{ "cells": [ { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Programmation Quantique\n", "\n", "### Nicolas Ollinger et Ioan Todinca\n", "\n", "\n", "#### M2 info, S9 2025/2026" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Enseignement hybride multi-lingue\n", "\n", "Cette année nous expérimentons une version de ce cours pour un public international.\n", " - les étudiants du **M2 ARIAS** de l'Université d'Orléans ;\n", " - des étudiants **GPEX** du programme Minerve de l'Université d'Orléans ;\n", " - des étudiants des universités partenaires du programme **Athena** avec évaluation ;\n", " - des étudiants auditeurs libres des universités partenaires du programme **Athena**.\n", " \n", " Les cours (CM) sont proposés à tous ces publics en hybride sur une même séance. Le cours se déroule en anglais avec une retransmission sur **Teams**.\n", " Le support de cours est disponible :\n", " - en **anglais** sur le canal Teams du cours ;\n", " - en **français** sur la page Celene du cours." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Descriptif du cours\n", "\n", "Ce cours propose de découvrir l'informatique quantique à\n", "travers la programmation de circuits quantiques. \n", "\n", "Les étudiants sont\n", "invités à construire des circuits et à simuler leur exécution pour\n", "comprendre ce que propose la technologie quantique actuelle et comment\n", "elle se distingue des modèles classiques de calcul booléen. Cette\n", "approche expérimentale permettra ensuite de présenter plus précisemment\n", "les promesses algorithmiques et les enjeux actuels de cette technologie.\n", "\n", "L'évaluation prend la forme d'un contrôle terminal et d'éléments à réaliser sur machine et à\n", "rendre à l'issu des TPs." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Plan de bataille\n", "\n", "$$\n", "\\begin{align*}\n", "\\textbf{ARIAS}\\quad 10\\mathrm{h~} &\\textbf{CM} + 10\\mathrm{h~} \\textbf{TD} + 10\\mathrm{h~} \\textbf{TP}\\\\\n", "\\textbf{GPEX}\\quad 10\\mathrm{h~} &\\textbf{CM} + \\phantom{1}6\\mathrm{h~} \\textbf{TD} + \\mbox{TP en autonomie}\\\\\n", "\\textbf{Athena}\\quad 10\\mathrm{h~} &\\textbf{CM} + \\mbox{documents traduits et sessions en ligne}\n", "\\end{align*}\n", "$$\n", "\n", "| Séance | Intervenant | Durée | Programme |\n", "| :-- | :-- | :-: | :-- |\n", "| CM1 | N. Ollinger | __2h__ | *Circuits quantiques et calcul réversible* |\n", "| CM2 | N. Ollinger | __2h__ | *Circuits et calcul quantique, l'algorithme de Bernstein-Vazirani* |\n", "| CM3 | I. Todinca | __2h__ | *Informatique quantique, algorithmes importants* |\n", "| CM4 | I. Todinca | __2h__ | *L'algorithme de recherche quantique de Grover* |\n", "| CM5 | I. Todinca | __2h__ | *Informatique quantique pour informaticien !* |" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Évaluation UO\n", "\n", "$$\n", "\\textbf{UE} = \\frac13 \\textbf{CC} + \\frac23 \\textbf{CT}\n", "$$\n", "\n", "$\\textbf{CC}$ : Des notebook Jupyter à compléter et à rendre sur [Celene](https://celene.univ-orleans.fr/course/view.php?id=12816).\n", "\n", "Exercices à réaliser à l'aide de Python et de la bibliothèque [Qiskit](https://qiskit.org) (v1.2)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "## Circuits quantiques ?\n", "\n", "Les ordinateurs quantiques d'aujourd'hui (ou plutôt de demain ?) s'utilisent comme des _coprocesseurs_ : on y fait subir une transformation unitaire à un registre de qubits initialement tous à zéro avant d'effectuer des mesures sur son état.