{ "cells": [ { "cell_type": "markdown", "id": "0f660102", "metadata": {}, "source": [ "# Find QSP and GQSP phases\n", "\n", "**Download Notebook** - {nb-download}`qsp_angle_finder.ipynb`\n", "\n", "Phase synthesis translates a target function into the classical parameters of a quantum signal-processing sequence. This notebook follows two routes: a Chebyshev approximation for QSP, and a Fourier approximation for generalized QSP (GQSP)." ] }, { "cell_type": "code", "execution_count": 1, "id": "49556fc8", "metadata": { "tags": [ "hide-input" ] }, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "from guppyalgos.utils import ChebyshevPolynomial, QSPAngleFinder\n", "from guppyalgos.utils import FourierPolynomial, GQSPAngleFinder" ] }, { "cell_type": "markdown", "id": "f3a13a73", "metadata": {}, "source": [ "## 1. QSP for an exponential filter\n", "\n", "On $x\\in[0,1]$, use the Gibbs-like filter $e^{-\\beta x}$. QSP requires a definite parity, so extend it evenly:\n", "\n", "$$\n", "f(x)=e^{-\\beta|x|},\\qquad f(-x)=f(x).\n", "$$\n", "\n", "This is a filter function, rather than a normalized probability distribution. The helper below can construct even or odd extensions; this example uses the even one." ] }, { "cell_type": "code", "execution_count": 2, "id": "16b955ea", "metadata": {}, "outputs": [], "source": [ "# Target functions \n", "\n", "def _gibbs_fun(x, beta):\n", " return np.exp(-beta * x)\n", "\n", "\n", "def generate_gibbs_fun(beta):\n", " def fun(x):\n", " return _gibbs_fun(x, beta)\n", "\n", " return fun\n", "\n", "\n", "def symmetrize_fun(fun, parity=0):\n", " if parity == 0:\n", "\n", " def neg_fun(x):\n", " return fun(-x)\n", "\n", " def pos_fun(x):\n", " return fun(x)\n", "\n", " if parity == 1:\n", "\n", " def neg_fun(x):\n", " return -fun(-x)\n", "\n", " def pos_fun(x):\n", " return fun(x)\n", "\n", " def sfun(x):\n", " if x < 0:\n", " return neg_fun(x)\n", " if x >= 0:\n", " return pos_fun(x)\n", "\n", " return np.vectorize(sfun)" ] }, { "cell_type": "code", "execution_count": 3, "id": "d1d88573", "metadata": {}, "outputs": [], "source": [ "beta = 2.5\n", "\n", "gibbs_fun = generate_gibbs_fun(beta)\n", "sym_gibbs_fun = symmetrize_fun(gibbs_fun, 0)\n", "antisym_gibbs_fun = symmetrize_fun(gibbs_fun, 1)" ] }, { "cell_type": "markdown", "id": "b55551a6", "metadata": {}, "source": [ "### Approximate the function\n", "\n", "`ChebyshevPolynomial` fits the even extension with a degree-16 polynomial:\n", "\n", "$$\n", "p_d(x)=\\sum_{k=0}^{d}c_kT_k(x),\\qquad d=16.\n", "$$\n", "\n", "The `.error` value reports the approximation error. Increasing the degree can improve the fit, at the cost of a longer quantum sequence." ] }, { "cell_type": "code", "execution_count": 4, "id": "d3cb1e6c", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(0.08752003120788343)" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d_phi = 16\n", "d_cheb = d_phi\n", "\n", "sym_gibbs_cheb = ChebyshevPolynomial(sym_gibbs_fun, d_cheb)\n", "sym_gibbs_cheb.error" ] }, { "cell_type": "markdown", "id": "d017829a", "metadata": {}, "source": [ "### Optimize the phases\n", "\n", "`QSPAngleFinder` chooses phase factors so that the QSP response approximates $p_d(x)$. Its `.opt_error` measures phase-synthesis error, separately from the polynomial approximation error. The plot compares the fitted polynomial with the synthesized response." ] }, { "cell_type": "code", "execution_count": 5, "id": "61835733", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "np.float64(1.143961726692128e-09)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "qsp_optimizer = QSPAngleFinder(d_phi=d_phi, target_polynomial=sym_gibbs_cheb)\n", "qsp_optimizer.opt_error" ] }, { "cell_type": "code", "execution_count": 6, "id": "2dfd8f97", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7, 3.5))\n", "x_vals=np.linspace(0, 1, 100)\n", "f_vals = qsp_optimizer(x=x_vals)\n", "plt.plot(x_vals, qsp_optimizer.target_polynomial(x_vals), label=\"Chebyshev