QuantumSimQubitMeasurement.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# QuantumSim - Qubit Measurement\n",
    "Author: Nico Kuijpers<br>\n",
    "Date: January 2, 2025\n",
    "\n",
    "In this notebook it is explained how the measurement of a single qubit is implemented in QuantumSim."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from quantumsim import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction\n",
    "For some cases such as error correction and quantum teleportation, it must be possible to measure the state of a single qubit $q$ and change the quantum state of the circuit accordingly. This is achieved by first obtaining the probabilities of measurement outcome $|0\\rangle$ or $|1\\rangle$ for qubit $q$ and then letting collapse its state to either $|0\\rangle$ or $|1\\rangle$ depending on a random number between $0$ and $1$.\n",
    "\n",
    "The probabilities $p_0$ and $p_1$ representing the probalitiy that a measurment results in $|0\\rangle$ or $|1\\rangle$, respectively, are defined by\n",
    "\n",
    "$p_0 = \\langle \\psi | P_0 | \\psi\\rangle$ and $p_1 = \\langle \\psi | P_1 | \\psi\\rangle$,\n",
    "\n",
    "where $\\psi$ is the quantum state of the circuit and $P_0$ and $P_1$ are projection operators.\n",
    "\n",
    "For a two-qubit system of which the first qubit is to be measured, $P_0$ and $P_1$ are defined by\n",
    "\n",
    "$P_0 = |0\\rangle \\langle 0| \\otimes \\mathbf{I}$ and $P_1 = |1\\rangle \\langle 1| \\otimes \\mathbf{I}$,\n",
    "\n",
    "where $\\mathbf{I}$ is the identity operator defined by\n",
    "\n",
    "$\\mathbf{I} = \\begin{pmatrix} 1 & 0 \\\\ 0 & 1 \\end{pmatrix}$.\n",
    "\n",
    "If, for example, the second qubit of a circuit of 4 qubits needs to be measured, $P_0$ and $P_1$ are defined by\n",
    "\n",
    "$P_0 = \\mathbf{I} \\otimes |0\\rangle \\langle 0| \\otimes \\mathbf{I} \\otimes \\mathbf{I}$ and\n",
    "$P_1 = \\mathbf{I} \\otimes |1\\rangle \\langle 1| \\otimes \\mathbf{I} \\otimes \\mathbf{I}$.\n",
    "\n",
    "After determining the new quantum state of qubit $q$, the new quantum state $|\\psi'\\rangle$ of the circuit is defined as follows.\n",
    "\n",
    "If the state of qubit $q$ becomes $|0\\rangle$, then\n",
    "\n",
    "$|\\psi'\\rangle = \\frac{P_0 |\\psi\\rangle}{\\sqrt{p_0}}$.\n",
    "\n",
    "If the state of qubit $q$ becomes $|1\\rangle$, then\n",
    "\n",
    "$|\\psi'\\rangle = \\frac{P_1 |\\psi\\rangle}{\\sqrt{p_1}}$.\n",
    "\n",
    "To implement this approach in QuantumSim, class *StateVector* has been extended with a method *measure_qubit()* as defined below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "\"\"\"\n",
    "Class representing the quantum state of a quantum circuit of N qubits.\n",
    "\"\"\"\n",
    "class StateVector:\n",
    "    def measure_qubit(self, q) -> int:\n",
    "        identity = QubitUnitaryOperation.get_identity()\n",
    "        ket_bra_00 = Dirac.ket_bra(2,0,0)\n",
    "        ket_bra_11 = Dirac.ket_bra(2,1,1)\n",
    "        P0 = np.eye(1,1)\n",
    "        P1 = np.eye(1,1)\n",
    "        for i in range(self.N):\n",
    "            if i == q:\n",
    "                P0 = np.kron(P0, ket_bra_00)\n",
    "                P1 = np.kron(P1, ket_bra_11)\n",
    "            else:\n",
    "                P0 = np.kron(P0, identity)\n",
    "                P1 = np.kron(P1, identity)\n",
    "        prob_0 = np.vdot(self.state_vector, P0.dot(self.state_vector)).real\n",
    "        prob_1 = np.vdot(self.state_vector, P1.dot(self.state_vector)).real\n",
    "        r = np.random.random()\n",
    "        if r <= prob_0:\n",
    "            self.state_vector = np.dot(P0,self.state_vector)/np.sqrt(prob_0)\n",
    "            return 0\n",
    "        else:\n",
    "            self.state_vector = np.dot(P1,self.state_vector)/np.sqrt(prob_1)\n",