\n", "\n", "Les transformations unitaires sont codées sous forme de circuits et la programmation quantique ressemble à de la programmation assembleur.\n", "\n", "La programmation quantique propose une nouvelle forme de parallélisme." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Illustré avec Qiskit\n", "\n", "Ce cours est aussi un notebook jupyter téléchargeable et exécutable dans le Cloud dont les exemples sont construits à l'aide de la bibliothèque __[Qiskit](https://qiskit.org)__ qui permet de manipuler des circuits quantiques en Python :\n", " 1. construire des circuits ;\n", " 2. exécuter ces circuits localement dans un simulateur ;\n", " 3. exécuter ces circuits sur des processeurs quantique (par exemple d'IBM) ;\n", " 4. analyser les résultats des exécutions." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "\n", "### Importons le nécessaire" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "from qiskit import QuantumCircuit, transpile\n", "from qiskit.providers.basic_provider import BasicProvider\n", "from qiskit_aer import UnitarySimulator\n", "from qiskit.visualization import plot_histogram\n", "import qiskit.quantum_info as qi\n", "from math import sqrt\n", "import numpy as np\n", "\n", "# Un simulateur de circuit complet\n", "sim = BasicProvider().get_backend('basic_simulator')\n", "\n", "# Un simulateur calculant la matrice de transformation\n", "usim = UnitarySimulator()\n", "\n", "# Afficher un circuit\n", "def draw_circ(circ): display(circ.draw(output='mpl'))\n", " \n", "# Calculer la matrice d'un circuit\n", "def mat_circ(circ): return usim.run(circ).result().get_unitary()\n", "\n", "def show(circ):\n", " draw_circ(circ)\n", " display(mat_circ(circ).draw('latex'))" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "fragment" } }, "source": [ "Mais au fait... C'est quoi un circuit quantique ?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "slide" } }, "source": [ "# Un zeste de théorie..." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Circuits booléens classiques\n", "\n", "Depuis les travaux de Shannon à la fin des années 30, l'algèbre booléenne et le système binaire fondent l'électronique numérique.\n", "\n", "Un registre de mémoire classique stocke un vecteur de bits qui prennent chacun une valeur parmi deux : $0$ ou $1$. Les bits sont indépendants, $n$ bits stockent un valeur parmi $2^n$.\n", "\n", "Des portes logiques réalisant des fonctions logiques ($\\operatorname{ET}$, $\\operatorname{OU}$, $\\operatorname{NON}$) permettent de calculer efficacement toute fonction booléenne $f : \\left\\{0,1\\right\\}^n \\longrightarrow \\left\\{0,1\\right\\}^m$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Un qubit\n", "\n", "Un registre de mémoire quantique est un système quantique discret fini constitué de qubits.\n", "\n", "Un bit quantique est une superposition de $0$ et de $1$ :\n", "$$\n", "\\alpha \\left|0\\right> + \\beta \\left|1\\right> \\quad\\mbox{avec}\\quad \\alpha, \\beta \\in \\mathbb{C}\n", "\\quad\\mbox{tels que}\\quad |\\alpha|^2+|\\beta|^2 = 1\n", "$$\n", "\n", "Par exemple $\\left|0\\right>$ ou encore $\\frac{1}{\\sqrt{2}}\\left(\\left|0\\right>+\\left|1\\right>\\right)$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Des qubits\n", "\n", "Un registre de $n$ qubits est une superposition de chacun des vecteurs de bits possibles, chacun muni d'une amplitude.