNmjRh/vz5LFq0iF27drFy5Ur69u1b7DEpKSlMmTKFMWPGOBrLX5bAtgP293fyrm2t68NdQ+3/7outeRuOZpXtseVROwF6/cT5427evDngPh06dCAjI8PvPu3bt3cqpAuiIdfrd8H/fWZv3/OzYy6deVSSGC/87ziIdehyq2jI9WffwYI19vYNJtdXVIXpo8sel1POxxpolpWUX6TmOlLjjjSm5tnkem7Xp9/BOzbG8YdugivDeGl3NHr/68ALl8d64bFboFr4r1Yv0bFT8Oi/Al9ydX1XGNopPDFFq71H4KlFgfe7tZ8uIxSzBaqNJtZFIxfb9nq9zJs3j6SkJFJTU5k4cSLx8fFMnjyZmJiYCwtti1xs+vTpgXeSEjUNPGu8TBrXdq6JFC2aXhma4yaE6G8oIhJuptfz3i2hRhVr7ZXSdG+uJpITBrSFSrHWmkKluTrRnCYSQK2q0Ld16T/3eKx4r2oTvpiiVeM60LFx6T/3eKB2NejWLHwxiYSCiXXRyEYSQGJiIsuWLePEiRPs2rWLGTNmsGHDBjp27EjVqlXdDk8MNG7cOLdDiFh1qoemmdSlqfPHjHRN61ovapzWVS+SRCRKmF7Pq1aCOwdDjcrFt59vLCU2hJ9cFf64olGd6vCrQVA5rvj2842l7s3hR93DHlZAo3tBUhPr+0sbjlXj4FeDoWaV8McVjX42AFrWs76/tOF4RVW481qrGSkSyUysixF1Wq1Zs4arripemR966CH+7//+j5ycHDZs2MDUqVNJT0+ndWs/HwWE0JgH04LaLs6xM+VPSubxwIBEeHulc8eM8erTtpLEeK27+Czyc2vgYFWrpE/bRCR6REI9b1wHpt0Ia3bA/NXWti4JVt1r1wi8Zq1xHtFa1bcuE/xyO7y3ztrWowX0b2P9zLD15AHrDqq/SIYt+2H5Fvh6l7X95p7WJVZVDZpBFemqVoK7hsC3e627s238YQmEn/SF7i2gckS92xUpmYl10dgZSZfKy8sjMzOTHj16FNs+Y8YMsrKyOHPmDIcOHSIrK8u1JlK0OJi7hxfem0rGrlXc81x/pj5/NbMXBr7LigTPpFz3amFdiuaUazua9WmbSbke2M7ZWUkju+rTNhGRcKsSZ11Wdd7EgdChsZpIoVC9MgzqUPTvnw2A1g3MbCKd5/FYs9Nuu6ZoW3J7NZFCweuFTglW8+68q9qoiSQSShHTSKpRowYFBQXcddddbocS9dZmLqFn4lAa1G7O03d8wrOTP+do3gF2ZG9wO7SoY1KuY2OsxQhjHHhR1rg2XGfYApIm5bpKnHOXPbRtYM1wEhERERERCQf1aSu49dvSePRvN9OqUVf2Hd5B68bdqFmtLlNG/YWqlYtWiYzxxuH1c5tbE6SkpLgdgl+RkOuEuvCzq+Hvn5d+t5FAdxCrUx1+meLuItuRkOv2jWBM76JLIkoSKNeNa1ufdOrTbxGJJqbXcxERkXAysS5GzIwkCY3OLQfSrmkfnklNo0urZO4e/QKnz54o9mZ7+95vyD2RQ/MGHV2MNLDZs2e7HYJfkZLrbs2sqcGXLiJqR8t6cM91VjPJTZGS66sT4af9yzb1umNjmDzEmu4vIhJNTK/nIiIi4WRiXVQjqYLLPrydRnVbAZCTu5ujeTm0atz1ws+PnTzMc+9O4f6xr7oVom2pqaluh+BXJOW6YxP4nxugdytrcehAalSBUT2txQ5DcUeyYEVSrnu1tHLdpan/2xufV7sajL/KmvWlJpKIRCPT67mIiEg4mVgXdWlbBff9vk00b5hEQWEBHo+XdVuW0LPtUAAKCvL5w5yfcvsNM6lbq6HLkQaWlpbmdgh+RVqua1SBCf3gR91g9XbYcRCyDsPJM9YCknWrQ8KV1iVaXZu6eynbpSIt13Wqw88HwuE8WL0Dvj8IWUfg1FmrkRdfw7rsMKmJ9eXVRwAiEsVMr+ciIiLhZGJdVCOpgtu5fxMdm/fjXP4ZjuYdYN2WpYwZeD8A6d/MI3P3al7+4DcATBrxJB1b9HMz3IgWqbmuVRWuTXI7iuBEaq7r1oBhnd2OQkREREREpHRqJFVwt177uwvfv3z/BtLXz8X7w3SHwd3HM7j7eLdCizrKdfgo1yIiIiIiIqGhCySkmOSu49wOocwyMjLcDiEokZzrSKNci4hEjkir5yIiIqFkYl3UjKQAmtSJzN9ds75zcUTC7wWYO3cu48aFv2FQEXPtFuVaRCT6uVXPRURETGRiXVQjKYDRvdyOoGzaDXY7gvB75JFHXDnBKmKu3aJci4hEP7fquYiIiIlMrIu6tE1ERERERERERGxRI0lERERERERERGxRI0mixgsvvOB2CCIiIlJOquciIiJFTKyLaiRJ1EhKSnI7BBERESkn1XMREZEiJtZFNZIkaiQnJ7sdgoiIiJST6rmIiEgRE+uiGkkiIiIiIiIiImKLGkkSNXr37u12CCIiIlJOquciIiJFTKyLaiRJ1Fi9erXbIYiIiEg5qZ6LiIgUMbEuqpEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkUWP+/PluhyAiIiLlpHouIiJSxMS6qEaSiIiIiIiIiIjYokaSRI0xY8a4HYKIiIiUk+q5iIhIERPrYqzbAZjunTWw54g7v7tJHRjdq2yP/e4TOH7A2XjsqFkf2g0O/+91k3ItYgadiyJS0bg17oHGPhGRikyNpAD2HIFtLhXo8jh+AI5muR1FxaBci5hB56KIVDQa90RExA26tE2ixuTJk90OQURERMpJ9VxERKSIiXVRjSSJGlOmTHE7BBERESkn1XMREZEiJtZFNZIkagwcONDtEEQqLJ8Pjpwo+veeI5Bf4F480czng4PHi/6dfRQKCl0LR8RxkVTPj58u+n7XITib714s0czng6Mni/6ddVg1RkQqDhProtZIkqiRk5PjdggiFYrPBzsPwheZkJENJ84U/ezpRRDjhWZ14ao20L05VFLFKTOfD7bst3KduR9OnS362f9+AHEx0CIe+rWBLk0hNsa9WEXKy/R6vi8XvtgCG3YXb2788UPweKBRbejdEvq0guqVXQszKuw+bI17m/YUb9rNXAxeDyTUhb6toVcLqBznWpgiIiFlYl3Uy/oK7P7ZKWR8v4KYmDi83hga1mnJrddOI7nrWLdDizrKtUSbIyfgn6tgc3bp+xQUwo6D1tf7X8O4PtC5adhCLFEknov7c2HOSqtpV5pzBVajact+uLIG/OQqaNsgfDGKVAQnz8J762DVttL38flg7xF47wgs/gZu7A7921pND7dE4rh3/BTMWw3f7C59n0KfNQts1yFY9DWM7g09mlvNPBERCS01kiq4CUMeYsKQBykoyOe95c/x5Fu30qZJd5rEt3E7tKB17NjR7RD8iqZcS8WWsRf+9jmcPmf/McdPw6ufWm+oxvQCr4sXVkfSubh2J8xZAflBXLp2KA+eXwrDOsPwznpTJZHHxHq+9wj8Na34DKRAzubD/NXWbJrbroHKLr7qjqRxb9sBeC0dTpwNvO95J87CG19Axh4Y38+aESsiEi1MrIsaZgWAmJhYRvT9JQWF+Wzb+7Xb4ZTJggUL3A7BlmjItVRc32XDK+nBNZEutnwLvL3K+tTebaafi2t3wJtfBNdEuth/NlgzwUQijWn1fF8uPLc0uCbSxTL2wl+XmbF+kunj3o4cePGT4JpIF1uzE/7+ORRq3TgRiSKm1UVQI0l+cC7/LO8vnw1AQnyiy9GUzcMPP+x2CLZEQ66lYjp2ypqJ5G9h52cnWF/+fLkdVvq5NCRcTD4X9x+DOavAX7/NTq4//hY2ZjkamkjImVTPzxXA659Zl7WVxs65uO0ALFrvbGxlYfK4d/KMletzfhbRtpPr9bshbbOzsYmIuMmkunie0Ze2FRYW8sc//pGXXnqJ3bt3065dO/785z9z++23k5yczF//+le3Q4x4b338OPPSZ3LqzHFiYuK4b+wrtGrcBYA9B7fy+Js/5k9TVhAXW4m5aU9z8sxxbhv2mMtRl2zevHk89piZsYH/XC/+8lWWrn3jwr7Zh7fTueU1/PbWf7gVrshlFqz2/2YqGO+uhQ6NoXY1Z44XDNPPRZ8P3l7h3B2J5n4JretD1UrOHE8k1Eyq5x9tsGYkOSF9M3Rrbi2MH26mj3sA730FuaecOdai9dA5AerVcuZ4IqHi81mvrXw+qFbZ3fXUol2hz2pYezxQrVJkXfpvUl08z+hG0qRJk3jnnXd46KGH6NmzJ8uXL2f8+PHk5ORw3333uR1eieb/PoVmnYbQZ9SDtra77dZrpzFhyIMcP3mEZ+ZNYv3WZYzoMwmAJvFtuLrzLbz9yZMM6fX/SPv6bZ6dstzliCOXv1yP6DPpwveHj+3jgZcGMXH4426GK1LMvlzrU16nnMmHz76DH3V37ph2mX4ubj1gLVDulGOnrFlgye2dO6ZIRXD6HHz6nXPH8wFLN8Evkp07pl2mj3tHT1rjlFPyC2HZZusmDyImKiyEFVutMWb/MWtbnepwTSIMbKe7rzopv8DK82eZ1s1iAOrXsvLcv42763ZGMmPTNmfOHF5//XUWLlzIAw88wKBBg5g2bRr9+vUjPz+fHj16uB1iVKlZrQ73jX2FVZs/YPnG9y5sH5fya1ZmvM8T/xhP6o3PUilW97Etr9JyDdYsvCfnTGDSiCdpWLeFOwGKlGD5FuePuXKbc7NuysLUc/GLTOeP+XmmGetSiUSStTuspreTNmUVvZFxg6nj3oqtzo9Ra3aUfT0/kVAqLIS/f2HdmfDAsaLtR07Awq9g9if+L/EU+84VwEvLrLxePPbmHLNuhvC3L7SmWlkZ20h64oknGD58OMnJxT+2adOmDXFxcXTp0oUjR45www03kJiYSNeuXbnuuuvYunWrSxFHvlrV6nLLNffx2oe/o/CHMyo2Jo7OrQaSd+oInVpe7XKE/qWnp7sdgm0l5RrgjSXTadmwMwM6jXIvOJESZO5z/pgnzsDeo84fNximnYs+X2hynXPcuUtGRELNlHoeinPRB2zd7/xxg2HauAeQme38Mc/mw/cOzu4UccoXW+DrXdb3JfVPtx2wbpgh5ffRBthSwph7Pu/rd8HnIfiw1Gmm1MWLGdlIysrKYuPGjYwdO/ayn+3atYukpCQqV66Mx+Nh6tSpZGZmsn79em644QYmTpzoQsTR4+Zr7uHwsWyWrP07ADv3bWLTzi/o3mYIi1a97HJ0/m3atMntEIJyaa7XbfmYtZkf8cvrn3I5MpHizuQXTbt22q5DoTluMEw6Fw+fcG4dqkvtNiDXInaYUs+zjoTmuLsPh+a4wTBp3CsshD1RnGuRi/l81mVWgZbnWb5Fs5LKK7/Aatr54wE+3Wz+rG1T6uLFPD6feWlbuXIl/fr144MPPmDkyJEXtp86dYrWrVszYsQIXn311cset2bNGkaNGkVWVuBb1Hhsrq51y7RlJHRIsR37/N+nsG/bKmLiil8Cdu50HleNfjSoNZKyMtJY8Pgg2/tfbOavltG1dUqZHnteYWEh97+YTOqNz5IQn8g9z/fnqduXUqdmg1Ifs35bGg+8WLaY/bn33nsD7jNr1qyA+82aNcupkC5wItfn1yR4YtJi29PJQ5VrkUvVqteSibOKL14R6K45pZl6ydqtq96dwcr5ztyJIhrOxUZt+zPukS+KbXMq18tev5Nvls4uY2TOuedN62XHn34aQatcRiBT82xyPb/UlNfPEBNbtEq9U+fillXzWPSXceWIrIhb4x44N/ZVqVGXO14s3ul2Ktdf/+fPpL9xTxkjc46p52M0Mj3X1a5owC+ftzfdcc6DPTmwc12II4pe9Zp349bHv7K17ytTGnPiaAimRtpkp+aFqy7abQ8Zudh2fLx1O4vMzMxijaSnnnqK7OxsevbsWeLjnn32WUaNGhWOEP3qc9O0EhfbjjT/XjGbtk16kphg5fu2YTN4YeFUpk2Y43Jk0efNpTM4cTqXp/9524VtTeu1Y+qYl9wLSuQHdhvvZTu2WRNj3T4XQ5nrwJ9/ikhxoTlnNO5dquLUGBGP1/4q2sHsK5dTrkPLyBlJhYWFdO/enezsbGbOnEmTJk2YP38+ixYtYteuXaxcuZK+ffsWe8z06dNZvHgxn3zyCdWqOXc/6b8ssa5TtcvJu7a1rg93DbX/uy+25m04GnhiluNqJ0Cvnzh/3M2bNwfcp0OHDmRkZPjdp317529bFG25FrnUqbPw23n29j3/KfKlnwqXZlRPSHHotIyGc3H/MXjy3/b2DTbX/3U1dG9etricdD7ess44EHtMzbPJ9fxSj7xjb22xYM/F/m1gXN/A+9nh1rgHzo19BYXwm39a/w0k2FwP7wzDu5Q9NqeYej5GI9NzXVAIj/4Ljp/2v19sDMwYDVUr+d9PSnf6HDy0IPAlgjWqwPSbIcbFvnOg2mhKXbyYkW16r9fLvHnzSEpKIjU1lYkTJxIfH8/kyZOJiYmhS5fiFeH3v/8977//Ph9++KGjTSSJLNOnT3c7BJGoVLUSxNcIzbGb1g3NcSNVvZpQOURzhROUa4kQptTzJnVCc9ymV4bmuJEqxguNaofm2KoxYpoYLwxI9L+PB+jdUk2k8qoSB71bBZ7zOKCtu00kO0ypixcz8tI2gMTERJYtW1Zs289+9jM6duxI1apVL2ybPn06ixYtYsmSJdSuXTvMUYpJxo1zZr0BEblcq/pwMM/ZY1aKUXPjUl4PtKwHmx2+TL9W1dA1A0WcZko9b10fvt3r/HFb1XP+mJGudX3IcnhhbK8Hmsc7e0wRJwzuAN/uKfmGIx7gyppwfdewhxWVRnaBLfvg4PGS75DXrC4M7hj2sIJmSl28mOG9t+LWrFlTbH2kTZs28eijj3Lo0CFSUlLo1q0b3bp1cy9AYMyDaSVevlbadnFOhw4d3A5BJGr1b+v8MXu2DN3sm0gWilz3awMhXX5JxEGm1PM+rZz/lLp1fWhwhbPHjAb92jh/zK7NrEtWRExTKRYmXwvJ7a3vz4v1Qt/WMPU6PXedUqMK3HOdldfYi8bzSrEwsB1MHhIZr0VNqYsXi4C0WfLy8sjMzOTOO++8sC0pKcn2quIiIlJ2za+0ZsrsyHHmeF6PVcDlcklNrEvcco47c7zKsdaaLCISnJpVrctLVm5z7piDzHsvYISGV0DHxs7NAPPg3Pp7IqFQOQ5u7gkju8J//9Pa9thoqFbZ/+MkeDWqwE+ught7wO9+WPNzxmjrbyBlFzGNpBo1alBQEGClLHHEwdw9zE17mkHdx/PiwnvxeLy0a9qb1BtDf6vdika5lkjh8cBP+sLTiyDfxoKogQztFLo1McrCpHMxxgvjr7Ju9uDERyU39oArtHygSJnc2N1qbhyzseh2IN2bQ6eE8h/HKSaNewBj+8Af3ocz+eU/1sD2uqxNIsPFs2HURAqtahetOaUmUvlF1KVtEh5rM5fQM3EoDWo35+k7PuHZyZ9zNO8AO7I3uB2aXykpKW6HELRIzbVUTA2ugDF9/O8z9R+B76bTtgEMTXIuLieYdi62qg8jAqyPYCfX3ZppNpJEHpPqebXK8LP+/i9xs3Mu1q8Ft/RyNrbyMm3cq1PdaqL7uwrXTq6bX6n1ZUQkuphUF8+LmBlJEhrrt6Xx6N9uplWjruw7vIPWjbtRs1pdpoz6C1UrF63MGuONw+uNcTHSwGbPnu12CH5FU66l4rqqNRQUwPzVZZstk9gQJg20bmvrlkg5F4cmQWEhfFjG93TdmsFP+2ttJIk8ptXztg3hF8nw2qeBbyNdkoZXwK8Gu7vmSaSMe92aW7Ne31oBhWUoMi3i4faU4uvOiIhEOtPqImhGUoXXueVA2jXtwzOpaXRplczdo1/g9NkTxV5UbN/7DbkncmjewOwl7VNTU90Owa9oyrVUbAMS4e7rrE/Y7Yr1wo+6wR2D3J9OHCnnoscDw7tYOasdxKVplWPhx33hv652t2EnUlYm1vMOjeE3I4O/49rAdnDv8ODO4VCIlHEPoFdLuG84NK5j/zFeDwzrDFOG6PIgEYk+JtZF9esruOzD22lUtxUAObm7OZqXQ6vGRfOBj508zHPvTuHBn851K0Tb0tLS3A7Br2jKtUjLevDrkfDV9/B5Zsm3sAWoXtmaxdS/LVxpyO3nI+1c7NAY/ucGWLMDvsiE7NyS97uiKvRra13KVqtqeGMUcZKp9bxeLZgyFDZlwedbIDO75JmZlWKhZwu4JjG4ZkgoRdq4l1AX7hsG63dbNaa0Gz1UqwS9W8HVba2/j4hINDKxLqqRVMF9v28TzRsmUVBYgMfjZd2WJfRsOxSAgoJ8/jDnp9x+w0zq1mrocqSRT7mWaBMXY90eu08rOHEGdh+Gw3ng80HVStYbgfia1ifFJonEc7FKHFydaH0dO2XlOveklesaVaxc162uy9hEQs3rgc5Nra/T52DPYThwHAoKrfO0cW1rPTl/ayq5IRLHvdgYqyHXswWcPANZR+BQnpXrqpWgSR2oXxO8huVaRKQiUCOpgtu5fxMdm/fjXP4ZjuYdYN2WpYwZeD8A6d/MI3P3al7+4DcATBrxJB1b9HMz3IimXEs0q14Z2jdyOwp7Iv1crFUVkpq4HYWIVImD1g2sL9NF+rhXrbK1xp6IiJhBjaQK7tZrf3fh+5fv30D6+rl4f/hoZ3D38QzuPt6t0IKWkZHhdgh+RVOuRSKZzkURs5lezyORxj0RkchlYl3UZFApJrnrOLdDKLO5c824rt+uSM61SDTRuShilkir55FI456ISOQwsS5qRlIATVxcJLE8v7tmfefiiITfC/DII48wblz4XxhVxFyLmEjnokh0cKueRyI3xx+NfSIi4WFiXVQjKYDRvdyOoGzaDXY7gopDuRYxg85FEaloNO6JiIgbdGmbiIiIiIiIiIjYokaSRI0XXnjB7RBERESknFTPRUREiphYF9VIkqiRlJTkdggiIiJSTqrnIiIiRUysi2okSdRITk52OwQREREpJ9VzERGRIibWRTWSRERERERERETEFjWSRERERERERETEFjWSJGr07t3b7RBERESknFTPRUREiphYF9VIkqixevVqt0MQERGRclI9FxERKWJiXVQjSUREREREREREbFEjSUREREREREREbFEjSaLG/Pnz3Q5BREREykn1XEREpIiJdVGNJBERERERERERsUWNJIkaY8aMcTsEERERKSfVcxERkSIm1sVYtwMw3TtrYM8Rd353kzowulfZHvvdJ3D8gLPx2FGzPrQbHP7f6yblWkTEfG6N1aDxWkTcoXFPAtH7GCkrNZIC2HMEtrk0AJfH8QNwNMvtKCoG5VpExHwaq0WkotG4J4HoOSJlpUvbJGpMnjzZ7RBERESknFTPRUREiphYF9VIkqgxZcoUt0MQERGRclI9FxERKWJiXdSlbRI1Bg4cyKeffup2GCIicpETZ+Cb3bDrEOzLLdo+ZyU0rQtdmkKtqu7FF01yT8GGH3J93p8+gkZXQLMroXNTqF7ZvfjsUj2XSHc2HzZmwc6DsPdo0fY3voCEutCpCdSr5Vp4UeXUWdiQBbsuyfU/VkCzutApAepUdy28Evl8sCMHMvfD7ovG65eWQUIdaNMA2jYEr8e9GKNFoQ+27LOWqtl9uGj7y2nWa5C2DaFVPfAYnmsT66IaSRXY/bNTyPh+BTExcXi9MTSs05Jbr51GctexbodWJjk5OW6HUKpoy7WISCC5J+GD9bDue8gvuPznq7ZZX++sga7N4PquEF8z/HFeKhLH65zj8MHXVsOu0Ff8ZztyrK/lW2H+GujZAkZ2hSsMbt6ZXM9F/Dl9Dj7aACu2wqlzl/987U7r67110K4RjOwCzePDHeXlInHcyzsNi76BNdvhbAk1ZvV26+udNVYz6fpu0PCKsIdZjM9n1cSlGyE79/KfZ+y1vpZsgitrwKAO0L+t+w2lSHx+FPpgxRZYlgEH8y7/+aY91teHG6znxZAkqz6a2lAysS6qkVTBTRjyEBOGPEhBQT7vLX+OJ9+6lTZNutMkvo3boUUd5VpEKoq1O2D+6pLfSF2q0AdffW99en9TDxjQ1v0XcpEyXvt88HkmLPwKzpXwRupS+QVW8+6b3TC2N/RoEfIQRSqMLfvhreVw5KS9/b/LhsxsGNzRau7GuLzgSKSMe2CNYXNXQd6ZwPv6sGYsZey18jyogzs1Ju+0NRN30x57+x/Ks+roup0wob/VWHJTJD0/DudZM9Ls3jBrXy68udx6LfKTq6BmldDGFy20RpIAEBMTy4i+v6SgMJ9te792O5wy6dixo9sh2BINuRYRKc0n38Iby+01kS52rsB60fzvr60GiQlMHq99PquBtGCNvSbSxU6dhb9/AWkZoYmtvCKlnouc981uePFj+02k83zAx9/C3z6HgsKQhBY0k8c9gOVb4LVP7TWRLpZfaI2Z874Mf43JPQV/XmK/iXSx7TnWJcr7jzkfV1mY/vw4cMzKV1nuur5pD/z5I2tGtWlMrItqJAkA5/LP8v7y2QAkxCe6HE3ZLFiwwO0QbImGXIuIlGTtTuuFenl88i18+p0j4ZSbyeN1+mZryn55vLvO+rTbNJFSz0XAWgfpb59BQTmaE9/stprCJjB53Nu0x2oElcfyrfCfjc7EY0d+gbX20YFyNIKOnbIalSeDbJ6FgsnPj5NnYfYnVuOurHKOW3+vYD+gCTUT66Iubavg3vr4cealz+TUmePExMRx39hXaNW4CwB7Dm7l8Td/zJ+mrCAuthJz057m5Jnj3DbsMZejLtnDDz/MY4+ZGRv4z/XiL19l6do3LuybfXg7nVtew29v/Ydb4YqIBCX3JMy38QL/2QnWf6f6Gd7+/TW0bwwNXFqM1vTxel8uvP+1/33s5BmsWWBtGpi14Lnp9VzkvHMF8NaKwE0kO+fj8i3WzQfaN3IuvmCYPu6dOANvr7RmcfljJ9cfbbAWPE+o61h4pfrPBth7xP8+dmI+chL+tQ4m9HMutmCY/vwAeHctHDnhfx87ud57FD78Bn7U3bHQys3Eumj0jKTCwkJmzpxJ27ZtqVKlCl27diU9PZ127dpx++23ux1eieb/PoUv3/297e1uu/Xaabw74yjzHz1In/YjWb912YWfNYlvw9Wdb+HtT54k+/AO0r5+m1uvneZitP7NmzfP7RD88pfrEX0m8UxqGs+kpjFtwttUqVSdicMfdzFaEZHgLP4m+MvZSpNfAAvXOXOssjB9vF64zrpMwwknz1p/O5OYXs9Fzvs8s3wzTS61YPXlC+aHi+nj3tJNcPy0M8cq9MG/1jpzLH+OnLAuXXTK6u3F78oZTqY/P3Yfgi+3O3e8T7611qkyhYl10ehG0qRJk5gxYwZ33HEHixcvZty4cYwfP57t27fTs2dPt8OLKjWr1eG+sa+wavMHLN/43oXt41J+zcqM93niH+NJvfFZKsVGwH2DDVdarsFqnj45ZwKTRjxJw7ot3AlQRCRIJ8/Amp3OHvPbPe6/iDNxvD543Fo01klrdljrJomIfYU/LHbvpJzj1q3K3WTiuHc2H1Zuc/aY2w5A9lFnj3mp5Vucbww6/ZwLlonPD4DPtzh7PB/W3ReldMY2kubMmcPrr7/OwoULeeCBBxg0aBDTpk2jX79+5Ofn06NHD7dDjDq1qtXllmvu47UPf0dhofVRZ2xMHJ1bDSTv1BE6tbza5QijR0m5BnhjyXRaNuzMgE6j3AtORCRIG7KsWURO8mHdQcVtpo3XX30f+NKOYJ0rsP6GImLfrkOhaXav3en8MYNl2ri3OTs0ze5Q53pdCGrYV9+7vzC7ac+PgsLQvF5Yu8P5Y0YTYxtJTzzxBMOHDyc5ObnY9jZt2hAXF0eXLtY1maNGjaJLly50796dPn36sHTpUjfCjRo3X3MPh49ls2Tt3wHYuW8Tm3Z+Qfc2Q1i06mWXo/MvPT3d7RCCcmmu1235mLWZH/HL659yOTIRkeDsDtFU+92HQ3PcYJk0XocqJ6bkGiKvnkvFFKpLjEI1ngbLpHEvEnN94kxoGo3nCmB/rvPHDZZJz48Dx6xZa047chLyHLqcsrxMrItGLradlZXFxo0buffeey/72a5du0hKSqJyZesSq9dff53atWsD8NVXX5GSksLhw4eJiYkJZ8jFfPne46xdNLPYtnOn82jWaYhLEZXsmdS0y7ZVr1KLdx6zXk0WFhbyp3d+xV03P09CfCL3PN+f/kk3UadmgzBHas+mTZuoX7++22GUKFCuDx/bx3PvTuGJSYuJi60U5uhERMonO0QvakN92UFJTB+vQ5WTfSE6blmYXM9FzgvVObPvGBQWgjeMH/ebPu7tC1WNCWFDJpRjanYuNK4TuuNfyvTnRyhfK2TnQtsqoTu+XSbWRWMbSQANGzYstv3UqVOkp6czYsSIC9vON5EAcnNz8Xg8+HyBJ317PB5bsdwybRkJHVJs7Xten5um0WfUg8W2zf99cMcASE9P4+7rBgX9OICZv1pG19bB/86L/XvFbNo26UligrUe1W3DZvDCwqlMmzCn1Mekp6fRe3zZYvanpKbipWbNmhVwv1mzZjkV0gVO5PrNpTM4cTqXp/9524VtTeu1Y+qYl0p9TKhyLSISrB9PX0XD1n2KbTt/Z5TSlPTzS++isnX793g8LcoX3A+cGKvB/fH653/aRc0rmxbb5i/Xpf3s0lx/+vkKpgztX87oAjO5nosE47o7/kaHa/5fsW1lGfeg+Pno80GlKlUpOFf+qRDRMu7d/N8f0azz0GLbnMh1zsGjeDyh6cg07zKMUb/50FZMgX5+6Xj9X7dNYlP6a+WIrkg0vI/pOPA2ht7+f8W2OZXr64aNZOf6xeWIzh47NS9cddFOLwUMbSTFx8cDkJmZyciRIy9sf+qpp8jOzr5soe3JkyezePFicnNzWbBgAbGxRv5vRZybBkwu9u8BnUZp7Z4QuXv089w9+nm3wxARKRMn3vCUJP/sqZActzzcHq9DlusQHVckWoXinPH5fODzUZhv1ur3bo97oRqf8s+FrsaEckw1rTZG6/MDzMu1STw+uy2nMCosLKR79+5kZ2czc+ZMmjRpwvz581m0aBG7du1i5cqV9O3b97LHpaenc++99/Lpp59So0YNR2L5yxJrVX+75v8+hWadhpQ4I6mk7f60rg93DQ28X0nWvA1HXVg4s3YC9PqJ88fdvHlzwH06dOhARkaG333at2/vVEgXRFuuRUSCNXcVLLd5d5PznwJe+qlfSbo0hZ8PLHtcF3NrrAZnx+tX0mGjjf+PYPIMcHVbGNMn8H7lZXI9FwlG2mZ41+Yt5IM5HxvUgt/+qOxxXSxaxr2FX1m3Y7cjmFy3bQCTQ7TyyPHT8NACe/sGO14/MAIS6pYtrktFw/uYPUfg6UX29g0214+NhlpVyxZXMALVRhPropGLbXu9XubNm0dSUhKpqalMnDiR+Ph4Jk+eTExMzIWFti+VnJyM1+vliy++CHPEYoLp06e7HYKISIXU9MoQHdehF8rRJFQ5CdXfsCxUzyUSNKsA56IpIjHXNatA7WrOHzfWCw2vcP64kazhFRAbguWRr6ganiaSHSbWRWOvAUtMTGTZsmXFtv3sZz+jY8eOVK1q/UXz8vI4dOgQzZs3B6zFtrdt20aHDh3CHu95Yx5MC2q7OGfcuHFuhyAiUiF1ToD5q52/JXG3Zs4eLxp0aw6Lv3H2mLFe6JTg7DHLQ/VcIkHzeKtRcPSks8ft3tzZ40WD9o2hciyccfjOXKHOdffmsMz/JJKgdWkamqZJJIvxQtemsHans8c16Vw0sS4aOSOpNGvWrCm2PtKJEyf48Y9/TKdOnejWrRupqam8+eabNGumV54VkZsNRBGRiqxGFejucOlt1wjq1XL2mNGgQS1IbBh4v2B0bwHVKzt7zPJQPZdIEOOF/m2dPWbd6tChkbPHjAZV4qB3K2eP2fzK0M96HdAW7N3eyb6rEx0+YJRwOi8erL+fKUysi8bOSLpUXl4emZmZ3HnnnRe2NWjQgJUrV7oYVXQ6mLuHuWlPM6j7eF5ceC8ej5d2TXuTeqPukOI05VpEosXIrrAhy5lPjGM8cFP38h/HKaaN1Td2hz9+CIUOrHJZJQ5GlrxigIgEkNwOVm2DQ3nOHO/mnuA15GN+08a9YZ3gq51wwoF1yD3AqJ4Bdyu3+JowsD2kB14azpZuzaCVQXeAN+k50rKeNYPoq++dOd417fRhViAR00iqUaMGBQUFbodRIazNXELPxKE0qN2cp+/4hEpxVXjyrQnsyN5Ay0ad3Q4vqijXIhIt6tawXpj/c5X//ewscDm8CzQOzR2Zy8S0sTqhLgzr7P8SN7sLid7cE+pUdyYukYqmchyMvwqeXwr++rp2zsdeLaFzU8dCKzfTxr2aVWFsH3j9c//72cn1oI5W4yEcru8KGXvhwLHS97ETc80qMKa3c3E5wbTnyC29YOt+a6Hz0tjJdb2acH03x8KKWhHTSJLQWL8tjUf/djOtGnVl3+EdtG7cjZrV6jJl1F+oWrnozncx3ji8XrMvyE1JSXE7BL+iKdciIiXp1waOnICPNpb9GP3bwpAk52IKVqSM1dd1stZmWWHzbnklGd4Z+rZ2LianmF7PRS7WpgHc2g/eWuG/meRPu0bw48tvSB02kTLudWsON52E99aV/Rg9W8ANXR0LKaBKsXDHIHhuqVUfy6JaJfjVYOsycrdEwnOkRhVIHQzPfwwnzpTtGHWqWbmubFiXxMS6aMjkSXFL55YDade0D8+kptGlVTJ3j36B02dPFBsQtu/9htwTOTRv0NHFSAObPXu22yH4FU25FhEpzciuMLY3xAX5OjLGa31yO7Y3eJxeVCIIkTJWezwwro+V75gg81Up1nrscEMvaTO9notcqncr+EVy2d7oX90Wfpkc/JjppEgZ9wAGdYAJ/azLcoPh9cDQJOux4b588MoacM91VtMxWAl1rMc2cXmWbqQ8RxrXgbuvs2buBqt1feuxV9YIvG+4mVgX1Uiq4LIPb6dRXWv1upzc3RzNy6FV46I2/bGTh3nu3SncP/ZVt0K0LTU11e0Q/IqmXIuI+DMgEf77eusuKt4ATQ4P0L4RPDAChnZyt4kEkTVWezzWzKT7R1g5DMTrga7NrL+N04sEO8n0ei5SkqQE+J/rrZmZdppCzePhzmthTB/378IVSeMeWI27/7nBml0UY+PdbNsGMHWYdbmSW2tQ1a5m/b3H9rZ3OXHNKnBDN7h3ODS4IuThBRRJz5EGteDeYfCjblDLRnO3TnXrssHJQ8y91NvEumjYpC0Jt+/3baJ5wyQKCgvweLys27KEnm2HAlBQkM8f5vyU22+YSd1aDt8iJgTS0tLcDsGvaMq1iEgg8TVh4kDr8quvvoddh2DfUThbYL3JanCFdcecbs2sfU0RiWN14zrWVPyc47B+F+w+BPuPwbkCa/ZRoyug2ZXWZSG1q7kdbWCm13OR0tSoYl2i9qNu8NUu+P4g7D0Cp85ZDY96Na2ZEp0SQn/HsGBE4rhXuxr8bADc1MOqMbsPwd6j1g0fYr1WjUmoa32gYUIjBqxm/oBEq9m4ORu27Ldq47FT1mWRNStDwpXWzJhOTdxvMF4s0p4jMV64NgmS28OmPbDtAOw+bK2f5AFqVbXOwbYNrTslmrLIfWlMrItqJFVwO/dvomPzfpzLP8PRvAOs27KUMQPvByD9m3lk7l7Nyx/8BoBJI56kY4t+boYb0ZRrEamIalezLkWIFJE8Vter6e76UiJiqVbZunW4SbcP9yeSx71aVa1mQSTxeqFjE+srUkTqcyQ2xpqJ27WZ25FEH4/P53Pg5rHR6y9LrA6mG1rXh7uGlu2xa96Go1nBPy59/VySu44r2y8FaidAr5+U+eGl2rw58H0zO3ToQEZGht992rd3vtJEW65FRKKRW2M1aLy+mMn1XCTaaNyTQPQ+xgyBaqOJddHwSVwSbuUtGm4KdHKZJpJzLSJSUWisDr9Iq+ci0UbjngSi50h4mVgXdWlbAG6ukF+e312zvnNxRMLvBZg7dy7jxoV/UKuIuRYRiTRujpkar4PjVj0XiTYa9yQQvY+JDCbWRV3aJhFBU+FFREQin+q5iIhIcbq0TUREREREREREopYaSSIiIiIiIiIiYosaSRI1XnjhBbdDEBERkXJSPRcRESliYl1UI0miRlJSktshiIiISDmpnouIiBQxsS6qkSRRIzk52e0QREREpJxUz0VERIqYWBfVSBIREREREREREVti3Q5AxA47tzN85JFHdDtgERERg6mei4iIFBeo5plYFz0+n8/ndhAiIiIiIiIiImI+XdomIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2qJEkIiIiIiIiIiK2/H/afw+jKxnQyQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1531.4x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "from qiskit.opflow import Z, I, X, OperatorBase, CircuitOp, PauliOp\n",
    "from qiskit.circuit import Parameter\n",
    "from qiskit.algorithms import QAOA\n",
    "from qiskit.algorithms.optimizers import COBYLA\n",
    "from qiskit.utils import QuantumInstance\n",
    "from qiskit import Aer\n",
    "from qiskit.quantum_info.operators import Operator\n",
    "\n",
    "# multiply 2 bits\n",
    "data = [1, 1]\n",
    "\n",
    "# qubitOps, offset =.get_tsp_qubitops(data)\n",
    "\n",
    "backend = Aer.get_backend('aer_simulator')\n",
    "\n",
    "qinstance=QuantumInstance(backend, shots=1, skip_qobj_validation=False)\n",
    " \n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "\n",
    "qreg_q = QuantumRegister(4, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q, creg_c)\n",
    "\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "\n",
    "qreg_q = QuantumRegister(4, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q, creg_c)\n",
    "\n",
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit\n",
    "from numpy import pi\n",
    "\n",
    "qreg_q = QuantumRegister(4, 'q')\n",
    "creg_c = ClassicalRegister(1, 'c')\n",
    "circuit = QuantumCircuit(qreg_q)  # , creg_c)\n",
    "\n",
    "# beta = Parameter('β')  # pi/4;  \n",
    "# gamma = Parameter('γ')  # pi/8; \n",
    "t1 = Parameter('t1') \n",
    "t2 = Parameter('t2') \n",
    "t3 = Parameter('t3') \n",
    "t4 = Parameter('t4') \n",
    "t5 = Parameter('t5') \n",
    "t6 = Parameter('t6') \n",
    "t7 = Parameter('t7') \n",
    "t8 = Parameter('t8') \n",
    "t9 = Parameter('t9') \n",
    "t10 = Parameter('t10') \n",
