configproblem/SolvingSATWithGrover.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ead2cbc8",
   "metadata": {},
   "source": [
    "# Solving SAT With Grover\n",
    "In this notebook, we aim to solve satisfyability formulae using grover search.\n",
    "For this, we first construct marking oracles for the basic gates of AND, OR and NOT.\n",
    "Then, we transform them into the required phase-oracle-form.\n",
    "\n",
    "The main resources used are this [Microsoft Kata](https://github.com/microsoft/QuantumKatas/blob/ec925ccfcb599a6bb29c8a39035d0b149f447f9a/SolveSATWithGrover/Workbook_SolveSATWithGrover.ipynb) and this [Qiskit Textbook Chapter](https://qiskit.org/textbook/ch-applications/satisfiability-grover.html).\n",
    "\n",
    "## Marking Oracles\n",
    "### And"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "52ca2a43",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit.circuit import Qubit, QuantumRegister, AncillaRegister, QuantumCircuit, Gate, ClassicalRegister\n",
    "from qiskit.quantum_info import Operator\n",
    "\n",
    "from typing import Dict, List, Tuple\n",
    "\n",
    "import numpy as np\n",
    "import math\n",
    "np.set_printoptions(threshold=1e6)\n",
    "\n",
    "\n",
    "def create_and_oracle(inp_reg: QuantumRegister, tar: Qubit) -> QuantumCircuit:\n",
    "    \"\"\"\n",
    "        Constructs an oracle for boolean AND,\n",
    "        that is a multi-controlled X gate\n",
    "    \"\"\"\n",
    "    tar_reg = QuantumRegister(bits=[tar])\n",
    "    qc = QuantumCircuit(inp_reg, tar_reg)\n",
    "\n",
    "    qc.mcx(inp_reg, tar_reg)\n",
    "\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c832fd6b",
   "metadata": {},
   "source": [
    "### Or"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "c15b61de",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_or_oracle(inp_reg: QuantumRegister, tar: Qubit) -> QuantumCircuit:\n",
    "    \"\"\"\n",
    "        Constructs an oracle for boolean OR,\n",
    "        from NOT (X) and AND oracles\n",
    "    \"\"\"\n",
    "    tar_reg = QuantumRegister(bits=[tar])\n",
    "    qc = QuantumCircuit(inp_reg, tar_reg)\n",
    "\n",
    "    # Negate all inputs\n",
    "    for i in inp_reg:\n",
    "        qc.x(i)\n",
    "    \n",
    "    # Call AND oracle\n",
    "    and_oracle = create_and_oracle(inp_reg, tar).to_gate(label=\"$U_{and}$\")\n",
    "    qc.append(and_oracle, inp_reg[:]+tar_reg[:])\n",
    "\n",
    "    # Inverse negation\n",
    "    for i in inp_reg:\n",
    "        # Inverse of x is x\n",
    "        qc.x(i)\n",
    "\n",
    "    # Flip target\n",
    "    qc.x(tar_reg[0])\n",
    "    \n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0476a398",
   "metadata": {},
   "source": [
    "While we could go on further and create _XOR_ and _AlternatingBits_ oracles but we don't need them for now so let's not :)\n",
    "\n",
    "## SAT Marking Oracles\n",
    "Using our marking gate-oracles, we can create oracles for evaluating SAT clauses and finally complete functions.\n",
    "\n",
    "### Single Clause Oracle\n",
    "A Clause is a disjunction of variables (qubits) that are potentially negated.\n",
    "The clause `x0 || !x1` may be represented by the input `[(0, true), (1, false)]`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "c1479873",
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_clause_qubits(inp_reg: QuantumRegister, clause: List[Tuple[int, bool]]) -> List[Qubit]:\n",
    "    \"\"\"\n",
    "        Return a register containing only relevant qubits for a SAT clause\n",
    "    \"\"\"\n",
    "\n",
    "    clause_qubits:list(Qubit) = []\n",
    "\n",
    "    for index, _ in clause:\n",
    "        clause_qubits.append(inp_reg[index])\n",
    "\n",
    "    return clause_qubits\n",
    "\n",
    "def create_clause_oracle(inp_reg: QuantumRegister, tar: Qubit, clause: List[Tuple[int, bool]]) -> QuantumCircuit:\n",
    "    \"\"\"\n",
    "        Create an oracle for a SAT clause\n",
    "    \"\"\"\n",
    "    tar_reg = QuantumRegister(bits=[tar], name=\"q_tar\")\n",
    "    qc = QuantumCircuit(inp_reg, tar_reg)\n",
    "\n",
    "    # Flip all qubits which are negated in the clause\n",
    "    for index, positive in clause:\n",
    "        if not positive:\n",
