superposition_adder.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "We are going to do a1+b1 and a2+b2.\n",
      "1 + 2 = 3\n",
      "2 + 3 = 5\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 1792.7x618.722 with 1 Axes>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, transpile, Aer\n",
    "from qiskit.circuit.library import QFT\n",
    "import numpy as np\n",
    "\n",
    "simulator = Aer.get_backend('aer_simulator')\n",
    "\n",
    "def inpt() :\n",
    "    while True:\n",
    "        try:\n",
    "            print('We are going to do a1+b1 and a2+b2.')\n",
    "            ns = [bin(int(n)).replace('0b', '') for n in input(f\"Give input in the form 'a1 b1 a2 b2': \").split(' ')]\n",
    "            d = max([len(n) for n in ns])\n",
    "            ns = [n.zfill(d) for n in ns]\n",
    "            if len(ns) == 4: break\n",
    "            else : raise Exception\n",
    "            \n",
    "        except:\n",
    "            print(\"Invalid input. Please try again!\")\n",
    "\n",
    "    return ns, d\n",
    "\n",
    "\n",
    "def initCirc(ns, ln) :\n",
    "    a = QuantumRegister(ln, 'a')\n",
    "    b = QuantumRegister(ln, 'b')\n",
    "    c = ClassicalRegister(ln, 'c')\n",
    "    qc = QuantumCircuit(a, b, c)\n",
    "\n",
    "    ln = 2**(ln)\n",
    "    sa = np.zeros(ln) ; sb = np.zeros(ln)\n",
    "    sa[int(ns[0], 2)] = np.sqrt(0.9) ; sb[int(ns[1], 2)] = np.sqrt(0.9)\n",
    "    sa[int(ns[2], 2)] = np.sqrt(0.1) ; sb[int(ns[3], 2)] = np.sqrt(0.1)\n",
    "\n",
    "    qc.initialize(sa, a)\n",
    "    qc.initialize(sb, b)\n",
    "    \n",
    "    return a, b, qc\n",
    "\n",
    "\n",
    "def calc(ns, ln):\n",
    "    ln = ln+1\n",
    "    a, b, qc = initCirc(ns, ln)\n",
    "\n",
    "    qc.append(QFT(ln, do_swaps=False), range(ln))\n",
    "\n",
    "    qc = addPhase(a, b, ln, np.pi, qc)\n",
    "\n",
    "    qc.append(QFT(ln, do_swaps=False, inverse=True), range(ln))\n",
    "\n",
    "    qc.measure(range(ln), range(ln))\n",
    "    compiled_circuit = transpile(qc, simulator)\n",
    "    job = simulator.run(compiled_circuit, shots=1000)\n",
    "    counts = job.result().get_counts(compiled_circuit)\n",
    "    \n",
    "    r1, r2 = max(counts, key=counts.get), min(counts, key=counts.get)\n",
    "\n",
    "    return r1, r2, qc\n",
    "\n",
    "\n",
    "def addPhase(a, b, ln, pie, qc) :\n",
    "\n",
    "    for i in range(ln-1, -1, -1) :\n",
    "        for j in range(i+1) :\n",
    "            qc.cp(pie/2**j, b[i-j], a[i])\n",
    "        qc.barrier()\n",
    "    \n",
    "    return qc\n",
    "\n",
    "\n",
    "opr = '+'\n",
    "\n",
    "ns, ln = inpt()\n",
    "r1, r2, qc = calc(ns, ln)\n",
    "print(f\"{int(ns[0], 2)} {opr} {int(ns[1], 2)} = {int(r1, 2)}\")\n",
    "print(f\"{int(ns[2], 2)} {opr} {int(ns[3], 2)} = {int(r2, 2)}\")\n",
    "qc.draw('mpl', filename='superposition_adder.svg')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Other attempts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'11': 464, '00': 536}\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 621.941x451.5 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import BasicAer, execute, QuantumCircuit, ClassicalRegister, QuantumRegister\n",
    "import numpy as np\n",
    "\n",
    "l = 2\n",
    "\n",
    "a = QuantumRegister(l, 'a')\n",
    "b = QuantumRegister(l, 'b')\n",
    "c = ClassicalRegister(l, 'c')\n",
    "qc = QuantumCircuit(a, b, c)\n",
    "\n",
    "qc.initialize([0, 0.6, 0.8, 0], a)\n",
    "qc.initialize([0, 0.6, 0.8, 0], b)\n",
    "\n",
    "for i in range(l) :\n",
    "    qc.cx(b[i], a[i])\n",
    "\n",
    "qc.measure(a, c)\n",
    "backend = BasicAer.get_backend('qasm_simulator')\n",
