two qubits system.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "95da44d9",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit.library.standard_gates import RXGate, RZGate, RYGate, CXGate, CZGate, SGate, HGate\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "02604014",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer\n",
    "from qiskit.utils import QuantumInstance, algorithm_globals\n",
    "\n",
    "seed = 50\n",
    "algorithm_globals.random_seed = seed\n",
    "\n",
    "simulator_backend = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "46af3fe0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_linear_entangelment_ansatz(num_of_qubits, thetas, input_state, circuit_depth=3):\n",
    "    quantum_register = QuantumRegister(num_of_qubits, name=\"qubit\")\n",
    "    quantum_circuit = QuantumCircuit(quantum_register)\n",
    "    quantum_circuit.initialize(input_state)\n",
    "\n",
    "    for iteration in range(circuit_depth):\n",
    "        for qubit_index in range(num_of_qubits):\n",
    "            RY_theta_index = iteration*2*num_of_qubits + qubit_index\n",
    "            RZ_theta_index = RY_theta_index + num_of_qubits\n",
    "            \n",
    "            quantum_circuit.append(RYGate(thetas[RY_theta_index]), [quantum_register[qubit_index]])\n",
    "            quantum_circuit.append(RZGate(thetas[RZ_theta_index]), [quantum_register[qubit_index]])\n",
    "            \n",
    "        for qubit_index in range(num_of_qubits - 1):\n",
    "            quantum_circuit.append(CXGate(), [quantum_register[qubit_index], quantum_register[qubit_index + 1]])\n",
    "\n",
    "    for qubit_index in range(num_of_qubits):\n",
    "            RY_theta_index = 2*num_of_qubits*circuit_depth + qubit_index\n",
    "            RZ_theta_index = RY_theta_index + num_of_qubits\n",
    "            quantum_circuit.append(RYGate(thetas[RY_theta_index]), [quantum_register[qubit_index]])\n",
    "            quantum_circuit.append(RZGate(thetas[RZ_theta_index]), [quantum_register[qubit_index]])\n",
    "\n",
    "    return quantum_circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5dd32781",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_full_entangelment_ansatz(num_of_qubits, thetas, input_state, circuit_depth=3):\n",
    "    quantum_register = QuantumRegister(num_of_qubits, name=\"qubit\")\n",
    "    quantum_circuit = QuantumCircuit(quantum_register)\n",
    "    quantum_circuit.initialize(input_state)\n",
    "\n",
    "    for iteration in range(circuit_depth):\n",
    "        for qubit_index in range(num_of_qubits):\n",
    "            RY_theta_index = iteration*2*num_of_qubits + qubit_index\n",
    "            RZ_theta_index = RY_theta_index + num_of_qubits\n",
    "            \n",
    "            quantum_circuit.append(RYGate(thetas[RY_theta_index]), [quantum_register[qubit_index]])\n",
    "            quantum_circuit.append(RZGate(thetas[RZ_theta_index]), [quantum_register[qubit_index]])\n",
    "        for qubit_index in range(num_of_qubits - 1):\n",
    "            for target_qubit_index in range(qubit_index + 1, num_of_qubits):\n",
    "                quantum_circuit.append(CXGate(), [quantum_register[qubit_index], quantum_register[target_qubit_index]])\n",
    "\n",
    "    for qubit_index in range(num_of_qubits):\n",
    "            RY_theta_index = 2*num_of_qubits*circuit_depth + qubit_index\n",
    "            RZ_theta_index = RY_theta_index + num_of_qubits\n",
    "            \n",
    "            quantum_circuit.append(RYGate(thetas[RY_theta_index]), [quantum_register[qubit_index]])\n",
    "            quantum_circuit.append(RZGate(thetas[RZ_theta_index]), [quantum_register[qubit_index]])\n",
    "\n",
    "    return quantum_circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "55d9e93e",
   "metadata": {},
   "outputs": [],
   "source": [
    "QUBITS_NUM = 2\n",
    "N = 2**QUBITS_NUM\n",
    "\n",
    "NUM_SHOTS = 1024\n",
    "NUM_ITERATIONS = 50\n",
    "\n",
    "CIRCUIT_DEPTH = 3\n",
    "PARAMS_NUM = 2*QUBITS_NUM*(CIRCUIT_DEPTH+1)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9dcb2186",
   "metadata": {},
   "source": [
    "#### convert hamiltonian to pauli strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "7c43a40b",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import Dict, Tuple, List"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "535bbb2f",
   "metadata": {},
   "outputs": [],
   "source": [
    "def transfrom_hamiltonian_into_pauli_strings(hamiltonian) -> List:\n",
