Example_3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "ceb481a2",
   "metadata": {},
   "source": [
    "# Noiseless simulation of the FSL method for piece-wise continuous functions"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e643e2e6",
   "metadata": {},
   "source": [
    "In this notebook, we review how to load piece-wise continuous functions using the FSL method and perform the simulation of loading a specific piece-wise continuous function.\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": "a21d1846",
   "metadata": {},
   "source": [
    "It is known that large oscillations appear in the truncated Fourier series approximation of piece-wise continuous functions. These oscillations are known as the Gibbs phenomenon. These large oscillations can be suppressed by applying Fourier filters, such as Lanczos filters, that amount to scaling factors applied to the original Fourier coefficients. For example, we can modify the Fourier coefficients as $c_{k} \\to \\big(\\text{sinc}(\\pi k/M)\\big)^{a} c_{k} \\, $, where $a$ is a positive number and $M$ is the order of the truncated Fourier series. A nice feauture of the FSL method is that it can easily incorporate these Fourier filters. In particular, once we find the Fourier coefficients of the target function, we modify them by multiplying them with the filtering function, and then load the filtered Fourier coefficients using the cascade of uniformly controlled rotations."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "11e109d3",
   "metadata": {},
   "source": [
    "## Example\n",
    "\n",
    "We now use the above method to perform the simulation of loading the following piece-wise discontinuous function on a quantum state of $n=20$ qubits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "876831d0",
   "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\n",
    "b0, b1, b2, b3 = 0.25, 0.2, 0.3, -0.05\n",
    "target_f = []\n",
    "for xx in x:\n",
    "    if xx<0.25:\n",
    "        target_f.append(b0*xx+b1)\n",
    "    elif xx < 0.55:\n",
    "        target_f.append(b0*xx+b2)\n",
    "    else:\n",
    "        target_f.append(b0*xx+b3)\n",
    "target_f = target_f/np.linalg.norm(target_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e891328c",
   "metadata": {},
   "source": [
    "Now we approximate the function using a Fourier series with $2^{m+1}$ Fourier terms. The first $2^{m+1}$ Fourier coefficients can be determined using the function `Fourier_state` which is defined in the code file `supplementary.py`. For concreteness, we choose $m=8$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "e0439076",
   "metadata": {},
   "outputs": [],
   "source": [
    "# No. of Fourier modes\n",
    "m = 8\n",
    "# Fourier state |c>\n",
    "state_c = supplementary.Fourier_state(target_f,m)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "224afbfc",
   "metadata": {},
   "source": [
    "Now we transform the Fourier coefficients by multiplying them with the Fourier coefficients as discussed above. In this example, we take $a = 2$ in the Fourier filter. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "c98ad0ab",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Applying Fourier filters [c_k -> (sinc(k/M))^2 * c_k]\n",
    "for k in range(1,2**m):\n",
    "    state_c[k] = ((np.sin(np.pi*k/(2**m))/(np.pi*k/(2**m)))**2)*state_c[k]\n",
    "    state_c[-k] = ((np.sin(np.pi*k/(2**m))/(np.pi*k/(2**m)))**2)*state_c[-k]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e0521f21",
   "metadata": {},
   "source": [
    "The rest of the code to implement the FSL method remains unchanged. That is, we first load the \"filtered\" Fourier coefficients on the last $m+1$ qubits, apply a cascade of CNOTs, and then apply the inverse quantum Fourier transform. \n",
    "\n",
    "Note that we perform the simulation using the Qiskit Aer `statevector_vector` simulator."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "5e3449ea",
   "metadata": {},
   "outputs": [],
   "source": [
    "# simulator\n",
    "simulator = Aer.get_backend('statevector_simulator')\n",
    "\n",
    "# Initialize a quantum circuit\n",
    "circ = QuantumCircuit(n)\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-1,n)\n",
    "circ.compose(U_c,qubits=Uc_qubits,inplace=True)\n",
    "\n",
    "# Apply a cascade of CNOTs\n",
    "for i in range(n-m-1):\n",
    "    circ.cx(n-m-1,i)\n",
    "\n",
    "# Finally, apply the inverse QFT.\n",
    "inv_qft = QFT(num_qubits=n, inverse=True)\n",
    "inv_qft = transpile(inv_qft, simulator)\n",
    "circ.compose(inv_qft,qubits=range(n-1,-1,-1),inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "077e2495",
   "metadata": {},
   "source": [
    "We now run the circuit and plot the simulated statevector. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3a528127",
   "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)\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=3,fontsize=20)\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "81acedd5",
   "metadata": {},
   "source": [
    "Finally, we 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": "10115f17",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.0007348920174424789\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 shown how to load a piece-wise continuous function using the FSL method."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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