Grover_Matsuo.ipynb

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  {
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   "source": [
    "# Qiskit Implementation for Grover Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Example of 2-qubit Grover Search"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Preparation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg' # Makes the images look nice\n",
    "\n",
    "# importing Qiskit\n",
    "from qiskit import IBMQ, Aer\n",
    "from qiskit.providers.ibmq import least_busy\n",
    "from qiskit import QuantumCircuit, ClassicalRegister, QuantumRegister, execute\n",
    "\n",
    "# import basic plot tools\n",
    "from qiskit.visualization import plot_histogram"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization circuit\n",
    "\n",
    "It Applies H gates to Input qubits and changes the state of the ancilla bit to $|-\\rangle$ "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialization(circuit):\n",
    "    # Initialization\n",
    "    n = circuit.num_qubits\n",
    "    # For input qubits\n",
    "    for qubit in range(n-1):\n",
    "        circuit.h(qubit)\n",
    "    # For the ancilla bit\n",
    "    circuit.x(n-1)\n",
    "    circuit.h(n-1)\n",
    "    circuit.barrier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
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    }
   ],
   "source": [
    "n = 2\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "initialization_circuit = QuantumCircuit(qr, anc)\n",
    "\n",
    "initialization(initialization_circuit)\n",
    "initialization_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Oracle circuit\n",
    "It changes the phase of the \"good\" state. In this case, the \"good\" state $|10\\rangle$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle(circuit):\n",
    "    circuit.x(1)\n",
    "    circuit.ccx(0,1,2)\n",
    "    circuit.x(1)\n",
    "    circuit.barrier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 484.008x204.68 with 1 Axes>"
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     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 2\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "oracle_circuit = QuantumCircuit(qr, anc)\n",
    "\n",
    "oracle(oracle_circuit)\n",
    "oracle_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Diffusion circuit\n",
    "A circuit for the inversion about the mean."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def diffusion(circuit):\n",
    "    input_qubits = circuit.num_qubits -1 \n",
    "    circuit.h(range(0, input_qubits))\n",
    "    circuit.x(range(0, input_qubits))\n",
    "    circuit.h(input_qubits-1)\n",
    "    circuit.mct([i for i in range(0, input_qubits-1)], input_qubits-1)\n",
    "    circuit.h(input_qubits-1)\n",
    "    circuit.x(range(0, input_qubits))\n",
    "    circuit.h(range(0, input_qubits))\n",
    "    circuit.barrier()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "n = 2\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "diffusion_circuit = QuantumCircuit(qr, anc)\n",
    "\n",
    "diffusion(diffusion_circuit)\n",
    "diffusion_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Let's try 2-qubit Grover search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 2\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "grover_circuit = QuantumCircuit(qr, anc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Grover search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the number of iterations\n",
    "num_iterations = 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
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     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "# Let's do Grover search\n",
    "initialization(grover_circuit)\n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    oracle(grover_circuit)\n",
    "    diffusion(grover_circuit)\n",
    "    \n",
    "# Clear the ancilla bit\n",
    "grover_circuit.h(n)\n",
    "grover_circuit.x(n)\n",
    "\n",
    "    \n",
    "grover_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Experiment with Simulators"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
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     "execution_count": 11,
     "metadata": {},
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   "source": [
    "grover_circuit.measure_all()\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(grover_circuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We got the correct answer $|10\\rangle$. Note that be careful with the order of qubits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Running on current least busy device:  ibmq_burlington\n"
     ]
    }
   ],
   "source": [
    "# Load IBM Q account and get the least busy backend device\n",
    "IBMQ.load_account()\n",
    "provider = IBMQ.get_provider(group = 'open')\n",
    "device = least_busy(provider.backends(filters=lambda x: x.configuration().n_qubits >= 3 and \n",
    "                                   not x.configuration().simulator and x.status().operational==True))\n",
    "print(\"Running on current least busy device: \", device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Job Status: job has successfully run\n"
     ]
    }
   ],
   "source": [
    "# Run our circuit on the least busy backend. Monitor the execution of the job in the queue\n",
    "from qiskit.tools.monitor import job_monitor\n",
    "job = execute(grover_circuit, backend=device, shots=1024, max_credits=10)\n",
    "job_monitor(job, interval = 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
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     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "# Check the results of the computation\n",
    "results = job.result()\n",
    "answer = results.get_counts(grover_circuit)\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## An Example of 3-qubit Grover Search"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "grover_circuit = QuantumCircuit(qr, anc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the number of iterations\n",
    "num_iterations = 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle(circuit):\n",
    "    circuit.mct([0,1,2],3)\n",
    "    circuit.barrier()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This time, $|111\\rangle$ is the \"good\" state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
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     "execution_count": 18,
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   "source": [
    "# Let's do Grover search\n",
    "initialization(grover_circuit)\n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    oracle(grover_circuit)\n",
    "    diffusion(grover_circuit)\n",
    "    \n",
    "# Clear the ancilla bit\n",
    "grover_circuit.h(n)\n",
    "grover_circuit.x(n)\n",
    "\n",
    "    \n",
    "grover_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
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     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "grover_circuit.measure_all()\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(grover_circuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
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  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### What happens if we iterate 3 times?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "grover_circuit = QuantumCircuit(qr, anc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the number of iterations\n",
    "num_iterations = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
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     },
     "execution_count": 22,
     "metadata": {},
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   ],
   "source": [
    "# Let's do Grover search\n",
    "initialization(grover_circuit)\n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    oracle(grover_circuit)\n",
    "    diffusion(grover_circuit)\n",
    "    \n",
    "# Clear the ancilla bit\n",
    "grover_circuit.h(n)\n",
    "grover_circuit.x(n)\n",
    "\n",
    "    \n",
    "grover_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
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     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "grover_circuit.measure_all()\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(grover_circuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### How about 4 times?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 3\n",
    "qr = QuantumRegister(n, 'q')\n",
    "anc = QuantumRegister(1, 'ancilla')\n",
    "grover_circuit = QuantumCircuit(qr, anc)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# the number of iterations\n",
    "num_iterations = 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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     "execution_count": 26,
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   ],
   "source": [
    "# Let's do Grover search\n",
    "initialization(grover_circuit)\n",
    "\n",
    "for i in range(0, num_iterations):\n",
    "    oracle(grover_circuit)\n",
    "    diffusion(grover_circuit)\n",
    "    \n",
    "# Clear the ancilla bit\n",
    "grover_circuit.h(n)\n",
    "grover_circuit.x(n)\n",
    "\n",
    "    \n",
    "grover_circuit.draw('mpl')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
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       "</svg>\n"
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      "text/plain": [
       "<Figure size 504x360 with 1 Axes>"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grover_circuit.measure_all()\n",
    "\n",
    "backend = Aer.get_backend('qasm_simulator')\n",
    "shots = 1024\n",
    "results = execute(grover_circuit, backend=backend, shots=shots).result()\n",
    "answer = results.get_counts()\n",
    "plot_histogram(answer)"
   ]
  },
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Repeating appropriate times is important!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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