    "    pauli_operators = hamiltonian.to_pauli_op().settings['oplist']\n",
    "    pauli_coeffs = list(map(lambda pauli_operator: pauli_operator.coeff, pauli_operators))\n",
    "    pauli_strings = list(map(lambda pauli_operator: pauli_operator.primitive, pauli_operators))\n",
    "    return pauli_coeffs, pauli_strings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "dc445cf1",
   "metadata": {},
   "outputs": [],
   "source": [
    "reducing_to_pauli_z_mapping = {\n",
    "    'I': 'I',\n",
    "    'Z': 'Z',\n",
    "    'X': 'Z',\n",
    "    'Y': 'Z'\n",
    "} "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "98123375",
   "metadata": {},
   "outputs": [],
   "source": [
    "def reduce_pauli_matrixes_into_sigma_z(pauli_string) -> str:\n",
    "    reduced_pauli_string = \"\"\n",
    "    for matrix_index in range(QUBITS_NUM):\n",
    "        pauli_matrix = str(pauli_string[matrix_index])\n",
    "        reduced_pauli_matrix = reducing_to_pauli_z_mapping[pauli_matrix]\n",
    "        reduced_pauli_string = reduced_pauli_matrix + reduced_pauli_string\n",
    "    \n",
    "    return reduced_pauli_string"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "726d3839",
   "metadata": {},
   "outputs": [],
   "source": [
    "def add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string, quantum_circuit):\n",
    "    quantum_registers = QuantumRegister(QUBITS_NUM, name=\"qubit\")\n",
    "    additional_circuit_layer = QuantumCircuit(quantum_registers)\n",
    "    \n",
    "    for quantum_register_index, pauli_matrix in enumerate(pauli_string):\n",
    "        if pauli_matrix == \"X\":\n",
    "            additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])\n",
    "        if pauli_string == \"Y\":\n",
    "            additional_circuit_layer.append(HGate(), [quantum_registers[quantum_register_index]])\n",
    "            additional_circuit_layer.append(SGate(), [quantum_registers[quantum_register_index]])\n",
    "                \n",
    "    extended_quantum_circuit = quantum_circuit.compose(additional_circuit_layer)\n",
    "    return extended_quantum_circuit"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1c30cfd5",
   "metadata": {},
   "source": [
    "#### probabilities distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "86f1189e",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import assemble, transpile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d61187be",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_probability_distribution(counts: Dict) -> Dict:\n",
    "    proba_distribution = {state: (count / NUM_SHOTS) for state, count in counts.items()}\n",
    "    return proba_distribution\n",
    "\n",
    "def calculate_probabilities_of_measurments_in_computational_basis(quantum_state_circuit) -> Dict:\n",
    "    quantum_state_circuit.measure_all()\n",
    "    \n",
    "    transpiled_quantum_state_circuit = transpile(quantum_state_circuit, simulator_backend) \n",
    "    Qobj = assemble(transpiled_quantum_state_circuit)\n",
    "    result = simulator_backend.run(Qobj).result()\n",
    "    counts = result.get_counts(quantum_state_circuit)\n",
    "    \n",
    "    return get_probability_distribution(counts)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "232e0503",
   "metadata": {},
   "source": [
    "#### Expectation value from probabilities"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "d463b826",
   "metadata": {},
   "outputs": [],
   "source": [
    "def sort_probas_dict_by_qubits_string_keys(proba_distribution: Dict) -> Dict:\n",
    "    return dict(sorted(proba_distribution.items()))\n",
    "\n",
    "def reset_power_of_minus_1(power_of_minus_1):\n",
    "    power_of_minus_1 = 0\n",
    "    return power_of_minus_1\n",
    "\n",
    "def convert_pauli_string_into_str(pauli_string) -> str:\n",
    "    return str(pauli_string)\n",
    "\n",
    "def calculate_expectation_value_of_pauli_string_by_measurments_probas(pauli_string, ansatz_circuit):\n",
    "    pauli_string_expectation_value = 0\n",
    "    power_of_minus_1 = 0\n",
    "    \n",
    "    pauli_string_str = convert_pauli_string_into_str(pauli_string)\n",
    "    extended_ansatz_circuit = add_layer_of_gates_for_reducing_paulis_to_sigma_z(pauli_string_str, ansatz_circuit)\n",
    "    probas_distribution = calculate_probabilities_of_measurments_in_computational_basis(extended_ansatz_circuit)\n",
    "    \n",
    "    reduced_pauli_string = reduce_pauli_matrixes_into_sigma_z(pauli_string)\n",
    "    sorted_probas_distribuition = sort_probas_dict_by_qubits_string_keys(probas_distribution)\n",
