Example_2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ceb481a2",
   "metadata": {},
   "source": [
    "# Noiseless simulation of the FSL method for non-periodic functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e643e2e6",
   "metadata": {},
   "source": [
    "As we discussed in Sec. (II) of our paper, the FSL method has to be modified for non-periodic functions. In this notebook, we provide a tutorial for using the FSL method to load non-periodic functions. \n",
    "\n",
    "We first import useful libraries."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "282e65d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Qiskit \n",
    "import qiskit\n",
    "from qiskit import QuantumCircuit, Aer, transpile\n",
    "from qiskit.circuit.library import QFT\n",
    "\n",
    "# Custom libraries\n",
    "import supplementary\n",
    "import uniformly_controlled_rotations as UCR"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e2be106",
   "metadata": {},
   "source": [
    "Approximating a non-periodic function by a truncated Fourier series leads to large oscillations near the boundary of the domain, also known as the Gibbs phenomenon. The FSL method loads a Fourier series approximation of the target function on a quantum computer and so we expect large oscillations in the amplitudes of the state prepared using the standard FSL method. To overcome this issue, we proposed the following modification to the FSL method. Instead of directly loading the $n$-qubit target state $|f\\rangle \\, = \\, \\sum_{k=0}^{2^{n}-1} \\, f_{k} |k\\rangle \\, $, we consider the $(n+1)$-qubit state\n",
    "\n",
    "$$ |F\\rangle \\, = \\, \\frac{1}{\\sqrt{2}} |0\\rangle \\, \\otimes \\,\\sum_{k=0}^{2^{n}-1} \\, f_{k} |k\\rangle \\, + \\, \\frac{1}{\\sqrt{2}} |1\\rangle \\, \\otimes \\,\\sum_{k=0}^{2^{n}-1} \\, f_{2^{n}-1-k} |k\\rangle \\, .$$\n",
    "\n",
    "The amplitudes of this state store the values of the function $F(x) = f(x)/\\sqrt{2}$ for $0 \\le x \\le 1$ and $F(x) = f(2-x)/\\sqrt(2)$ for $1 \\le x \\le 2$. By construction, $F(x)$ is periodic on the domain $[0,2]$, its Fourier series approximation does not suffer from large oscillations. Hence, we can prepare the $(n+1)$-qubit state $|F\\rangle$ with high fidelity using the standard FSL method. Once we have prepared the state $|F\\rangle$, we pass it through the circuit shown below. This circuit is designed to disentangle the ancilla qubit from the other $n$ qubits and map the state of the $n$ qubits to the target $|f\\rangle$. \n",
    "\n",
    "<img src=\"figures/non-periodic_fsl.jpg\" alt=\"FSL circuit for non-periodic functions\" style=\"height: 200px; width:550px;\"/>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "252bc13a",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "As a example, we now perform the simulation of loading $f(x) = \\mathcal{N}^{-1/2} \\tanh\\big(4(x-1/2)\\big)$ for $0\\le x \\le 1$ on a state of $n=20$ qubits using the modified FSL method. The normalization constant $\\mathcal{N}$ ensures that the state $|f\\rangle$ is normalized. We start by encoding the values of $f(x)$ and $F(x)$ on the `list`s `target_f` and `target_F`, respectively. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "aac4cd5b",
   "metadata": {},
   "outputs": [],
   "source": [
    "# no. of qubits \n",
    "n = 20 \n",
    "# Discretizing the domain [0,1]\n",
    "x = [k/(2**n) for k in range(2**n)]\n",
    "\n",
    "# Target function f\n",
    "target_f = [np.tanh(4*(xx-0.5)) for xx in x]\n",
    "target_f = target_f/np.linalg.norm(target_f)\n",
    "\n",
    "# Target function F\n",
    "target_F = [*target_f,*target_f[::-1]]\n",
    "target_F = target_F/np.sqrt(2)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f94bd21f",
   "metadata": {},
   "source": [
    "To load $F(x)$ using the FSL method, we first need to approximate it by a truncated Fourier series. We do this using the function `Fourier_state` defined in the code file `supplementary.py`. This function takes the list `target_F` and an `int` $m$ as inputs and returns a `list` of length $2^{(m+1)}$, $[c_{0}, c_{1}, \\dots , c_{2^{m}-1}, 0, c_{-2^{m}+1}, \\dots, c_{-1} ] \\, $, where $c_{\\ell}$ are the discrete Fourier coeffiecents of $F(x)$.  \n",