    "            qc.x(index)\n",
    "    \n",
    "    \n",
    "    # Get Clause Qubits\n",
    "    clause_qubits = get_clause_qubits(inp_reg, clause)\n",
    "    clause_reg = QuantumRegister(bits=clause_qubits)\n",
    "\n",
    "    # Create an OR oracle for clause\n",
    "    clause_oracle = create_or_oracle(clause_reg, tar).to_gate(label=\"$U_{or}$\")\n",
    "    qc.append(clause_oracle, clause_reg[:]+tar_reg[:])\n",
    "\n",
    "    # Inverse the initial flips\n",
    "    for index, positive in clause:\n",
    "        if not positive:\n",
    "            qc.x(index)\n",
    "\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bbf077cc",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 296.766x264.88 with 1 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Debug Clause Oracle\n",
    "inp_reg = QuantumRegister(3, name=\"q_in\")\n",
    "tar = Qubit()\n",
    "tar_reg = QuantumRegister(bits=[tar])\n",
    "clause = [(0, True),(1, False),(2,False)]\n",
    "\n",
    "clause_circuit = create_clause_oracle(inp_reg, tar, clause)\n",
    "clause_circuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5962e20a",
   "metadata": {},
   "source": [
    "### k-SAT Oracle\n",
    "Using our single clause oracle, we can take their conjunction and create a marking oracle for the entire expression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "b777fed3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_ksat_oracle(inp_reg: QuantumRegister, tar: Qubit, clauses: List[List[Tuple[int, bool]]]) -> Gate:\n",
    "    \"\"\"\n",
    "        Create an Oracle for a kSAT problem\n",
    "    \"\"\"\n",
    "    ancilla_reg = AncillaRegister(len(clauses), name=\"a\")\n",
    "    tar_reg = QuantumRegister(bits=[tar], name=\"q_tar\")\n",
    "    qc = QuantumCircuit(inp_reg, tar_reg, ancilla_reg)\n",
    "\n",
    "    # Compose individual clauses\n",
    "    for index, clause in enumerate(clauses):\n",
    "        # Use one ancilla for each clause\n",
    "        clause_oracle = create_clause_oracle(inp_reg, ancilla_reg[index], clause).to_gate(label=\"$U_{clause}$\")\n",
    "        qc.append(clause_oracle, inp_reg[:]+[ancilla_reg[index]])\n",
    "    \n",
    "    # Store the conjugate transpose (inverse) for later qubit cleanup\n",
    "    inverse_qc = qc.inverse()\n",
    "    \n",
    "    # Use and oracle onto ancilla register and target\n",
    "    and_oracle = create_and_oracle(ancilla_reg, tar).to_gate(label=\"$U_{and}$\")\n",
    "    qc.append(and_oracle, ancilla_reg[:]+tar_reg[:])\n",
    "\n",
    "    # Inverse clause oracles\n",
    "    qc = qc.compose(inverse_qc)\n",
    "\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68bf5f17",
   "metadata": {},
   "source": [
    "**DONE** We can now formulate a SAT problem and create a marking oracle for it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "224fa5a0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 838.566x505.68 with 1 Axes>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# f(x) = (B + !D + E) * (A + !C)\n",
    "# g(x) = (!A+!C)(!B+C)\n",
    "problem_f = [[(1, True),(3, False),(4, True)],\n",
    "          [(0, True),(2, False)]]\n",
    "\n",
    "problem_g = [[(0, False)], [(1, True), (2, True)]]\n",
    "\n",
    "problem = np.array(problem_f, dtype=object)\n",
    "n_variables = 5\n",
    "\n",
    "inp_reg = QuantumRegister(n_variables, name=\"q_in\")\n",
    "tar = Qubit()\n",
    "tar_reg = QuantumRegister(bits=[tar])\n",
    "\n",
    "problem_circuit = create_ksat_oracle(inp_reg, tar, problem)\n",
    "problem_circuit.draw(output=\"mpl\", justify=\"left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bccd06b0",
   "metadata": {},
   "source": [
    "## Converting the oracles into phase oracles for Grover"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c75a1ce0",
   "metadata": {},
   "outputs": [],
   "source": [
    "def oracle_converter(oracle_qc: QuantumCircuit, target_idx: int) -> QuantumCircuit:\n",
    "    \"\"\"\n",
    "        Convert a bit-flip into a phase oracle\n",
    "    \"\"\"\n",
    "    phase_qc = oracle_qc.copy()\n",
    "\n",
    "    qc_conv = QuantumCircuit(1, name=\"$U_{phase}$\")\n",
    "    qc_conv.x(0)\n",
    "    qc_conv.h(0)\n",
    "    # Prepend the phase transformation\n",