\n", "\n", "$$\n", "\\left|\\varphi\\right> = \\sum_{x\\in\\{0,1\\}^n} \\alpha_x\\left|x\\right> \\quad\\mbox{tels que}\\quad \\sum_{x\\in\\{0,1\\}^n} |\\alpha_x|^2 = 1\n", "$$\n", "\n", "Par exemple $\\frac12\\left|1000\\right>+\\frac12\\left|0100\\right>+\\frac12\\left|0010\\right>+\\frac12\\left|0001\\right>$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "### Produit tensoriel\n", "\n", "La composition de deux registres quantiques s'obtient par l'opérateur bilinéaire de produit tensoriel $\\otimes$ qui satisfait $\\left|x\\right> \\otimes \\left|y\\right> = \\left|xy\\right>$.\n", "\n", "$$\n", "\\left|1\\right> \\otimes \\frac{1}{\\sqrt{2}}\\left(\\left|0\\right>+\\left|1\\right>\\right) =\n", "\\frac{1}{\\sqrt{2}}\\left(\\left|10\\right>+\\left|11\\right>\\right)\n", "$$\n", "\n", "Contrairement au cas classique, tout registre n'est pas décomposable en sous-registres ! \n", "\n", "Exemple d'état intriqué : $\\frac{1}{\\sqrt{2}}\\left(\\left|00\\right>+\\left|11\\right>\\right)$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Mesure quantique (observation)\n", "\n", "" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Mesure quantique d'un qubit particulier\n", "\n", "Partant d'un état $\\left|\\varphi\\right> = \\sum_x \\alpha_x\\left|x\\right>$, si on mesure le qubit numéro $i$, on observe la valeur $r$ avec la probabilité $p_r$ et le système change d'état :\n", "\n", "$$\n", "\\sum_{x\\in\\left\\{0,1\\right\\}^n} \\alpha_x\\left|x\\right> \\underset{\\phantom{blop}p_r\\phantom{blop}}{\\longrightarrow}\n", "\\frac{1}{\\sqrt{p_r}} \\sum_{x\\in\\left\\{0,1\\right\\}^n | x_i = r} \\alpha_x\\left|x\\right>\n", "$$\n", " \n", "$$\n", "\\mbox{avec}\\quad p_r = \\sum_{x\\in\\left\\{0,1\\right\\}^n | x_i = r}|\\alpha_x|^2\n", "$$" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Évolution unitaire\n", "\n", "En l'absence de mesure, lorsqu'il est isolé, l'état d'un système quantique évolue de manière unitaire.\n", "\n", "$$\n", "U : \\mathbb{C}^{\\{0,1\\}^n} \\rightarrow \\mathbb{C}^{\\{0,1\\}^n}\n", "$$\n", "\n", "1. $U$ est linéaire : $$\n", "U\\left(\\alpha\\left|\\varphi\\right>+\\beta\\left|\\psi\\right>\\right) = \\alpha U\\left|\\varphi\\right>+\\beta U\\left|\\psi\\right>\\quad;\n", "$$\n", "2. $U$ préserve la norme : $\\left\\| U\\left|\\varphi\\right> \\right\\| = \\left\\| \\left|\\varphi\\right> \\right\\|$." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Porte quantique\n", "\n", "Un circuit quantique code une transformation unitaire obtenue par composition de portes quantiques elles aussi unitaires, donc réversibles, avec autant de qubits en entrée qu'en sortie.\n", "- composition séquentielle : produit de matrices ;\n", "- composition parallèle : produit tensoriel.\n", "\n", "Quelle famille de portes universelles ?" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Portes sur 1 qubit\n", "\n", "$$\n", "\\begin{array}{clclcl}\n", "X :& \\left|0\\right> \\mapsto \\left|1\\right> & H :& \\left|0\\right> \\mapsto \\frac{\\left|0\\right>+\\left|1\\right>}{\\sqrt2} & R_\\theta :& \\left|0\\right> \\mapsto \\left|0\\right>\\\\\n", " & \\left|1\\right> \\mapsto \\left|0\\right> & & \\left|1\\right> \\mapsto \\frac{\\left|0\\right>-\\left|1\\right>}{\\sqrt2} & & \\left|1\\right> \\mapsto e^{i\\theta}\\left|1\\right> \\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\n", "\\begin{bmatrix}\n", "\\frac{1}{2} + \\frac{i}{2} & \\frac{1}{2} - \\frac{i}{2} \\\\\n", " \\frac{1}{2} - \\frac{i}{2} & \\frac{1}{2} + \\frac{i}{2} \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from math import pi\n", "circuit = QuantumCircuit(1)\n", "# remplacer