    "t11 = Parameter('t11') \n",
    "\n",
    "# circuit.reset(qreg_q[0])\n",
    "# circuit.reset(qreg_q[1])\n",
    "# circuit.reset(qreg_q[2])\n",
    "# circuit.reset(qreg_q[3])\n",
    "# circuit.barrier(qreg_q)\n",
    "circuit.h(qreg_q)\n",
    "circuit.rx(2*t1, qreg_q[0])\n",
    "circuit.rx(2*t1, qreg_q[1])\n",
    "circuit.rx(2*t1, qreg_q[2])\n",
    "circuit.rx(2*t1, qreg_q[3])\n",
    "circuit.barrier(qreg_q)\n",
    "circuit.rz(2*t2, qreg_q[0])\n",
    "circuit.rz(2*t3, qreg_q[1])\n",
    "circuit.rz(2*t4, qreg_q[2])\n",
    "circuit.rz(2*t5, qreg_q[3])\n",
    "circuit.cx(qreg_q[0], qreg_q[1])\n",
    "circuit.rz(2*t6, qreg_q[1])\n",
    "circuit.cx(qreg_q[0], qreg_q[1])\n",
    "circuit.cx(qreg_q[0], qreg_q[2])\n",
    "circuit.rz(2*t7, qreg_q[2])\n",
    "circuit.cx(qreg_q[0], qreg_q[2])\n",
    "circuit.cx(qreg_q[0], qreg_q[3])\n",
    "circuit.rz(2*t8, qreg_q[3])\n",
    "circuit.cx(qreg_q[0], qreg_q[3])\n",
    "circuit.barrier(qreg_q)\n",
    "circuit.cx(qreg_q[1], qreg_q[2])\n",
    "circuit.rz(2*t9, qreg_q[2])\n",
    "circuit.cx(qreg_q[1], qreg_q[2])\n",
    "circuit.cx(qreg_q[1], qreg_q[3])\n",
    "circuit.rz(2*t10, qreg_q[3])\n",
    "circuit.cx(qreg_q[1], qreg_q[3])\n",
    "circuit.cx(qreg_q[2], qreg_q[3])\n",
    "circuit.rz(2*t11, qreg_q[3])\n",
    "circuit.cx(qreg_q[2], qreg_q[3])\n",
    "circuit.barrier(qreg_q) \n",
    "\n",
    "# following binder will be used to iterate\n",
    "\n",
    "# the values are currently random\n",
    "circuit = circuit.bind_parameters({\n",
    "    t1: pi/4, t2: pi/4, t3: pi/4, t4: pi/4, t5: pi/4, t6: pi/4,\n",
    "    t7: pi/4, t8: pi/4, t9: pi/4, t10: pi/4, t11: pi/4})\n",
    "\n",
    "# To verify\n",
    "# t1 = -beta \n",
    "# t2 = -gamma * b0\n",
    "# t3 = -gamma * b1\n",
    "# t4 = -gamma * b2\n",
    "# t5 = -gamma * b3\n",
    "# t6 = -gamma * c00\n",
    "# t7 = -gamma * c01\n",
    "# t8 = -gamma * c02\n",
    "# t9 = -gamma * c03\n",
    "# t10 = -gamma * c04\n",
    "# t11 = -gamma * c05\n",
    "\n",
    "\n",
    "# circuit.measure(qreg_q[0], creg_c[0])\n",
    "# circuit.measure(qreg_q[1], creg_c[0])\n",
    "# circuit.measure(qreg_q[2], creg_c[0])\n",
    "# circuit.measure(qreg_q[3], creg_c[0])\n",
    "# @columns [0,0,0,0,1,1,1,1,2,2,2,2,3,3,3,3,4,4,4,4,5,5,5,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,24,24,24,25,26,27,28]\n",
    "circuit.draw('mpl') \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "610dbc23",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(0.12499999999999996+0.12499999999999996j) * IIII\n",
      "+ (-0.12499999999999996+0.12499999999999996j) * IIIX\n",
      "+ (-0.12499999999999996+0.12499999999999997j) * IIXI\n",
      "+ (-0.12499999999999996-0.12499999999999996j) * IIXX\n",
      "+ (-0.12499999999999996+0.12499999999999996j) * IXII\n",
      "+ (-0.12499999999999994-0.12499999999999996j) * IXIX\n",
      "+ (-0.12499999999999994-0.12499999999999997j) * IXXI\n",
      "+ (0.12499999999999997-0.12499999999999997j) * IXXX\n",
      "+ (-0.12499999999999996+0.12499999999999996j) * XIII\n",
      "+ (-0.12499999999999994-0.12499999999999997j) * XIIX\n",
      "+ (-0.12499999999999997-0.12499999999999997j) * XIXI\n",
      "+ (0.12499999999999997-0.12499999999999997j) * XIXX\n",
      "+ (-0.12499999999999996-0.12499999999999996j) * XXII\n",
      "+ (0.12499999999999996-0.12499999999999997j) * XXIX\n",
      "+ (0.12499999999999994-0.12499999999999997j) * XXXI\n",
      "+ (0.12499999999999994+0.12499999999999996j) * XXXX\n",
      "+ (-0.12499999999999997+0.12499999999999996j) * YYYY\n",
      "+ (0.12499999999999997-0.12499999999999997j) * YYYZ\n",
      "+ (0.12499999999999996-0.12499999999999996j) * YYZY\n",
      "+ (-0.12499999999999997+0.12499999999999996j) * YYZZ\n",
      "+ (0.12499999999999996-0.12499999999999996j) * YZYY\n",
      "+ (-0.12499999999999997+0.12499999999999997j) * YZYZ\n",
      "+ (-0.12499999999999997+0.12499999999999997j) * YZZY\n",
      "+ (0.12499999999999996-0.12499999999999996j) * YZZZ\n",
      "+ (0.12499999999999996-0.12499999999999997j) * ZYYY\n",
      "+ (-0.12499999999999997+0.12499999999999997j) * ZYYZ\n",
      "+ (-0.12499999999999997+0.12499999999999997j) * ZYZY\n",
      "+ (0.12499999999999996-0.12499999999999997j) * ZYZZ\n",
      "+ (-0.12499999999999996+0.12499999999999997j) * ZZYY\n",
      "+ (0.12499999999999996-0.12499999999999997j) * ZZYZ\n",
      "+ (0.12499999999999996-0.12499999999999996j) * ZZZY\n",
      "+ (-0.12499999999999997+0.12499999999999997j) * ZZZZ\n"