    "            return 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Bell state\n",
    "Below, a circuit of $2$ qubits is defined to create the $|\\phi^{+}\\rangle$ Bell state defined by\n",
    "\n",
    "$|\\phi^{+}\\rangle = \\frac{1}{\\sqrt{2}} (|00\\rangle + |11\\rangle)$.\n",
    "\n",
    "After establishing the Bell state, the two qubits are measured. Upon measuring the state of qubit 0, also the state of qubit $1$ is determined.\n",
    "\n",
    "Intermediate probabilities are shown using function *QuantumUtil.show_all_probabilities()*. \n",
    "It can be observed that measuring the state of qubit $0$ also determines the state of qubit $1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measured state |11>\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 600x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit = Circuit(2)\n",
    "circuit.hadamard(0)\n",
    "circuit.cnot(0,1)\n",
    "circuit.measure_qubit(0)\n",
    "circuit.measure_qubit(1)\n",
    "circuit.execute()\n",
    "circuit.measure()\n",
    "state_as_string = circuit.get_classical_state_as_string()\n",
    "print(f'Measured state {state_as_string}')\n",
    "QuantumUtil.show_all_probabilities(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Run the code block above multiple times and confirm that the state after measuring qubit $0$ is either $|00\\rangle$ or $|11\\rangle$ and remains unchanged when qubit $1$ is measured.\n",
    "\n",
    "Now, we run this circuit $1000$ times using method *QuantumUtil.run_circuit()*. \n",
    "A histogram showing the occurrences of measured classical states is then created by calling method *QuantumUtil.histogram_of_classical_states()*. \n",
    "The states $|00\\rangle$ and $|11\\rangle$ should each occur about $500$ times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = QuantumUtil.run_circuit(circuit, nr_runs=1000)\n",
    "QuantumUtil.histogram_of_classical_states(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example: Greenberger-Horne-Zeilinger state\n",
    "The Greenberger-Horne-Zeilinger (GHZ) state is an entangled quantum state involving $3$ or more qubits. The GHZ state for $3$ qubits is defined by\n",
    "\n",
    "$|\\text{GHZ}\\rangle = \\frac{|000\\rangle + |111\\rangle}{\\sqrt{2}}$\n",
    "\n",
    "Below a circuit of $3$ qubits is defined to create a GHZ state. \n",
    "After establishing the GHZ state, qubit $1$ is measured. Upon measuring the state of qubit $1$, also the state of the other qubits is determined.\n",
    "\n",
    "As before, intermediate probabilities are shown. Run the code block below multiple times to confirm that measuring qubit $1$ determines the final state to be either $|000\\rangle$ or $|111\\rangle$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Measured state |000>\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 700x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "circuit = Circuit(3)\n",
    "circuit.hadamard(0)\n",
    "circuit.cnot(0,1)\n",
    "circuit.cnot(1,2)\n",
    "circuit.measure_qubit(1)\n",
    "circuit.execute()\n",
    "circuit.measure()\n",
    "state_as_string = circuit.get_classical_state_as_string()\n",
    "print(f'Measured state {state_as_string}')\n",
    "QuantumUtil.show_all_probabilities(circuit)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "Now, we run this circuit $1000$ times and create a histogram showing the occurrences of measured classical states. \n",
    "The states $|000\\rangle$ and $|111\\rangle$ should each occur about $500$ times."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "result = QuantumUtil.run_circuit(circuit, nr_runs=1000)\n",
    "QuantumUtil.histogram_of_classical_states(result)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "base",
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}