approximation\")\n", "plt.plot(x_vals, f_vals, linestyle=\"dotted\", label=\"QSP curve\")\n", "for x_j in qsp_optimizer.x_Chebyshev_roots:\n", " plt.plot(\n", " [x_j],\n", " [qsp_optimizer.target_polynomial(x_j)],\n", " color=\"C3\",\n", " marker=\"X\",\n", " markersize=5,\n", " )\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"Filter response\")\n", "plt.grid(alpha=0.25)\n", "plt.tight_layout()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "93e257c9", "metadata": {}, "source": [ "## 2. GQSP from a Fourier series\n", "\n", "GQSP represents a function of a unitary using a Laurent polynomial:\n", "\n", "$$\n", "F(z)=\\sum_{k=-20}^{20}c_kz^k,\\qquad z=e^{i\\pi x}.\n", "$$\n", "\n", "For the periodic extension of $e^{-\\tau\\pi|x|}$ on $[-1,1]$, use\n", "\n", "$$\n", "c_k=\\frac{\\tau\\bigl(1-(-1)^k e^{-\\pi\\tau}\\bigr)}{\\pi(\\tau^2+k^2)}.\n", "$$\n", "\n", "`FourierPolynomial` stores these coefficients. The first plot shows the truncated series and its target." ] }, { "cell_type": "code", "execution_count": 7, "id": "80fd6019", "metadata": {}, "outputs": [], "source": [ "tau = 1.2\n", "degree = 40\n", "\n", "d_max = degree // 2\n", "d_min = - degree // 2\n", "\n", "f_coeffs = {\n", " k : (tau*(1+((-1)**(k+1))*np.exp(-np.pi*tau)))/(np.pi*(tau**2 + k**2))\n", " for k in range(d_min, d_max+1)\n", "}\n", "\n", "f = FourierPolynomial(f_coeffs, d_max, d_min)" ] }, { "cell_type": "code", "execution_count": 8, "id": "11f873d5", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7, 3.5))\n", "xax = np.linspace(-1, 1, 200)\n", "plt.plot(xax, f(xax).real, label=rf'Re$[f_{{{degree}}}(x)]$', color='C0')\n", "plt.plot(xax, f(xax).imag, label=rf'Im$[f_{{{degree}}}(x)]$', color='C1')\n", "plt.plot(xax, np.exp(-tau*np.pi*np.abs(xax)), label=rf'$e^{{-{float(tau):.3} \\pi |x|}}$', color='C2')\n", "plt.legend()\n", "plt.xlim(-1, 1)\n", "plt.ylim(-0.05,1.05)\n", "plt.xlabel(r'$x$')\n", "plt.tight_layout()" ] }, { "cell_type": "markdown", "id": "4677a889", "metadata": {}, "source": [ "### Construct the complementary polynomial\n", "\n", "`GQSPAngleFinder` constructs a second polynomial $Q$ so that, on the unit circle,\n", "\n", "$$\n", "|F(z)|^2+|Q(z)|^2=1.\n", "$$\n", "\n", "This is the normalization needed to embed the polynomial in a unitary. The construction requires a bounded target; finite-precision arithmetic can leave a small numerical residual." ] }, { "cell_type": "code", "execution_count": 9, "id": "cfcd348a", "metadata": {}, "outputs": [], "source": [ "angle_finder = GQSPAngleFinder(f)" ] }, { "cell_type": "code", "execution_count": 10, "id": "ebb4c8c2", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(7, 3.5))\n", "# Let us plot the complementary function h(x)\n", "\n", "q = angle_finder.complementary_polynomial\n", "plt.plot(xax, q(xax).real, label=r'Re$[ Q(x) ]$', color='C3')\n", "plt.plot(xax, q(xax).imag, label=r'Im$[ Q(x) ]$', color='C4')\n", "plt.xlim(-1,1)\n", "plt.xlabel(r'x')\n", "plt.grid()\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 11, "id": "1683aa7e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Maximum normalization residual on the grid: 1.63e-13\n" ] } ], "source": [ "residual = np.max(np.abs(np.abs(f(xax))**2 + np.abs(q(xax))**2 - 1))\n", "print(f\"Maximum normalization residual on the grid: {residual:.2e}\")" ] }, { "cell_type": "markdown", "id": "56bb3ac7", "metadata": {}, "source": [ "### Retrieve the phase factors\n", "\n", "`.phase_factors` contains the parameters for the GQSP sequence. The preceding residual checks the complementary-polynomial condition; it is not a measure of the original Fourier approximation error." ] }, { "cell_type": "code", "execution_count": 12, "id": "fd2ee229", "metadata": {}, "outputs": [], "source": [ "phase_factors = angle_finder.phase_factors" ] } ], "metadata": { "kernelspec": { "display_name": "guppy-algorithms (3.13.2)", "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": "3.12.13" } }, "nbformat": 4, "nbformat_minor": 5 }