     ]
    }
   ],
   "source": [
    "paulies = CircuitOp(circuit).to_pauli_op().reduce()\n",
    "print(paulies)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "223c4e2d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_qaoa(paulies, qinstance):\n",
    "    qaoa = QAOA(optimizer=COBYLA(), quantum_instance=qinstance)  # , mixer=mixed)\n",
    "    result = qaoa.compute_minimum_eigenvalue(paulies)\n",
    "    print(result.eigenstate)\n",
    "    print(result.eigenvalue)\n",
    "    return result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "a280d0f5",
   "metadata": {},
   "outputs": [
    {
     "ename": "ValueError",
     "evalue": "Operator contains complex coefficients, which are not supported.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "Input \u001b[0;32mIn [16]\u001b[0m, in \u001b[0;36m<cell line: 1>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0m \u001b[43mcompute_qaoa\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpaulies\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mqinstance\u001b[49m\u001b[43m)\u001b[49m\n",
      "Input \u001b[0;32mIn [15]\u001b[0m, in \u001b[0;36mcompute_qaoa\u001b[0;34m(paulies, qinstance)\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mcompute_qaoa\u001b[39m(paulies, qinstance):\n\u001b[1;32m      2\u001b[0m     qaoa \u001b[38;5;241m=\u001b[39m QAOA(optimizer\u001b[38;5;241m=\u001b[39mCOBYLA(), quantum_instance\u001b[38;5;241m=\u001b[39mqinstance)  \u001b[38;5;66;03m# , mixer=mixed)\u001b[39;00m\n\u001b[0;32m----> 3\u001b[0m     result \u001b[38;5;241m=\u001b[39m \u001b[43mqaoa\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mcompute_minimum_eigenvalue\u001b[49m\u001b[43m(\u001b[49m\u001b[43mpaulies\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m      4\u001b[0m     \u001b[38;5;28mprint\u001b[39m(result\u001b[38;5;241m.\u001b[39meigenstate)\n\u001b[1;32m      5\u001b[0m     \u001b[38;5;28mprint\u001b[39m(result\u001b[38;5;241m.\u001b[39meigenvalue)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/algorithms/minimum_eigen_solvers/vqe.py:496\u001b[0m, in \u001b[0;36mVQE.compute_minimum_eigenvalue\u001b[0;34m(self, operator, aux_operators)\u001b[0m\n\u001b[1;32m    492\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mquantum_instance\u001b[38;5;241m.\u001b[39mcircuit_summary \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;01mTrue\u001b[39;00m\n\u001b[1;32m    494\u001b[0m \u001b[38;5;66;03m# this sets the size of the ansatz, so it must be called before the initial point\u001b[39;00m\n\u001b[1;32m    495\u001b[0m \u001b[38;5;66;03m# validation\u001b[39;00m\n\u001b[0;32m--> 496\u001b[0m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_check_operator_ansatz\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    498\u001b[0m \u001b[38;5;66;03m# set an expectation for this algorithm run (will be reset to None at the end)\u001b[39;00m\n\u001b[1;32m    499\u001b[0m initial_point \u001b[38;5;241m=\u001b[39m _validate_initial_point(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39minitial_point, \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mansatz)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/algorithms/minimum_eigen_solvers/qaoa.py:149\u001b[0m, in \u001b[0;36mQAOA._check_operator_ansatz\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m    147\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m operator \u001b[38;5;241m!=\u001b[39m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cost_operator:\n\u001b[1;32m    148\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_cost_operator \u001b[38;5;241m=\u001b[39m operator\n\u001b[0;32m--> 149\u001b[0m     \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mansatz \u001b[38;5;241m=\u001b[39m \u001b[43mQAOAAnsatz\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    150\u001b[0m \u001b[43m        \u001b[49m\u001b[43moperator\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_reps\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43minitial_state\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_initial_state\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mmixer_operator\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_mixer\u001b[49m\n\u001b[1;32m    151\u001b[0m \u001b[43m    \u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mdecompose\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/blueprintcircuit.py:96\u001b[0m, in \u001b[0;36mBlueprintCircuit.decompose\u001b[0;34m(self, gates_to_decompose, reps)\u001b[0m\n\u001b[1;32m     94\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mdecompose\u001b[39m(\u001b[38;5;28mself\u001b[39m, gates_to_decompose\u001b[38;5;241m=\u001b[39m\u001b[38;5;28;01mNone\u001b[39;00m, reps\u001b[38;5;241m=\u001b[39m\u001b[38;5;241m1\u001b[39m):\n\u001b[1;32m     95\u001b[0m     \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;129;01mnot\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_built:\n\u001b[0;32m---> 96\u001b[0m         \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_build\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m     97\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28msuper\u001b[39m()\u001b[38;5;241m.