Superposition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AccountProvider for IBMQ(hub='ibm-q', group='open', project='main')>"
      ]
     },
     "execution_count": 1,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import *\n",
    "import qiskit.tools.jupyter\n",
    "import numpy as np\n",
    "IBMQ.load_account()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.aqua.components.variational_forms import VariationalForm\n",
    "from qiskit.aqua.components.initial_states import Zero, VarFormBased\n",
    "from qiskit.aqua.operators import MatrixOperator, TPBGroupedWeightedPauliOperator\n",
    "from qiskit.aqua.operators.op_converter import to_tpb_grouped_weighted_pauli_operator\n",
    "from qiskit.aqua.components.optimizers import SPSA\n",
    "from qiskit.aqua.algorithms.adaptive import VQE"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.sparse import *\n",
    "from scipy import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Parameters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# even space\n",
    "# [0.13028114, -1.18048464, 0.17737505]\n",
    "# [ 0.12398951, -1.18068356,  0.15356187]\n",
    "t0_1 = 0.13028114 # theta-angle values\n",
    "t1_1 = -1.18048464\n",
    "t2_1 = 0.17737505\n",
    "# odd space\n",
    "# [-0.30306561, -1.02142291,  0.15013751\n",
    "# [ 2.8238186 , -5.22031494,  0.16478762]\n",
    "t0_2 = 2.8238186\n",
    "t1_2 = -5.22031494\n",
    "t2_2 = 0.16478762\n",
    "def angle(theta=0., phi=0., lam=0.):\n",
    "    return [theta, phi, lam]\n",
    "t1 = [angle(t_i) for t_i in [t0_1, t1_1, t2_1]]\n",
    "t2 = [angle(t_i) for t_i in [t0_2, t1_2, t2_2]]\n",
    "# define number of qubits and bits\n",
    "nqubits = 2 \n",
    "# create registers\n",
    "q0 = QuantumRegister(nqubits, name=\"q0\")\n",
    "q1 = QuantumRegister(nqubits, name=\"q1\")\n",
    "a = QuantumRegister(1, name=\"a\")\n",
    "c0 = ClassicalRegister(nqubits, name=\"c0\")\n",
    "c1 = ClassicalRegister(nqubits, name=\"c1\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Even subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=1057x159 at 0x125ABF860>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create registers\n",
    "q_even = QuantumRegister(nqubits, name=\"qe\")\n",
    "c_even = ClassicalRegister(nqubits, name=\"ce\")\n",
    "regs0 = [q_even, c_even]\n",
    "# create circuit\n",
    "circ0 = QuantumCircuit(*regs0, name=\"even\")\n",
    "circ0.u3(*(t1[1]), 0)  # u3(*angles, q)\n",
    "circ0.u3(*(t1[0]), 1)\n",
    "############\n",
    "circ0.cx(0, 1)    # cx(ctrl, tgt)\n",
    "############\n",
    "circ0.u3(*(t1[0]), 1)\n",
    "circ0.iden(0)\n",
    "############\n",
    "circ0.cx(0, 1)\n",
    "############\n",
    "circ0.u3(*(t1[2]), 1)\n",
    "circ0.iden(0)\n",
    "# measurement circuit\n",
    "meas0 = QuantumCircuit(*regs0, name=\"meas0\")\n",
    "# barrier prevents optimizations\n",
    "# from reordering gates across its source line\n",
    "meas0.barrier(range(2)) \n",
    "############ MEASURE ANCILLARY QUBIT\n",
    "meas0.measure(q_even, c_even)#  map qubits to clbits\n",
    "# Full circuit\n",
    "qc0 = circ0 + meas0\n",
    "qc0.draw(output='latex', scale=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Odd subspace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=1059x159 at 0x10815DBE0>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create registers\n",
    "q_odd = QuantumRegister(nqubits, name=\"qo\")\n",
    "c_odd = ClassicalRegister(nqubits, name=\"co\")\n",
    "regs1 = [q_odd, c_odd]\n",
    "# create circuit\n",
    "circ1 = QuantumCircuit(*regs1, name=\"odd\")\n",
    "############\n",
    "circ1.u3(*(t2[1]), 0)  # u3(*angles, q)\n",
    "circ1.u3(*(t2[0]), 1)\n",
    "############\n",
    "circ1.cx(0, 1)    # cx(ctrl, tgt)\n",
    "############\n",