    "results = execute(qc, backend, shots=1000).result().get_counts()\n",
    "print(results)\n",
    "\n",
    "display(qc.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{4} |000\\rangle- \\frac{\\sqrt{2}}{4} |001\\rangle+\\frac{\\sqrt{2} i}{4} |010\\rangle- \\frac{\\sqrt{2} i}{4} |011\\rangle+(\\frac{1}{4} + \\frac{i}{4}) |100\\rangle+(- \\frac{1}{4} - \\frac{i}{4}) |101\\rangle+(- \\frac{1}{4} + \\frac{i}{4}) |110\\rangle+(\\frac{1}{4} - \\frac{i}{4}) |111\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 371.107x284.278 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit, transpile, Aer\n",
    "\n",
    "\n",
    "simulator = Aer.get_backend('aer_simulator')\n",
    "\n",
    "n = 3\n",
    "\n",
    "circuit = QuantumCircuit(n)\n",
    "circuit.x(0)\n",
    "circuit.append(QFT(n, do_swaps=False), range(n))\n",
    "circuit.save_statevector('psi')\n",
    "\n",
    "result = simulator.run(transpile(circuit, simulator)).result()\n",
    "data = result.data()\n",
    "\n",
    "psi = data['psi']\n",
    "\n",
    "display(psi.draw(output='latex'))\n",
    "display(circuit.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Statevector([ 3.53553391e-01+0.j        , -3.53553391e-01+0.j        ,\n",
      "              2.16489014e-17+0.35355339j, -2.16489014e-17-0.35355339j,\n",
      "              2.50000000e-01+0.25j      , -2.50000000e-01-0.25j      ,\n",
      "             -2.50000000e-01+0.25j      ,  2.50000000e-01-0.25j      ],\n",
      "            dims=(2, 2, 2))\n",
      "[1, 2]\n",
      "State of qubit 0:\n",
      " [0.5+0.j 0.5+0.j]\n",
      "[0, 2]\n",
      "State of qubit 1:\n",
      " [0.5+0.j 0.5+0.j]\n",
      "[0, 1]\n",
      "State of qubit 2:\n",
      " [0.5+0.j 0.5+0.j]\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 287.496x284.278 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import partial_trace, Statevector\n",
    "\n",
    "# define your two states as circuits\n",
    "n = 3\n",
    "circuit = QuantumCircuit(n)\n",
    "circuit.x(0)\n",
    "circuit.append(QFT(n, do_swaps=False), range(n))\n",
    "\n",
    "full_statevector = Statevector(circuit)\n",
    "print(full_statevector)\n",
    "tl = np.arange(n)\n",
    "for i in tl:\n",
    "    ttl = list(np.delete(tl, np.where(tl == i)))\n",
    "    print(ttl)\n",
    "    partial_density_matrix = partial_trace(full_statevector, ttl)\n",
    "    partial_statevector = np.diagonal(partial_density_matrix)\n",
    "    print(f'State of qubit {i}:\\n', partial_statevector)\n",
    "# partial_density_matrix = partial_trace(full_statevector, [1, 2])\n",
    "\n",
    "\n",
    "display(circuit.draw('mpl'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0.9999999999999998, 0.0, 0.0], [0.0, 0.0, -0.9999999999999998]]\n"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumCircuit\n",
    "from qiskit.quantum_info import Statevector\n",
    "from qiskit.visualization import plot_bloch_multivector\n",
    "from qiskit.visualization.state_visualization import _bloch_multivector_data\n",
    "\n",
    "qc = QuantumCircuit(2)\n",
    "qc.h(0)\n",
    "qc.x(1)\n",
    "\n",
    "state = Statevector(qc)\n",
    "plot_bloch_multivector(state)\n",
    "print(_bloch_multivector_data(state))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "ename": "QiskitError",