    "    phase_qc = phase_qc.compose(qc_conv, qubits=[target_idx], front=True)\n",
    "    # Append the phase transformation \n",
    "    phase_qc = phase_qc.compose(qc_conv.inverse(), qubits=[target_idx])\n",
    "\n",
    "    return phase_qc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "e0dba889",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1079.37x505.68 with 1 Axes>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phase_problem_circuit = oracle_converter(problem_circuit, len(inp_reg))\n",
    "phase_problem_circuit.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6e17b214",
   "metadata": {},
   "source": [
    "### Analyzing Oracles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "8bf045b8",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_matrix(circuit):\n",
    "    \"\"\"\n",
    "        Prints the matrix of a given quantum circuit (oracle) and analyzes it regarding positive and negative values\n",
    "    \"\"\"\n",
    "    ppod = Operator(circuit).data\n",
    "    print(\"Values in Operator\", set(ppod.flatten()))\n",
    "    print(f\"Oracle Shape: {ppod.shape}\", f\"Elements;; nonzero:{np.count_nonzero(ppod)}, 1: {np.count_nonzero(ppod.real > 0.99)}, -1: {np.count_nonzero(ppod.real < -0.99)}\")\n",
    "    print(\"Diagonal values: \", [round(ppod[x][x].real) for x in range(len(ppod[0]))])\n",
    "    print(ppod)\n",
    "    \n",
    "# print_matrix(phase_problem_circuit)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "4a22c7bc",
   "metadata": {},
   "outputs": [],
   "source": [
    "def print_diagonal_analysis(circuit, measurements=None):\n",
    "    \"\"\"\n",
    "        Prints analysis data about a given quantum circuit (oracle).\n",
    "        This method was used to determine whether one could trivially derive valid states from a given oracle.\n",
    "        \n",
    "        Keyword Arguments\"\n",
    "        circuit -- qiskit quantum circuit representing a grover oracle\n",
    "        measurements -- dictionary of states and measurement counts as derived by qiskits counts() method after simulation\n",
    "    \"\"\"\n",
    "    od = Operator(circuit).data\n",
    "    diagonal_values = [round(od[x][x].real) for x in range(len(od[0]))]\n",
    "    bspace_padding = math.ceil(math.log(len(diagonal_values), 2))\n",
    "    \n",
    "    if measurements is not None:\n",
    "        measurement_threshold = max(measurements.values()) / (2**2)\n",
    "        measurements = {key:val for key, val in measurements.items() if val > measurement_threshold}\n",
    "    \n",
    "    for i, v in enumerate(diagonal_values):\n",
    "        vs = \" 1\" if  v == 1 else \"-1\"\n",
    "        state_str = format(i, f\"0{bspace_padding}b\")\n",
    "        \n",
    "        # when measurements are available, check if a phase flipped state may be good\n",
    "        state_marking = \"\"\n",
    "        if measurements is not None and v == -1:\n",
    "            if list(filter(state_str.endswith, measurements.keys())) != []:\n",
    "                state_marking = \"good\"\n",
    "            else:\n",
    "                input_size = len(list(measurements)[0])\n",
    "                ancilla_State = int(state_str[:-input_size])\n",
    "                if ancilla_State == 0:\n",
    "                    state_marking = \"!AMBIGUOUS!\"\n",
    "                else:\n",
    "                    state_marking = \"invalid\"\n",
    "        \n",
    "        print(vs, state_str, state_marking)\n",
    "        \n",
    "count_dummy = {'01010': 1, '11000': 2, '11011': 7, '00011': 1, '01111': 3, '00010': 8, '00101': 4, '10101': 5, '01011': 6, '00001': 8, '11010': 5, '10010': 10, '00000': 1, '01001': 87, '10000': 6, '11001': 4, '11111': 2, '10110': 89, '11101': 3, '00110': 75, '11110': 87, '10111': 5, '01101': 79, '01110': 87, '10011': 7, '00100': 78, '01100': 78, '10001': 3, '01000': 91, '11100': 72, '00111': 4, '10100': 82}\n",
    "# print_diagonal_analysis(phase_problem_circuit, count_dummy)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "752eee7d",
   "metadata": {},
   "source": [
    "# Plugging Oracles into Grover\n",
    "As we can now create phase oracles, we can model a complete grover loop.\n",
    "\n",
    "1. Create uniform superposition over q_in (an & target stay |0>)\n",