    "circ1.u3(*(t2[0]), 1)\n",
    "circ1.iden(0)\n",
    "############\n",
    "circ1.cx(0, 1)\n",
    "############\n",
    "circ1.u3(*(t2[2]), 1)\n",
    "circ1.iden(0)\n",
    "# measurement circuit\n",
    "meas1 = QuantumCircuit(*regs1, name=\"meas1\")\n",
    "# barrier prevents optimizations\n",
    "# from reordering gates across its source line\n",
    "meas1.barrier(range(2)) \n",
    "############ MEASURE ANCILLARY QUBIT\n",
    "meas1.measure(q_odd, c_odd)#  map qubits to clbits\n",
    "# Full circuit\n",
    "qc1 = circ1 + meas1\n",
    "qc1.draw(output='latex', scale=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Superposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## +"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1358.8x232.2 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# create registers\n",
    "q = QuantumRegister(nqubits, name=\"q\")\n",
    "a = QuantumRegister(1, name=\"a\")\n",
    "c = ClassicalRegister(nqubits, name=\"c\")\n",
    "ca = ClassicalRegister(1, name=\"ca\")\n",
    "regs = [q, a, ca, c]\n",
    "circ = QuantumCircuit(*regs, name=\"superposition +\")\n",
    "# Construct circuit\n",
    "circ.iden(q[0])\n",
    "circ.iden(q[1])\n",
    "circ.h(a[0])\n",
    "############\n",
    "circ.barrier(range(3)) \n",
    "# even parity\n",
    "circ.cu3(*(t1[1]), a[0], q[0])  # u3(*angles, q)\n",
    "circ.cu3(*(t1[0]), a[0], q[1])\n",
    "############\n",
    "circ.ccx(a[0], q[0], q[1])    # cx(ctrl, tgt)\n",
    "############\n",
    "circ.cu3(*(t1[0]), a[0], q[1])\n",
    "circ.iden(q[0])\n",
    "############\n",
    "circ.ccx(a[0], q[0], q[1])\n",
    "############\n",
    "circ.cu3(*(t1[2]), a[0], q[1])\n",
    "circ.iden(q[0])\n",
    "############\n",
    "circ.barrier(range(3)) \n",
    "# switch ancilla\n",
    "circ.iden(q[0])\n",
    "circ.iden(q[1])\n",
    "circ.x(a[0])\n",
    "############\n",
    "circ.barrier(range(3)) \n",
    "# odd parity\n",
    "circ.cu3(*(t2[1]), a[0], q[0])  # u3(*angles, q)\n",
    "circ.cu3(*(t2[0]), a[0], q[1])\n",
    "############\n",
    "circ.ccx(a[0], q[0], q[1])    # cx(ctrl, tgt)\n",
    "############\n",
    "circ.cu3(*(t2[0]), a[0], q[1])\n",
    "circ.iden(q[0])\n",
    "############\n",
    "circ.ccx(a[0], q[0], q[1])\n",
    "############\n",
    "circ.cu3(*(t2[2]), a[0], q[1])\n",
    "circ.iden(q[0])\n",
    "# measurement circuit\n",
    "meas = QuantumCircuit(*regs, name=\"meas_circuit\")\n",
    "# barrier prevents optimizations\n",
    "# from reordering gates across its source line\n",
    "# meas.barrier(range(3)) \n",
    "############ apply another hadamard, \n",
    "# meas.iden(q[0])\n",
    "# meas.iden(q[1])\n",
    "# meas.h(a[0])\n",
    "############ MEASURE ANCILLARY QUBIT\n",
    "# meas.iden(q[0])\n",
    "# meas.iden(q[1])\n",
    "# meas.measure(a[0], ca[0])\n",
    "############\n",
    "meas.barrier(range(3)) \n",
    "############\n",
    "meas.measure(q, c)#  map qubits to clbits\n",
    "meas.measure(a[0], ca[0])\n",
    "# meas.measure(q1, c1)#  map qubits to clbits\n",
    "# Full circuit\n",
    "qc = circ + meas\n",
    "qc.draw(output='mpl', scale=0.5, filename='my_circuit.png', plot_barriers=True, fold=40)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## -"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Measurements"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "nshots = 1021 * 16\n",
    "backend_sim = Aer.get_backend('qasm_simulator')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Expected coefficients\n",
    "# outcome ordering: 00, 01, 10, 11\n",
    "cf0 = [0.810968, 0.18047, -0.554375, -0.0492955]\n",
    "cf1 = [0.84982, -0.197185, 0.487421, 0.036659]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.6576691  0.03256942 0.30733164 0.00243005]\n",