     "evalue": "'No statevector for experiment \"<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x000001EC4C355F90>\"'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "File \u001b[1;32mc:\\Users\\Rishi Vora\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\qiskit\\result\\result.py:314\u001b[0m, in \u001b[0;36mResult.get_statevector\u001b[1;34m(self, experiment, decimals)\u001b[0m\n\u001b[0;32m    312\u001b[0m \u001b[39mtry\u001b[39;00m:\n\u001b[0;32m    313\u001b[0m     \u001b[39mreturn\u001b[39;00m postprocess\u001b[39m.\u001b[39mformat_statevector(\n\u001b[1;32m--> 314\u001b[0m         \u001b[39mself\u001b[39;49m\u001b[39m.\u001b[39;49mdata(experiment)[\u001b[39m\"\u001b[39;49m\u001b[39mstatevector\u001b[39;49m\u001b[39m\"\u001b[39;49m], decimals\u001b[39m=\u001b[39mdecimals\n\u001b[0;32m    315\u001b[0m     )\n\u001b[0;32m    316\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mKeyError\u001b[39;00m \u001b[39mas\u001b[39;00m ex:\n",
      "\u001b[1;31mKeyError\u001b[0m: 'statevector'",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[1;31mQiskitError\u001b[0m                               Traceback (most recent call last)",
      "Cell \u001b[1;32mIn[37], line 34\u001b[0m\n\u001b[0;32m     32\u001b[0m \u001b[39m# circuit.append(QFT(n, do_swaps=False), range(n))\u001b[39;00m\n\u001b[0;32m     33\u001b[0m \u001b[39mfor\u001b[39;00m q \u001b[39min\u001b[39;00m \u001b[39mrange\u001b[39m(n):\n\u001b[1;32m---> 34\u001b[0m     get_state(n, q, circuit, simulator)\n",
      "Cell \u001b[1;32mIn[37], line 11\u001b[0m, in \u001b[0;36mget_state\u001b[1;34m(n, q, circuit, simulator)\u001b[0m\n\u001b[0;32m      8\u001b[0m result \u001b[39m=\u001b[39m simulator\u001b[39m.\u001b[39mrun(transpile(circuit, simulator))\u001b[39m.\u001b[39mresult()\n\u001b[0;32m      9\u001b[0m \u001b[39m# data = result.data()\u001b[39;00m\n\u001b[0;32m     10\u001b[0m \u001b[39m# psi = data['psi']\u001b[39;00m\n\u001b[1;32m---> 11\u001b[0m sv \u001b[39m=\u001b[39m result\u001b[39m.\u001b[39;49mget_statevector(circuit)\n\u001b[0;32m     12\u001b[0m display(sv\u001b[39m.\u001b[39mdraw(output\u001b[39m=\u001b[39m\u001b[39m'\u001b[39m\u001b[39mlatex\u001b[39m\u001b[39m'\u001b[39m))\n\u001b[0;32m     13\u001b[0m \u001b[39m# for index, instruction in enumerate(circuit.data):\u001b[39;00m\n\u001b[0;32m     14\u001b[0m \u001b[39m#     print(index, instruction.operation.name, [ circuit.find_bit(q).index for q in instruction.qubits])\u001b[39;00m\n\u001b[0;32m     15\u001b[0m \u001b[39m# print(circuit.data)\u001b[39;00m\n",
      "File \u001b[1;32mc:\\Users\\Rishi Vora\\AppData\\Local\\Programs\\Python\\Python311\\Lib\\site-packages\\qiskit\\result\\result.py:317\u001b[0m, in \u001b[0;36mResult.get_statevector\u001b[1;34m(self, experiment, decimals)\u001b[0m\n\u001b[0;32m    313\u001b[0m     \u001b[39mreturn\u001b[39;00m postprocess\u001b[39m.\u001b[39mformat_statevector(\n\u001b[0;32m    314\u001b[0m         \u001b[39mself\u001b[39m\u001b[39m.\u001b[39mdata(experiment)[\u001b[39m\"\u001b[39m\u001b[39mstatevector\u001b[39m\u001b[39m\"\u001b[39m], decimals\u001b[39m=\u001b[39mdecimals\n\u001b[0;32m    315\u001b[0m     )\n\u001b[0;32m    316\u001b[0m \u001b[39mexcept\u001b[39;00m \u001b[39mKeyError\u001b[39;00m \u001b[39mas\u001b[39;00m ex:\n\u001b[1;32m--> 317\u001b[0m     \u001b[39mraise\u001b[39;00m QiskitError(\u001b[39mf\u001b[39m\u001b[39m'\u001b[39m\u001b[39mNo statevector for experiment \u001b[39m\u001b[39m\"\u001b[39m\u001b[39m{\u001b[39;00m\u001b[39mrepr\u001b[39m(experiment)\u001b[39m}\u001b[39;00m\u001b[39m\"\u001b[39m\u001b[39m'\u001b[39m) \u001b[39mfrom\u001b[39;00m \u001b[39mex\u001b[39;00m\n",
      "\u001b[1;31mQiskitError\u001b[0m: 'No statevector for experiment \"<qiskit.circuit.quantumcircuit.QuantumCircuit object at 0x000001EC4C355F90>\"'"
     ]
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, Aer\n",
    "\n",
    "def get_state(n, q, circuit, simulator) :\n",
    "    tl = np.arange(n)\n",
    "    tm = list(np.delete(tl, np.where(tl == q)))\n",
    "    circuit.measure(tm, list(range(n-1)))\n",