    "2. Make oracle: ksat_for_problem(...) & phase_oracle(...)\n",
    "3. Grover Loop (k-times? correctness-check?)\n",
    "    1. Append Phase_Oracle over all q registers\n",
    "    2. Append Grover Diffuser over all q registers\n",
    "3. Add classical registers for output measurements\n",
    "5. Measure q_in into classical registers and check solution (histogram)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "5ed7acb9",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Input:\n",
    "# f(x) = (x0 + !x1) * (!x2 + !x3) * (x2 + x3) * (!x4 + x5) # Poster Problem\n",
    "#problem = [[(0, True), (1, True)], [(2, False), (3, False)], [(2, True), (3, True)], [(4, False), (5, True)]]\n",
    "# n_variables = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "14be65eb",
   "metadata": {},
   "source": [
    "(1.) Create uniform superposition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "bfdb0d7a",
   "metadata": {},
   "outputs": [],
   "source": [
    "def initialize_s(qc, qubits):\n",
    "    \"\"\"\n",
    "        Apply a H-gate to 'qubits' in qc\n",
    "    \"\"\"\n",
    "    for q in qubits:\n",
    "        qc.h(q)\n",
    "    return qc"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bab8c1c8",
   "metadata": {},
   "source": [
    "(2.) Make oracle for specific sat problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "03853f32",
   "metadata": {},
   "outputs": [],
   "source": [
    "def init_sat_circuit(problem):\n",
    "    \"\"\"\n",
    "        Returns calculated number of qubits, created circuit\n",
    "    \"\"\"\n",
    "\n",
    "    # Number of input qubits\n",
    "    num_vars = len(set([statement[0] for clause in problem for statement in clause]))\n",
    "    # Number of ancialla qubits\n",
    "    num_clauses = len(problem)\n",
    "    num_qubits = num_vars + num_clauses + 1\n",
    "\n",
    "    # Init registers and qubits\n",
    "    inp_reg = QuantumRegister(num_vars, name=\"q_in\")\n",
    "    tar = Qubit()\n",
    "    tar_reg = QuantumRegister(bits=[tar], name=\"q_tar\")\n",
    "    ancilla_reg = AncillaRegister(num_clauses, name=\"a\")\n",
    "\n",
    "    # Create oracle for this SAT problem instance\n",
    "    qc_oracle = QuantumCircuit(num_qubits)\n",
    "    qc_oracle.append(create_ksat_oracle(inp_reg, tar, problem).to_gate(label=\"$U_{ksat}$\"), qc_oracle.qubits)\n",
    "    qc_phase_oracle = oracle_converter(qc_oracle, len(inp_reg))\n",
    "\n",
    "    # Construct main quantum circuit\n",
    "    c_regs = ClassicalRegister(num_vars, 'c')\n",
    "    main_qc = QuantumCircuit(inp_reg, tar_reg, ancilla_reg, c_regs)\n",
    "\n",
    "    # Create uniform superposition\n",
    "    main_qc = initialize_s(main_qc, range(num_vars))\n",
    "\n",
    "    return (num_vars, num_qubits, main_qc, qc_oracle, qc_phase_oracle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "1901d48e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1049.8x505.68 with 1 Axes>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_, _, _, _, qc_phase_oracle = init_sat_circuit(problem)\n",
    "qc_phase_oracle_decomposed = qc_phase_oracle.decompose() # .decompose().decompose().decompose()\n",
    "qc_phase_oracle_decomposed.draw(output=\"mpl\", justify=\"left\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d319782b",
   "metadata": {},
   "source": [
    "(3.) Grover Loop"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "11b6fe28",
   "metadata": {},
   "outputs": [],
   "source": [
    "def create_ksat_grover(problem: List[List[Tuple[int, bool]]], k) -> Tuple[QuantumCircuit, QuantumCircuit]:\n",
    "    \"\"\"\n",
    "        Creates an circuit for the SAT problem instance and applies Grover k times\n",
    "    \"\"\"\n",
    "\n",
    "    # Init sat circuit\n",
    "    num_inp_qubits, num_qubits, main_qc, qc_oracle, qc_phase_oracle = init_sat_circuit(problem)\n",
    "\n",
    "    # Add grover diffuser\n",
    "    from grover import diffuser\n",
    "    diff = diffuser(num_inp_qubits)\n",
    "\n",
    "    # Grover loop: add the oracle and diffusor step k times\n",
    "    phase_oracle_gate = qc_phase_oracle.to_gate(label='U$_{oracle}$')\n",
    "    register_map = list(range(num_inp_qubits))\n",
    "    for i in range(k):\n",
