{ "cells": [ { "cell_type": "markdown", "id": "86c26a84", "metadata": {}, "source": [ "# Negative Power Functions" ] }, { "cell_type": "markdown", "id": "a444def8", "metadata": {}, "source": [ "## Overview" ] }, { "cell_type": "markdown", "id": "a4ab914e", "metadata": {}, "source": [ "Now that we have considered the quantum linear system problem (QLSP), it is natural to consider the following generalization: given access to an invertible matrix A and a normalized quantum state $|b\\rangle$, we want to construct a quantum state\n", "$$ |x\\rangle := \\frac{A^{-c} |b\\rangle}{\\| A^{-c} |b\\rangle \\|_2}, $$\n", "where $c$ is an integer larger than 1. The implementation boils down to a scalar function $f(x) = x^{-c}$. Without loss of generality, we assume the matrix is normalized. As before, we want a polynomial with parity approximating $f(x)$ over the interval $D_\\kappa := [-1,-\\kappa] \\cup [-\\kappa,1]$." ] }, { "cell_type": "markdown", "id": "6a5f11c2", "metadata": {}, "source": [ "## Setup" ] }, { "cell_type": "markdown", "id": "653abb7b", "metadata": {}, "source": [ "Just as with QLSP, we will let $\\kappa = 10$ and scale the target function for numerical stability. For $c = 2$, we can use the scaling factor $1/(2\\kappa^c)$, i.e., \n", "$$ f(x)=\\frac{1}{2(\\kappa x)^c}, \\quad \\max_{x \\in D_\\kappa} |f(x)| = \\frac{1}{2}. $$" ] }, { "cell_type": "code", "execution_count": 1, "id": "e94bd673", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "\n", "kappa = 10\n", "targ = lambda x: 1/(x**2)\n", "deg = 150\n", "parity = deg % 2\n", "\n", "opts = {\n", " 'intervals': [1/kappa, 1],\n", " 'objnorm': np.inf,\n", " 'epsil': 0.2,\n", " 'npts': 400,\n", " 'fscale': 1/(2*kappa**2),\n", " 'isplot': True,\n", " 'method': 'cvxpy'\n", "}" ] }, { "cell_type": "markdown", "id": "13369131", "metadata": {}, "source": [ "## Polynomial approximation" ] }, { "cell_type": "markdown", "id": "78e7c015", "metadata": {}, "source": [ "As before, we want to find the best approximation polynomial with degree up to $d$ in terms of the $L_\\infty$ norm. We call `cvx_poly_coef` with the above `opts` to solve the optimization problem and output the Chebyshev coefficients of the best approximation polynomial. Once again, the solver outputs all coefficients while we have to post-select those of odd order due to the parity constraint." ] }, { "cell_type": "code", "execution_count": 2, "id": "ebc2c783", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "norm error = 3.5569099550603056e-05\n", "max of solution = 0.7999999443448723\n" ] }, { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from qsppack.utils import cvx_poly_coef\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": "markdown", "id": "7c58ba99", "metadata": {}, "source": [ "We can again use Newton's method to find the phase factors and verify the solution." ] }, { "cell_type": "code", "execution_count": 3, "id": "387bb391", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "iter err \n", " 1 +1.4304e-01\n", " 2 +1.0329e-02\n", " 3 +8.1428e-05\n", " 4 +5.3832e-09\n", "Stop criteria satisfied.\n", "The residual error is\n", "6.661338147750939e-15\n" ] }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "opts.update({\n", " 'maxiter': 100,\n", " 'criteria': 1e-14,\n", " 'useReal': False,\n", " 'targetPre': True,\n", " 'method': 'Newton'\n", "})\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", "xlist1 = np.linspace(-1,-1/kappa,500)\n", "xlist2 = np.linspace(1/kappa,1,500)\n", "xlist = np.concatenate([xlist1, xlist2])\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. Gilyén, A., Su, Y., Low, G. H., & Wiebe, N. (2019, June). Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics. In *Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing* (pp. 193-204).\n", "\n", "2. Dong, Y., Meng, X., Whaley, K. B., & Lin, L. (2021). Efficient phase-factor evaluation in quantum signal processing. *Physical Review A*, 103(4), 042419." ] } ], "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 }