    "    circuit.save_statevector('psi')\n",
    "    result = simulator.run(transpile(circuit, simulator)).result()\n",
    "    data = result.data()\n",
    "    psi = data['psi']\n",
    "    display(psi.draw(output='latex'))\n",
    "    # for index, instruction in enumerate(circuit.data):\n",
    "    #     print(index, instruction.operation.name, [ circuit.find_bit(q).index for q in instruction.qubits])\n",
    "    # print(circuit.data)\n",
    "    circuit = QuantumCircuit.from_instructions([item for item in circuit.data if item.operation.name != 'measure' and item.operation.name != 'save_statevector'])\n",
    "    for index, instruction in enumerate(circuit.data):\n",
    "        print(index, instruction.operation.name, [ circuit.find_bit(q).index for q in instruction.qubits])\n",
    "    display(circuit.draw('mpl'))\n",
    "    \n",
    "\n",
    "\n",
    "simulator = Aer.get_backend('aer_simulator')\n",
    "\n",
    "n = 3\n",
    "\n",
    "a = QuantumRegister(n, 'a')\n",
    "c = ClassicalRegister(n-1, 'c')\n",
    "circuit = QuantumCircuit(a, c)\n",
    "circuit.h(0)\n",
    "circuit.x(1)\n",
    "# circuit.append(QFT(n, do_swaps=False), range(n))\n",
    "for q in range(n):\n",
    "    get_state(n, q, circuit, simulator)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$$- \\frac{\\sqrt{2}}{2} |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$- \\frac{\\sqrt{2} i}{2} |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$\\frac{\\sqrt{2}}{2} |0\\rangle+(\\frac{1}{2} + \\frac{i}{2}) |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$(0.6532814824 - 0.2705980501 i) |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$$(0.6935199227 - 0.1379496896 i) |0\\rangle+\\frac{\\sqrt{2}}{2} |1\\rangle$$"
      ],
      "text/plain": [
       "<IPython.core.display.Latex object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'q_0': DensityMatrix([[ 0.5+0.j, -0.5+0.j],\n",
      "               [-0.5+0.j,  0.5+0.j]],\n",
      "              dims=(2,)), 'q_1': DensityMatrix([[5.00000000e-01+0.j , 2.63784264e-17-0.5j],\n",
      "               [2.63784264e-17+0.5j, 5.00000000e-01+0.j ]],\n",
      "              dims=(2,)), 'q_2': DensityMatrix([[0.5       +0.j        , 0.35355339-0.35355339j],\n",
      "               [0.35355339+0.35355339j, 0.5       +0.j        ]],\n",
      "              dims=(2,)), 'q_3': DensityMatrix([[0.5       +0.j        , 0.46193977-0.19134172j],\n",
      "               [0.46193977+0.19134172j, 0.5       +0.j        ]],\n",
      "              dims=(2,)), 'q_4': DensityMatrix([[0.5       +0.j        , 0.49039264-0.09754516j],\n",
      "               [0.49039264+0.09754516j, 0.5       +0.j        ]],\n",
      "              dims=(2,))}\n"
     ]
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 2210.55x953.167 with 1 Axes>"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import QuantumRegister, ClassicalRegister, QuantumCircuit, transpile, Aer\n",
    "from qiskit.circuit.library import QFT\n",
    "from qiskit_aer import AerSimulator\n",
    "\n",
    "n = 5\n",
    "simulator = AerSimulator()\n",
    "\n",
    "circ = QuantumCircuit(5)\n",
    "circ.x(0)\n",
    "circ.append(QFT(n, do_swaps=False), range(n))\n",
    "for q in range(n):\n",
    "    circ.save_density_matrix(qubits=[q], label=f'q_{q}')\n",
    "\n",
    "circ = transpile(circ, backend=simulator)\n",
    "job = simulator.run(circ)\n",
    "state = job.result().data()\n",
    "for i,dm in state.items() :\n",
    "    display(dm.to_statevector().draw('latex'))\n",
    "    # print(dm)\n",
    "print(state) #\n",
    "circ.draw('mpl')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.2"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}