    "        main_qc.append(phase_oracle_gate, range(num_qubits))\n",
    "        main_qc = main_qc.compose(diff, register_map)\n",
    "        \n",
    "    # Add measurements of input qubits\n",
    "    main_qc.measure(register_map, register_map)\n",
    "#     main_qc.measure_all()\n",
    "    \n",
    "    return (main_qc, qc_phase_oracle)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "294a5d11",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 718.166x565.88 with 1 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# A suitable k could be calculated using quantum phase estimation\n",
    "k=1\n",
    "\n",
    "# Create the circuit\n",
    "main_qc, qc_oracle = create_ksat_grover(problem, k)\n",
    "\n",
    "\n",
    "main_qc.draw(output=\"mpl\", justify=\"left\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "511d16cd",
   "metadata": {},
   "source": [
    "The Quantum Circuit is completed! Simulate it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "76689a4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 4000x1000 with 1 Axes>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit import Aer, transpile\n",
    "from qiskit.visualization import plot_histogram\n",
    "from qiskit.providers.aer import StatevectorSimulator\n",
    "\n",
    "transpiled_grover_circuit = transpile(main_qc, StatevectorSimulator())\n",
    "results = StatevectorSimulator().run(transpiled_grover_circuit, shots=1000).result()\n",
    "counts = results.get_counts()\n",
    "histogram = plot_histogram(counts, figsize=(40, 10))\n",
    "histogram # For display purposes in jupyter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b6163e0d",
   "metadata": {},
   "source": [
    "## Warmstarting other Quantum circuits\n",
    "If we want to use this result to warmstart other quantum circuits, we need the list of complex amplitudes of that statevector!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "f70d490e",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Get the statevector from counts.\n",
    "def calc_statevector_from(counts, width=None):\n",
    "    threshold = max(counts.values())/1e2 # one order of magnitude below the most often measured results\n",
    "    count_vector = []\n",
    "    shots = 0 # measured shots\n",
    "    \n",
    "    # derive width from counts if not given\n",
    "    if width is None:\n",
    "        width = len(list(counts.keys()))\n",
    "    \n",
    "    # create statevector by using counts\n",
    "    for i in range(2**width):\n",
    "        b = format(i, f\"0{width}b\")\n",
    "        c = counts.get(b)\n",
    "        # print(i, b, c)\n",
    "        if c is None:\n",
    "            count_vector.append(0)\n",
    "        else:\n",
    "            count_vector.append(c)\n",
    "            shots += c\n",
    "    \n",
    "    # normalize vector\n",
    "    count_arr = np.array(count_vector)\n",
    "    norm_vector = count_arr / count_arr.sum()\n",
    "    \n",
    "    # sqrt vector\n",
    "    statevector = np.sqrt(norm_vector)\n",
    "    return statevector"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6fd904e3",
   "metadata": {},
   "source": [
    "This function can be used to calculate a statevector from a set of measurements!\n",
    "Now double check that this vector yields the same result"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "9f2a7124",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "array([0.05477226, 0.05477226, 0.07071068, 0.05477226, 0.3       ,\n",
      "       0.06324555, 0.28284271, 0.07745967, 0.30331502, 0.29832868,\n",
      "       0.03162278, 0.05477226, 0.2236068 , 0.28284271, 0.27386128,\n",
      "       0.06324555, 0.04472136, 0.06324555, 0.04472136, 0.07071068,\n",
      "       0.31304952, 0.05477226, 0.3082207 , 0.07071068, 0.07071068,\n",
      "       0.08944272, 0.04472136, 0.07745967, 0.29325757, 0.06324555,\n",
      "       0.28635642, 0.07071068])\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1136.39x385.28 with 1 Axes>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_vars = n_variables # restrict to n qubits defined near the problems because we don't care about our ancillas\n",
    "manual_statevector = calc_statevector_from(counts, num_vars)\n",
    "print(repr(manual_statevector))\n",