ici le x par h ou t (=r(pi/4)) ou sx (sqrt(x))\n", "circuit.sx(0)\n", "show(circuit)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Portes contrôlées\n", "\n", "$$\n", "\\begin{array}{cl}\n", "CX :& \\left|00\\right> \\mapsto \\left|00\\right> \\\\\n", " & \\left|01\\right> \\mapsto \\left|01\\right> \\\\\n", " & \\left|10\\right> \\mapsto \\left|11\\right> \\\\\n", " & \\left|11\\right> \\mapsto \\left|10\\right> \\\\\n", "\\end{array}\n", "$$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 1 & 0 \\\\\n", " 0 & 1 & 0 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circuit = QuantumCircuit(2)\n", "circuit.cx(0,1)\n", "show(circuit)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": { "image/png": { "height": 229, "width": 169 } }, "output_type": "display_data" }, { "data": { "text/latex": [ "$$\n", "\n", "\\begin{bmatrix}\n", "1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", " 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 \\\\\n", " 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 \\\\\n", " 0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 \\\\\n", " 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 \\\\\n", " \\end{bmatrix}\n", "$$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circuit = QuantumCircuit(3) \n", "circuit.ccx(0,1,2)\n", "show(circuit)" ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Universalité\n", "\n", "La famille de portes $\\left\\{H, CX, R_\\theta\\right\\}_{\\theta\\in[0,2\\pi[}$ est universelle pour les transformations unitaires.\n", "\n", "La famille de portes $\\left\\{H, CX, R_{\\frac{\\Pi}4}\\right\\}$ est approximativement universelle pour les transformations unitaires : elle les réalise avec une erreur $\\varepsilon$ souhaitée.\n", "\n", "Le théorème de Solovay-Kitaev nous assure que toutes les familles de portes approximativement universelles le sont efficacement." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Compatibilité\n", "\n", "Toute fonction classique $f : \\{0,1\\}^n \\rightarrow \\{0,1\\}^m$ est simulée par un circuit quantique de taille similaire.\n", "\n", "$$\n", "\\begin{array}{ccccc}\n", "U_f &:& \\mathbb{C}^{\\{0,1\\}^{m+n}} & \\rightarrow & \\mathbb{C}^{\\{0,1\\}^{m+n}}\\\\\n", " & & \\left|x,y\\right> & \\mapsto & \\left|x, f(x)\\oplus y \\right>\n", "\\end{array}\n", "$$\n", "\n", "C'est un résultat de calcul réversible." ] }, { "cell_type": "markdown", "metadata": { "slideshow": { "slide_type": "subslide" } }, "source": [ "## Algorithme quantique\n", "\n", "La plupart des algorithmes quantiques fonctionnent sur le principe suivant :\n", "1. créer une superposition pertinente de qubits à partir de $\\left|00\\cdots 0\\right>$ ;\n", "2. effectuer en parallèle un calcul classique sur la superposition des entrées ;\n", "3. effectuer une transformation quantique pertinente ;\n", "4. observer le résultat grâce à des mesures." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "circ = QuantumCircuit(3,3)\n", "for i in range(2): circ.h(i)\n", "circ.barrier()\n", "circ.cx(0,2)\n", "circ.t(1)\n", "circ.ccx(1,2,0)\n", "circ.barrier()\n", "for i in range(3): circ.measure(i,i)\n", "draw_circ(circ)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "res = sim.run(circ, shots=1024).result()\n", "display(plot_histogram(res.get_counts()))" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "slideshow": { "slide_type": "subslide" } }, "outputs": [ { "data": { "image/png": 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