      "[0.72219403 0.03888192 0.23757923 0.00134388]\n"
     ]
    }
   ],
   "source": [
    "pb0 = np.array(cf0)**2\n",
    "pb1 = np.array(cf1)**2\n",
    "print(pb0)\n",
    "print(pb1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Even"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# execute the circuit on qasm_simulator backend;\n",
    "# set repeats (measurement shots) at 1024 (default)\n",
    "# memory = True:\n",
    "#   per-shot measurement bitstrings are returned \n",
    "#   as well (provided the backend supports it)\n",
    "job_sim0 = execute(qc0, backend_sim, shots=nshots, memory=True)\n",
    "result_sim0 = job_sim0.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 37, '01': 5079, '10': 541, '00': 10679}\n"
     ]
    }
   ],
   "source": [
    "# can get counts from result object using get_counts() method:\n",
    "counts0 = result_sim0.get_counts(qc0)\n",
    "print(counts0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts0 = result_sim0.get_counts(qc0)\n",
    "plot_histogram(counts0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Odd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "# execute the circuit on qasm_simulator backend;\n",
    "# set repeats (measurement shots) at 1024 (default)\n",
    "# memory = True:\n",
    "#   per-shot measurement bitstrings are returned \n",
    "#   as well (provided the backend supports it)\n",
    "job_sim1 = execute(qc1, backend_sim, shots=nshots, memory=True)\n",
    "result_sim1 = job_sim1.result()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 39, '01': 4164, '10': 670, '00': 11463}\n"
     ]
    }
   ],
   "source": [
    "# can get counts from result object using get_counts() method:\n",
    "counts1 = result_sim1.get_counts(qc1)\n",
    "print(counts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts1 = result_sim1.get_counts(qc1)\n",
    "plot_histogram(counts1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'00': (0.6688324064016342, 0.0051803584953980415),\n",
       " '01': (0.2897534817457199, 0.004959148504295891),\n",
       " '10': (0.03958307206630707, 0.002145388528592462),\n",
       " '11': (0.0018310397863388062, 0.00046907548273070784)}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "{'00': (0.6688324064016342, 0.0051803584953980415),\n",
    " '01': (0.2897534817457199, 0.004959148504295891),\n",
    " '10': (0.03958307206630707, 0.002145388528592462),\n",
    " '11': (0.0018310397863388062, 0.00046907548273070784)}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Superposition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### +"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'01 1': 2016, '01 0': 2556, '10 1': 311, '11 1': 18, '00 0': 5383, '10 0': 254, '11 0': 8, '00 1': 5790}\n"
     ]
    }
   ],
   "source": [
    "# execute the circuit on qasm_simulator backend;\n",
    "# set repeats (measurement shots) at 1024 (default)\n",
    "# memory = True:\n",
    "#   per-shot measurement bitstrings are returned \n",
    "#   as well (provided the backend supports it)\n",
    "job_sim = execute(qc, backend_sim, shots=nshots, memory=True)\n",
    "result_sim = job_sim.result()\n",
    "counts = result_sim.get_counts(qc)\n",
    "print(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.32883455, 0.01628471, 0.15366582, 0.00121502])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pb0/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.36109702, 0.01944096, 0.11878962, 0.00067194])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pb1/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "counts = result_sim.get_counts(qc)\n",
    "plot_histogram(counts)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python (Qiskitenv)",
   "language": "python",
   "name": "qiskitenv"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}