    "\n",
    "For concreteness, we choose $m=6$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "dac9cd21",
   "metadata": {},
   "outputs": [],
   "source": [
    "# No. of Fourier modes\n",
    "m = 6\n",
    "# Fourier state |c>\n",
    "state_c = supplementary.Fourier_state(target_F,m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0523c437",
   "metadata": {},
   "source": [
    "Now we can construct the FSL circuit to prepare the state $|F\\rangle \\, $. Note that this circuit acts on $(n+1)$ qubits. Also, note that we perform the simulation using the Qiskit Aer `statevector_vector` simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "98e7e6d4",
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulator\n",
    "simulator = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "# Initialize a quantum circuit\n",
    "circ = QuantumCircuit(n+1)\n",
    "\n",
    "# Uniformly controlled rotation\n",
    "# to prepare the state |c>\n",
    "U_c = UCR.cascade_UCRs(state_c)\n",
    "\n",
    "# Apply U_c on the last (m+1) qubits\n",
    "Uc_qubits = range(n-m,n+1)\n",
    "circ.compose(U_c,qubits=Uc_qubits,inplace=True)\n",
    "\n",
    "# Apply a cascade of CNOTs\n",
    "for i in range(n-m):\n",
    "    circ.cx(n-m,i)\n",
    "\n",
    "# Finally, apply the inverse QFT.\n",
    "inv_qft = QFT(num_qubits=n+1, inverse=True)\n",
    "inv_qft = transpile(inv_qft, simulator)\n",
    "circ.compose(inv_qft,qubits=range(n,-1,-1),inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "767c8060",
   "metadata": {},
   "source": [
    "Once we have the circuit to prepare the state $|F\\rangle \\, $, we now apply the CNOT gates to disentangle the ancilla qubit from the other $n$ qubits and to map the state of the $n$ qubits to $|f\\rangle \\, $. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "cdea5319",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<qiskit.circuit.instructionset.InstructionSet at 0x78020a24e580>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Disentangle the ancilla qubit \n",
    "# using a cascade of CNOTs and\n",
    "# a Hadamard\n",
    "for i in range(1,n+1):\n",
    "    circ.cx(0,i)\n",
    "circ.h(0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "96b157a6",
   "metadata": {},
   "source": [
    "Finally, we run the circuit and plot the simulated statevector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "0162d328",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Run the circuit\n",
    "# and get the statevector\n",
    "job = simulator.run(circ)\n",
    "output_state = job.result().get_statevector(circ)\n",
    "\n",
    "# Qubit reordering\n",
    "simulated_f = supplementary.output_reordering(output_state)[:2**n]\n",
    "\n",
    "# Plottting the simulated statevectors \n",
    "fig=plt.figure(figsize=(8, 7))\n",
    "ax = fig.add_subplot(111)\n",
    "plt.grid()\n",
    "line, = ax.plot(x, target_f, 'blue', lw=7, alpha=0.3,label='Target')\n",
    "line1, = ax.plot(x, np.real(simulated_f), 'red', lw=2,label='FSL Simulation')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('f(x)')\n",
    "plt.legend(loc=2,fontsize=20)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2251e1de",
   "metadata": {},
   "source": [
    "This shows that we can load a non-periodic function on a quantum computer with high fidelity using the FSL method. We also calculate the infidelity, $1 - |\\langle f_{FSL} | f_{target} \\rangle|^2$, between the target state and the simulated state."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "c0ee5869",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.033165022069966e-09\n"
     ]
    }
   ],
   "source": [
    "# Calculate infidelity\n",
    "infidelity = 1 - np.abs(np.dot(np.conjugate(simulated_f),target_f))**2\n",
    "print(infidelity)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0812e89f",
   "metadata": {},
   "source": [
    "## Conclusion\n",
    "\n",
    "In this notebook, we have reviewed how to load a non-periodic function on a quantum state using the FSL method and have provided a worked example. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "d1196a3d",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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