    "\n",
    "qc_vec = QuantumCircuit(QuantumRegister(num_vars), ClassicalRegister(num_vars))\n",
    "qc_vec.initialize(manual_statevector)\n",
    "qc_vec.measure(list(range(num_vars)), list(range(num_vars)))\n",
    "qc_vec.draw(output=\"mpl\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "89438d6e",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Circuit Depth: 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 4000x1000 with 1 Axes>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "transpiled_vec_circuit = transpile(qc_vec, StatevectorSimulator())\n",
    "print(f\"Circuit Depth: {transpiled_vec_circuit.depth()}\")\n",
    "results = StatevectorSimulator().run(transpiled_vec_circuit, shots=1000).result()\n",
    "counts = results.get_counts()\n",
    "histogram = plot_histogram(counts, figsize=(40, 10))\n",
    "histogram # For display purposes in jupyter"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1eb48186",
   "metadata": {},
   "source": [
    "# Importing Feature Models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "c31049c7",
   "metadata": {},
   "outputs": [],
   "source": [
    "from qiskit import Aer, transpile\n",
    "from util.xml_reader import Extended_Modelreader\n",
    "from util.dimacs_reader import DimacsReader\n",
    "from util.cnf import CNF\n",
    "import os \n",
    "\n",
    "def create_grover_for_model(rel_path, k=1):\n",
    "    # load given model\n",
    "    current_folder = globals()['_dh'][0]\n",
    "    some_model_path = os.path.join(current_folder, rel_path)\n",
    "    \n",
    "    if rel_path.split('.')[-1] == \"xml\":\n",
    "        reader = Extended_Modelreader()\n",
    "        feature_model, constraints = reader.readModel(some_model_path)\n",
    "        # transform to cnf and then to problem\n",
    "        feature_cnf = feature_model.build_cnf(constraints)\n",
    "        print(feature_cnf)\n",
    "        problem = feature_cnf.to_problem()\n",
    "    \n",
    "    elif rel_path.split('.')[-1] in [\"dimacs\", \"cnf\"]:\n",
    "        rd = DimacsReader()\n",
    "        rd.fromFile(some_model_path)\n",
    "        problem = CNF().from_dimacs(rd).to_problem()\n",
    "    \n",
    "    # create grover circuit\n",
    "    problem_qc, problem_oracle = create_ksat_grover(problem, k) # Create the circuit\n",
    "    return problem_qc\n",
    "    \n",
    "model = \"../benchmarks/featureide-examples/car.dimacs\"\n",
    "# model = \"../benchmarks/problem_f.cnf\"\n",
    "model_circuit = create_grover_for_model(model, k=5)\n",
    "# model_circuit.draw(output=\"mpl\")\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b7e47d23",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 4000x1000 with 1 Axes>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from qiskit.providers.aer import StatevectorSimulator, QasmSimulator\n",
    "\n",
    "    \n",
    "def collect_circuit_info(circuit, backend=\"aer_simulator\", shots=100, simulate=False):\n",
    "    # transpile and collect meta data\n",
    "    info = {}\n",
    "    simulator = Aer.get_backend(backend)\n",
    "    transpiled_grover_circuit = transpile(circuit, backend=simulator)\n",
    "    info['depth'] = transpiled_grover_circuit.depth()\n",
    "    info['width'] = transpiled_grover_circuit.num_qubits\n",
    "    \n",
    "    # try to run/simulate\n",
    "    if simulate:\n",
    "        results = simulator.run(transpiled_grover_circuit, shots=shots).result()\n",
    "        info['counts'] = results.get_counts()\n",
    "    \n",
    "    return info\n",
    "\n",
    "# gather backend metrics\n",
    "# from qiskit import IBMQ, assemble, transpile\n",
    "# provider = IBMQ.load_account()\n",
    "\n",
    "# print(provider.backends())\n",
    "# simulate_circuit(model_circuit, provider.backend.ibmq_geneva)    \n",
    "\n",
    "# actual simulation\n",
    "info = collect_circuit_info(model_circuit, shots=100, simulate=True)\n",
    "plot_histogram(info['counts'], figsize=(40, 10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "9e5a8234",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.11.1"
  },
  "vscode": {
   "interpreter": {
    "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
   }
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}