    "    for qubits_string, proba in sorted_probas_distribuition.items():\n",
    "        for string_index in range(QUBITS_NUM):\n",
    "            if(str(qubits_string[string_index])==\"1\" and str(reduced_pauli_string[string_index])==\"Z\"):\n",
    "                power_of_minus_1 += 1\n",
    "            \n",
    "        pauli_string_expectation_value += pow(-1, power_of_minus_1)*proba\n",
    "        power_of_minus_1 = reset_power_of_minus_1(power_of_minus_1)\n",
    "        \n",
    "    return pauli_string_expectation_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "9b47e3f6",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_expectation_value(ansatz_circuit, pauli_coeffs, pauli_strings):\n",
    "    total_expection_value = 0\n",
    "    \n",
    "    for pauli_coeff, pauli_string in zip(pauli_coeffs, pauli_strings):\n",
    "        total_expection_value += pauli_coeff*calculate_expectation_value_of_pauli_string_by_measurments_probas(\n",
    "                                                                                    pauli_string, ansatz_circuit)\n",
    "    \n",
    "    return total_expection_value"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ae112df4",
   "metadata": {},
   "source": [
    "## MUBs d=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8e87cc05",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing import List\n",
    "\n",
    "class MUB:\n",
    "    def __init__(self, name: str, color: str, basis_vectors, dim: int):\n",
    "        self.name = name\n",
    "        self.color = color\n",
    "        self.basis_vectors = basis_vectors\n",
    "        self.results = []\n",
    "        \n",
    "    def add_result(self, result:int):\n",
    "        self.results.append(result)\n",
    "        \n",
    "    def restart_results(self):\n",
    "        self.results = []"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "2d873cbf",
   "metadata": {},
   "outputs": [],
   "source": [
    "M0_vectors = np.identity(N)\n",
    "\n",
    "M1_vectors = [np.vectorize(complex)([0.5,0.5,0.5,0.5]),\n",
    "      np.vectorize(complex)([0.5,0.5,-0.5,-0.5]),\n",
    "      np.vectorize(complex)([0.5,-0.5,-0.5,0.5]),\n",
    "      np.vectorize(complex)([0.5,-0.5,0.5,-0.5])]\n",
    "\n",
    "M2_vectors = [np.vectorize(complex)([0.5,0.5,0,0],[0,0,-0.5,-0.5]),\n",
    "      np.vectorize(complex)([0.5,-0.5,0,0],[0,0,0.5,0.5]),\n",
    "      np.vectorize(complex)([0.5,0.5,0,0],[0,0,0.5,-0.5]),\n",
    "      np.vectorize(complex)([0.5,0.5,0,0],[0,0,-0.5,0.5])]\n",
    "\n",
    "M3_vectors = [np.vectorize(complex)([0.5,0,0,-0.5],[0,-0.5,-0.5,-0]),\n",
    "      np.vectorize(complex)([0.5,0,0,0.5],[0,-0.5,0.5,0]),\n",
    "      np.vectorize(complex)([0.5,0,0,-0.5],[0,0.5,0.5,0]),\n",
    "      np.vectorize(complex)([0.5,0,0,0.5],[0,0.5,-0.5,0])]\n",
    "\n",
    "M4_vectors = [np.vectorize(complex)([0.5,0,-0.5,0],[0,-0.5,0,-0.5]),\n",
    "      np.vectorize(complex)([0.5,0,0.5,0],[0,-0.5,0,0.5]),\n",
    "      np.vectorize(complex)([0.5,0,-0.5,0],[0,0.5,0,0.5]),\n",
    "      np.vectorize(complex)([0.5,0,0.5,0],[0,0.5,0,-0.5])]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "27fc0c32",
   "metadata": {},
   "outputs": [],
   "source": [
    "M0 = MUB(name='M0', color='b', basis_vectors=M0_vectors, dim=4)\n",
    "M1 = MUB(name='M1', color='c', basis_vectors=M1_vectors, dim=4)\n",
    "M2 = MUB(name='M2', color='y', basis_vectors=M2_vectors, dim=4)\n",
    "M3 = MUB(name='M3', color='m', basis_vectors=M3_vectors, dim=4)\n",
    "M4 = MUB(name='M4', color='r', basis_vectors=M4_vectors, dim=4)\n",
    "\n",
    "mubs_d_5 = [M0, M1, M2, M3, M4]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e5f3dd26",
   "metadata": {},
   "source": [
    "### H2 Molecule 2 qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8d571b53",
   "metadata": {},
   "outputs": [],
   "source": [
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "e1fd90aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.opflow import X, Z, I\n",
    "\n",
    "H2_molecule_Hamiltonian_2_qubits = -0.5053051899926562*(I^I) + \\\n",
    "                            -0.3277380754984016*(Z^I) + \\\n",
    "                            0.15567463610622564*(Z^Z) + \\\n",
    "                            -0.3277380754984016*(I^Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "55d6ae9e",
   "metadata": {},
   "outputs": [],
   "source": [
    "thetas = np.random.uniform(low=0, high=360, size=PARAMS_NUM)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a12ec8dc",
   "metadata": {},
