{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Kaiser Window State" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "The Kaiser window state is defined as\n", "$$ |\\Psi \\rangle := \\frac{1}{\\sqrt{\\sum_x |f(x)|^2}} \\sum_{x=0}^{N-1} f(x) |x\\rangle, $$\n", "where the amplitude is described by the Kaiser window function $f(x) = \\frac{I_0(\\beta \\sqrt{1-x^2})}{I_0(\\beta)}$. Here, $I_0$ is the zeroth modified Bessel function of the first kind. The Kaiser window function can be used in quantum phase estimation to boost the success probability without coherently calculating the median of several phase evaluations.\n", "\n", "Just as the preprint [1] proposed the Gaussian state preparation procedure, the authors also proposed a procedure for preparing Kaiser window states. It leverages the same block encoding as before, i.e. $\\sum_x \\sin(x/N)|x\\rangle \\langle x|$. The problem can then be reduced to finding phase factors generating the following function:\n", "$$ h(z) = f(\\arcsin(z)) \\propto I_0 \\left( \\beta \\sqrt{1-\\arcsin^2(z)} \\right), $$\n", "where $z=\\sin(x)$ transforms the domain to $z \\in [0,\\sin(1)]$." ] }, { "cell_type": "markdown", "id": "6a5f11c2", "metadata": {}, "source": [ "## Setup and approximate target function" ] }, { "cell_type": "code", "execution_count": 1, "id": "de5ced3e", "metadata": {}, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/jameslarsen/miniconda3/envs/qspy/lib/python3.13/site-packages/qsppack/utils.py:282: ComplexWarning: Casting complex values to real discards the imaginary part\n", " fx[ind_union] = opts['fscale'] * func(xpts[ind_union])\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ "norm error = 1.9280569363289146e-09\n", "max of solution = 0.9799999996847971\n" ] }, { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.special import jv\n", "import numpy as np\n", "from qsppack.utils import cvx_poly_coef\n", "\n", "beta = 8\n", "targ = lambda x: jv(0, 1j*beta * np.sqrt(np.complex128(1 - 2*np.arcsin(x)**2))) / jv(0, 1j*beta)\n", "targ = np.vectorize(targ)\n", "deg = 100\n", "parity = deg % 2\n", "\n", "opts = {\n", " 'intervals': [0, np.sin(1)],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.01,\n", " 'npts': 500,\n", " 'fscale': 0.98,\n", " 'isplot': True,\n", " 'method': 'cvxpy',\n", " 'maxiter': 100,\n", " 'criteria': 1e-12,\n", " 'useReal': True,\n", " 'targetPre': True\n", "}\n", "\n", "coef_full = cvx_poly_coef(targ, deg, opts)\n", "coef = coef_full[parity::2]" ] }, { "cell_type": "markdown", "id": "722e4f20", "metadata": {}, "source": [ "## Solving the phase factors and verifying" ] }, { "cell_type": "code", "execution_count": 2, "id": "387bb391", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +1.4970e-01\n", " 2 +3.1540e-02\n", " 3 +4.7445e-03\n", " 4 +2.2484e-04\n", " 5 +6.1825e-07\n", " 6 +4.7276e-12\n", "Stop criteria satisfied.\n", "The residual error is\n", "7.993605777301127e-15\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opts['method'] = 'Newton'\n", "\n", "from qsppack.solver import solve\n", "phi_proc, out = solve(coef, parity, opts)\n", "\n", "from qsppack.utils import chebyshev_to_func, get_entry\n", "import matplotlib.pyplot as plt\n", "\n", "xlist = np.linspace(0, np.sin(1), 500)\n", "func = lambda x: chebyshev_to_func(x, coef, parity, True)\n", "targ_value = targ(xlist)\n", "func_value = func(xlist)\n", "QSP_value = get_entry(xlist, phi_proc, out)\n", "err = np.linalg.norm(QSP_value - func_value, np.inf)\n", "print('The residual error is')\n", "print(err)\n", "\n", "plt.plot(xlist, QSP_value - func_value)\n", "plt.xlabel('$x$', fontsize=12)\n", "plt.ylabel('$g(x,\\\\Phi^*)-f_\\\\mathrm{poly}(x)$', fontsize=12)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "5e9d5b71", "metadata": {}, "source": [ "## Reference\n", "1. McArdle, S., Gilyén, A., & Berta, M. (2022). Quantum state preparation without coherent arithmetic. *arXiv:2210.14892*." ] } ], "metadata": { "kernelspec": { "display_name": "qspy", "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": "3.13.2" } }, "nbformat": 4, "nbformat_minor": 5 }