{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pennylane as pl\n",
    "from pennylane import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 1: The QFT matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_qubits = 4\n",
    "dev = pl.device(\"default.qubit\", wires=n_qubits)\n",
    "wires = list(range(n_qubits))\n",
    "\n",
    "def matrix():\n",
    "    N = 2 ** n_qubits\n",
    "    m = np.empty([N,N]).astype(complex)\n",
    "    # define the QFT matrix\n",
    "    return m\n",
    "\n",
    "print(matrix())\n",
    "\n",
    "@pl.qnode(dev)\n",
    "def circuit(k):\n",
    "    bits = [int(x) for x in np.binary_repr(k, width=n_qubits)]\n",
    "    print(bits)\n",
    "    pl.BasisStatePreparation(bits, wires=wires)\n",
    "    pl.QubitUnitary(matrix(), wires=wires)\n",
    "    return pl.state()\n",
    "\n",
    "results = pl.snapshots(circuit)(3)\n",
    "# plot the results\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 2: The 2-qubit QFT circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_qubits = 2\n",
    "dev = pl.device(\"default.qubit\", wires=n_qubits)\n",
    "wires = list(range(n_qubits))\n",
    "\n",
    "@pl.qnode(dev)\n",
    "def circuit(k):\n",
    "    bits = [int(x) for x in np.binary_repr(k, width=n_qubits)]\n",
    "    pl.BasisStatePreparation(bits, wires=wires)\n",
    "    # build the 2-qubit QFT circuit\n",
    "    return pl.state()\n",
    "\n",
    "pl.draw_mpl(circuit, style=\"black_white\")(1);\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = pl.snapshots(circuit)(1)\n",
    "# plot the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 3: The recursive QFT circuit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_qubits = 4\n",
    "dev = pl.device(\"default.qubit\", wires=n_qubits)\n",
    "wires = list(range(n_qubits))\n",
    "\n",
    "def subcircuit(wires):\n",
    "    # build the subcircuit on the given wires\n",
    "\n",
    "def QFT():\n",
    "    # put all the subcircuits together\n",
    "\n",
    "@pl.qnode(dev)\n",
    "def circuit(k):\n",
    "    bits = [int(x) for x in np.binary_repr(k, width=n_qubits)]\n",
    "    pl.BasisStatePreparation(bits, wires=wires)\n",
    "    QFT()\n",
    "    return pl.state()\n",
    "\n",
    "pl.draw_mpl(circuit, style=\"black_white\", decimals=2)(3);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "results = pl.snapshots(circuit)(1)\n",
    "# plot the results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 4: Using the QFT for period-finding"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "n_qubits = 6\n",
    "period = 10\n",
    "dev = pl.device(\"default.qubit\", wires=n_qubits)\n",
    "wires = list(range(n_qubits))\n",
    "\n",
    "def periodicstatecircuit():\n",
    "    # set up a circuit that output a periodic state, using pl.ControlledSequence and pl.PhaseShift\n",
    "\n",
    "@pl.qnode(dev)\n",
    "def periodicstate():\n",
    "    periodicstatecircuit()\n",
    "    return pl.state()\n",
    "\n",
    "state = periodicstate().real[:2**(n_qubits-1)]\n",
    "# plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "@pl.qnode(dev)\n",
    "def circuit():\n",
    "  periodicstatecircuit()\n",
    "  pl.QFT(wires=wires)\n",
    "  return pl.probs(wires=wires)\n",
    "\n",
    "state = circuit()[:2**(n_qubits-1)]\n",
    "# plot the results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Find the most probable answer and translate that in the the most likely period\n",
    "print(2**(n_qubits)/6)"
   ]
  }
 ],
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