   "source": [
    "### full entangelment"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "dda98152",
   "metadata": {},
   "outputs": [],
   "source": [
    "for basis in mubs_d_5:\n",
    "    basis.restart_results()\n",
    "    for vector in basis.basis_vectors:\n",
    "        pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(H2_molecule_Hamiltonian_2_qubits)\n",
    "        ansatz_state = get_full_entangelment_ansatz(QUBITS_NUM, thetas, vector)\n",
    "\n",
    "        L = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)\n",
    "        basis.add_result(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b346b118",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M0_points = plt.scatter(x=range(1,5),y=M0.results, marker='x', color=M0.color)\n",
    "M1_points = plt.scatter(x=range(5,9),y=M1.results, marker='x', color=M1.color)\n",
    "M2_points = plt.scatter(x=range(10,14),y=M2.results, marker='x', color=M2.color)\n",
    "M3_points = plt.scatter(x=range(15,19),y=M3.results, marker='x', color=M3.color)\n",
    "M4_points = plt.scatter(x=range(20,24),y=M4.results, marker='x', color=M4.color)\n",
    "\n",
    "plt.legend((M0_points, M1_points, M2_points, M3_points, M4_points),\n",
    "           (M0.name, M1.name, M2.name, M3.name, M4.name),\n",
    "           scatterpoints=1,\n",
    "           loc='best',\n",
    "           ncol=3,\n",
    "           fontsize=8)\n",
    "\n",
    "plt.xlabel('iteration number')\n",
    "plt.ylabel('energy for specific vector from a mub')\n",
    "plt.title('H2 Energy Landscape')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec5a0483",
   "metadata": {},
   "outputs": [],
   "source": [
    "v0 = M0_vectors[2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "eb3bad07",
   "metadata": {},
   "outputs": [],
   "source": [
    "v1 = np.vectorize(complex)([0,0,0,0],[0,0,1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "8f5cec9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.48834251803032236\n"
     ]
    }
   ],
   "source": [
    "pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(H2_molecule_Hamiltonian_2_qubits)\n",
    "ansatz_state = get_full_entangelment_ansatz(QUBITS_NUM, thetas, v1)\n",
    "\n",
    "L = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)\n",
    "print(L)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce91e859",
   "metadata": {},
   "source": [
    "## Transverse Ising Model 2 qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3bba1d3b",
   "metadata": {},
   "outputs": [],
   "source": [
    "transverse_ising_2_qubits = 0.13755727363376802 * (I^X) \\\n",
    "                            + 0.43305656297810435 * (X^I) \\\n",
    "                            + 0.8538597608997253 * (Z^Z)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "3bcfb1f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "for basis in mubs_d_5:\n",
    "    basis.restart_results()\n",
    "    for vector in basis.basis_vectors:\n",
    "        pauli_coeffs, pauli_strings = transfrom_hamiltonian_into_pauli_strings(transverse_ising_2_qubits)\n",
    "        ansatz_state = get_full_entangelment_ansatz(QUBITS_NUM, thetas, vector)\n",
    "\n",
    "        L = get_expectation_value(ansatz_state, pauli_coeffs, pauli_strings)\n",
    "        basis.add_result(L)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "1aef45f0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "M0_points = plt.scatter(x=range(1,5),y=M0.results, marker='x', color=M0.color)\n",
    "M1_points = plt.scatter(x=range(5,9),y=M1.results, marker='x', color=M1.color)\n",
    "M2_points = plt.scatter(x=range(10,14),y=M2.results, marker='x', color=M2.color)\n",
    "M3_points = plt.scatter(x=range(15,19),y=M3.results, marker='x', color=M3.color)\n",
    "M4_points = plt.scatter(x=range(20,24),y=M4.results, marker='x', color=M4.color)\n",
    "\n",
    "plt.legend((M0_points, M1_points, M2_points, M3_points, M4_points),\n",
    "           (M0.name, M1.name, M2.name, M3.name, M4.name),\n",
    "           scatterpoints=1,\n",
    "           loc='best',\n",
    "           ncol=3,\n",
    "           fontsize=8)\n",
    "\n",
    "plt.xlabel('iteration number')\n",
    "plt.ylabel('energy for specific vector from a mub')\n",
    "plt.title('Transverse Ising Model Energy Landscape')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "94ac89ec",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (Mubsenv)",
   "language": "python",
   "name": "mubsenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.15"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}