\u001b[39mdecompose(gates_to_decompose, reps)\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/n_local/qaoa_ansatz.py:261\u001b[0m, in \u001b[0;36mQAOAAnsatz._build\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    258\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39m_is_built:\n\u001b[1;32m    259\u001b[0m     \u001b[38;5;28;01mreturn\u001b[39;00m\n\u001b[0;32m--> 261\u001b[0m \u001b[38;5;28;43msuper\u001b[39;49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_build\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    263\u001b[0m \u001b[38;5;66;03m# keep old parameter order: first cost operator, then mixer operators\u001b[39;00m\n\u001b[1;32m    264\u001b[0m num_cost \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m \u001b[38;5;28;01mif\u001b[39;00m _is_pauli_identity(\u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mcost_operator) \u001b[38;5;28;01melse\u001b[39;00m \u001b[38;5;241m1\u001b[39m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/evolved_operator_ansatz.py:174\u001b[0m, in \u001b[0;36mEvolvedOperatorAnsatz._build\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    171\u001b[0m         \u001b[38;5;28;01mif\u001b[39;00m _is_pauli_identity(op):\n\u001b[1;32m    172\u001b[0m             \u001b[38;5;28;01mcontinue\u001b[39;00m\n\u001b[0;32m--> 174\u001b[0m         evolved_op \u001b[38;5;241m=\u001b[39m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mevolution\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mconvert\u001b[49m\u001b[43m(\u001b[49m\u001b[43m(\u001b[49m\u001b[43mcoeff\u001b[49m\u001b[43m \u001b[49m\u001b[38;5;241;43m*\u001b[39;49m\u001b[43m \u001b[49m\u001b[43mop\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43mexp_i\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\u001b[43m)\u001b[49m\u001b[38;5;241m.\u001b[39mreduce()\n\u001b[1;32m    175\u001b[0m         circuits\u001b[38;5;241m.\u001b[39mappend(evolved_op\u001b[38;5;241m.\u001b[39mto_circuit())\n\u001b[1;32m    177\u001b[0m \u001b[38;5;28mself\u001b[39m\u001b[38;5;241m.\u001b[39mrotation_blocks \u001b[38;5;241m=\u001b[39m []\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/opflow/evolutions/pauli_trotter_evolution.py:106\u001b[0m, in \u001b[0;36mPauliTrotterEvolution.convert\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m     92\u001b[0m \u001b[38;5;124mr\u001b[39m\u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m     93\u001b[0m \u001b[38;5;124;03mTraverse the operator, replacing ``EvolvedOps`` with ``CircuitOps`` containing\u001b[39;00m\n\u001b[1;32m     94\u001b[0m \u001b[38;5;124;03mTrotterized evolutions equalling the exponentiation of -i * operator.\u001b[39;00m\n\u001b[0;32m   (...)\u001b[0m\n\u001b[1;32m    100\u001b[0m \u001b[38;5;124;03m    The converted operator.\u001b[39;00m\n\u001b[1;32m    101\u001b[0m \u001b[38;5;124;03m\"\"\"\u001b[39;00m\n\u001b[1;32m    102\u001b[0m \u001b[38;5;66;03m# TODO uncomment when we implement Abelian grouped evolution.\u001b[39;00m\n\u001b[1;32m    103\u001b[0m \u001b[38;5;66;03m# if self._grouper:\u001b[39;00m\n\u001b[1;32m    104\u001b[0m \u001b[38;5;66;03m#     # Sort into commuting groups\u001b[39;00m\n\u001b[1;32m    105\u001b[0m \u001b[38;5;66;03m#     operator = self._grouper.convert(operator).reduce()\u001b[39;00m\n\u001b[0;32m--> 106\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m \u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_recursive_convert\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/opflow/evolutions/pauli_trotter_evolution.py:119\u001b[0m, in \u001b[0;36mPauliTrotterEvolution._recursive_convert\u001b[0;34m(self, operator)\u001b[0m\n\u001b[1;32m    117\u001b[0m pauli \u001b[38;5;241m=\u001b[39m operator\u001b[38;5;241m.\u001b[39mprimitive\u001b[38;5;241m.\u001b[39mprimitive\n\u001b[1;32m    118\u001b[0m time \u001b[38;5;241m=\u001b[39m operator\u001b[38;5;241m.\u001b[39mcoeff \u001b[38;5;241m*\u001b[39m operator\u001b[38;5;241m.\u001b[39mprimitive\u001b[38;5;241m.\u001b[39mcoeff\n\u001b[0;32m--> 119\u001b[0m evo \u001b[38;5;241m=\u001b[39m \u001b[43mPauliEvolutionGate\u001b[49m\u001b[43m(\u001b[49m\n\u001b[1;32m    120\u001b[0m \u001b[43m    \u001b[49m\u001b[43mpauli\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43mtime\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[43mtime\u001b[49m\u001b[43m,\u001b[49m\u001b[43m \u001b[49m\u001b[43msynthesis\u001b[49m\u001b[38;5;241;43m=\u001b[39;49m\u001b[38;5;28;43mself\u001b[39;49m\u001b[38;5;241;43m.\u001b[39;49m\u001b[43m_get_evolution_synthesis\u001b[49m\u001b[43m(\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    121\u001b[0m \u001b[43m\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    122\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m CircuitOp(evo)\n\u001b[1;32m    123\u001b[0m \u001b[38;5;66;03m# operator = EvolvedOp(operator.primitive.to_pauli_op(), coeff=operator.coeff)\u001b[39;00m\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/pauli_evolution.py:102\u001b[0m, in \u001b[0;36mPauliEvolutionGate.__init__\u001b[0;34m(self, operator, time, label, synthesis)\u001b[0m\n\u001b[1;32m    100\u001b[0m     operator \u001b[38;5;241m=\u001b[39m [_to_sparse_pauli_op(op) \u001b[38;5;28;01mfor\u001b[39;00m op \u001b[38;5;129;01min\u001b[39;00m operator]\n\u001b[1;32m    101\u001b[0m \u001b[38;5;28;01melse\u001b[39;00m:\n\u001b[0;32m--> 102\u001b[0m     operator \u001b[38;5;241m=\u001b[39m \u001b[43m_to_sparse_pauli_op\u001b[49m\u001b[43m(\u001b[49m\u001b[43moperator\u001b[49m\u001b[43m)\u001b[49m\n\u001b[1;32m    104\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m synthesis \u001b[38;5;129;01mis\u001b[39;00m \u001b[38;5;28;01mNone\u001b[39;00m:\n\u001b[1;32m    105\u001b[0m     synthesis \u001b[38;5;241m=\u001b[39m LieTrotter()\n",
      "File \u001b[0;32m~/Documents/IITd/labs/qcqml/lib/python3.8/site-packages/qiskit/circuit/library/pauli_evolution.py:172\u001b[0m, in \u001b[0;36m_to_sparse_pauli_op\u001b[0;34m(operator)\u001b[0m\n\u001b[1;32m    169\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124mf\u001b[39m\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mUnsupported operator type for evolution: \u001b[39m\u001b[38;5;132;01m{\u001b[39;00m\u001b[38;5;28mtype\u001b[39m(operator)\u001b[38;5;132;01m}\u001b[39;00m\u001b[38;5;124m.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    171\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m \u001b[38;5;28many\u001b[39m(np\u001b[38;5;241m.\u001b[39miscomplex(sparse_pauli\u001b[38;5;241m.\u001b[39mcoeffs)):\n\u001b[0;32m--> 172\u001b[0m     \u001b[38;5;28;01mraise\u001b[39;00m \u001b[38;5;167;01mValueError\u001b[39;00m(\u001b[38;5;124m\"\u001b[39m\u001b[38;5;124mOperator contains complex coefficients, which are not supported.\u001b[39m\u001b[38;5;124m\"\u001b[39m)\n\u001b[1;32m    174\u001b[0m \u001b[38;5;28;01mreturn\u001b[39;00m sparse_pauli\n",
      "\u001b[0;31mValueError\u001b[0m: Operator contains complex coefficients, which are not supported."
     ]
    }
   ],
   "source": [
    "compute_qaoa(paulies, qinstance)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b52c966",
   "metadata": {},
   "source": [
    "# To try with the lectured algo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "4ab53200",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<h3>Version Information</h3><table><tr><th>Qiskit Software</th><th>Version</th></tr><tr><td><code>qiskit-terra</code></td><td>0.22.3</td></tr><tr><td><code>qiskit-aer</code></td><td>0.11.2</td></tr><tr><td><code>qiskit-ibmq-provider</code></td><td>0.19.2</td></tr><tr><td><code>qiskit</code></td><td>0.39.4</td></tr><tr><td><code>qiskit-optimization</code></td><td>0.4.0</td></tr><tr><th>System information</th></tr><tr><td>Python version</td><td>3.8.14</td></tr><tr><td>Python compiler</td><td>GCC 7.5.0</td></tr><tr><td>Python build</td><td>default, Sep  8 2022 00:02:10</td></tr><tr><td>OS</td><td>Linux</td></tr><tr><td>CPUs</td><td>4</td></tr><tr><td>Memory (Gb)</td><td>7.648113250732422</td></tr><tr><td colspan='2'>Sun Jan 08 16:47:32 2023 IST</td></tr></table>"
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      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "import qiskit.tools.jupyter\n",
    "\n",
    "%qiskit_version_table"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "8ab82f3a",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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