diff --git a/exercises/cv_submissions/cv_tutorial_ines.ipynb b/exercises/cv_submissions/cv_tutorial_ines.ipynb new file mode 100644 index 0000000..358aaba --- /dev/null +++ b/exercises/cv_submissions/cv_tutorial_ines.ipynb @@ -0,0 +1,792 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "a2a951ef-f733-40f5-bdc1-c424efd75ba0", + "metadata": { + "tags": [] + }, + "source": [ + "# Continuous Variables\n", + "\n", + "A qubit is a discrete-variable (DV) quantum system with basis states\n", + "\n", + "\\begin{equation}\n", + "|0\\rangle,\\qquad |1\\rangle\n", + "\\end{equation}\n", + "\n", + "A general qubit is\n", + "\n", + "\\begin{equation}\n", + "|\\psi\\rangle\n", + "=\n", + "\\alpha |0\\rangle\n", + "+\n", + "\\beta |1\\rangle\n", + "\\end{equation}\n", + "\n", + "For continuous-variable (CV) systems, instead of encoding information in two basis states, they encode information in observables that take continuous values, such as the quadratures\n", + "\n", + "\\begin{equation}\n", + "\\hat X\n", + "\\quad\\text{and}\\quad\n", + "\\hat P\n", + "\\end{equation}\n", + "\n", + "These satisfy\n", + "\n", + "\\begin{equation}\n", + "[\\hat X,\\hat P]=i\n", + "\\end{equation}\n", + "\n", + "Every optical mode behaves mathematically as a quantum harmonic oscillator, making continuous variables the natural language of quantum optics." + ] + }, + { + "cell_type": "markdown", + "id": "67bcbf9b-af9e-46bc-9d60-07fb78287699", + "metadata": {}, + "source": [ + "# The Quantum Harmonic Oscillator\n", + "\n", + "The Hamiltonian of the quantum harmonic oscillator is\n", + "\n", + "\\begin{equation}\n", + "\\hat H\n", + "=\n", + "\\hbar \\omega (\\hat n + \\frac12)\n", + "\\end{equation}\n", + "\n", + "Its energy eigenstates are called Fock states:\n", + "\n", + "\\begin{equation}\n", + "|0\\rangle,\n", + "|1\\rangle,\n", + "|2\\rangle,\n", + "\\ldots\n", + "\\end{equation}\n", + "\n", + "where\n", + "\n", + "\\begin{equation}\n", + "\\hat H|n\\rangle\n", + "=\n", + "\\hbar\\omega\n", + "\\left(\n", + "n+\\frac12\n", + "\\right)\n", + "|n\\rangle\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "id": "5d906744-b646-421a-9af3-dd740b086c0f", + "metadata": {}, + "source": [ + "Rather than using Pauli matrices, the harmonic oscillator is conveniently described using ladder operators $\\hat a$ and $\\hat a^\\dagger$, which satisfy $[\\hat a,\\hat a^\\dagger]=1$.\n", + "\n", + "Acting on a Fock state,\n", + "\n", + "\\begin{equation}\n", + "\\hat a|n\\rangle\n", + "=\n", + "\\sqrt n\n", + "|n-1\\rangle\n", + "\\end{equation}\n", + "\n", + "and\n", + "\n", + "\\begin{equation}\n", + "\\hat a^\\dagger|n\\rangle\n", + "=\n", + "\\sqrt{n+1}\n", + "|n+1\\rangle\n", + "\\end{equation}\n", + "\n", + "The quadratures are\n", + "\n", + "\\begin{equation}\n", + "\\hat X\n", + "=\n", + "\\frac{\\hat a+\\hat a^\\dagger}{\\sqrt2}\n", + "\\end{equation}\n", + "\n", + "\\begin{equation}\n", + "\\hat P\n", + "=\n", + "\\frac{\\hat a-\\hat a^\\dagger}{i\\sqrt2}\n", + "\\end{equation}" + ] + }, + { + "cell_type": "markdown", + "id": "54317b92-ea54-406b-a900-17020220f11e", + "metadata": { + "tags": [] + }, + "source": [ + "# Position Wavefunctions\n", + "\n", + "Although Fock states are labelled by the discrete integer $ n = 0,1,2,\\ldots$, they actually describe states of a continuous position variable.\n", + "\n", + "The position basis satisfies\n", + "\n", + "$$\n", + "\\hat{x}\\,|x\\rangle = x\\,|x\\rangle\n", + "$$\n", + "\n", + "Every quantum state may therefore be written as\n", + "\n", + "$$\n", + "|\\psi\\rangle\n", + "=\n", + "\\int_{-\\infty}^{\\infty}\n", + "\\psi(x)\\,|x\\rangle\\,dx\n", + "$$\n", + "\n", + "where\n", + "\n", + "$$\n", + "\\psi(x)\n", + "=\n", + "\\langle x|\\psi\\rangle\n", + "$$\n", + "\n", + "is called the wavefunction.\n", + "\n", + "For the quantum harmonic oscillator, the energy eigenstates are\n", + "\n", + "$$\n", + "\\psi_n(x)\n", + "=\n", + "\\frac{\n", + "H_n(x)\\,e^{-x^2/2}\n", + "}{\n", + "\\sqrt{2^n n!\\sqrt{\\pi}}\n", + "},\n", + "$$\n", + "\n", + "where $H_n(x)$ are the Hermite polynomials.\n", + "\n", + "Unlike qubits, whose state space is finite-dimensional, these wavefunctions exist over the continuous position coordinate $x$." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "2ab5d5b3-71c5-4699-979d-43cda34f9bb0", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy.special import eval_hermite, factorial\n", + "\n", + "x = np.linspace(-4,4,500)\n", + "\n", + "plt.figure(figsize=(8,5))\n", + "\n", + "for n in range(5):\n", + "\n", + " psi = (\n", + " eval_hermite(n,x)\n", + " *np.exp(-x**2/2)\n", + " /\n", + " np.sqrt((2**n)*factorial(n)*np.sqrt(np.pi))\n", + " )\n", + "\n", + " plt.plot(x,psi,label=f\"$n={n}$\")\n", + "\n", + "plt.xlabel(r\"$x$\")\n", + "plt.ylabel(r\"$\\psi_n(x)$\")\n", + "plt.title(\"Quantum Harmonic Oscillator Wavefunctions\")\n", + "plt.grid(alpha=0.3)\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "dde9628d-c8ee-4ff2-aaf3-890936a58f9e", + "metadata": {}, + "source": [ + "The probability of measuring the particle near position x is\n", + "\n", + "$$\n", + "P(x)=|\\psi(x)|^2\n", + "$$\n", + "\n", + "Higher-energy states become increasingly oscillatory while remaining normalized, satisfying:\n", + "\n", + "$$\n", + "\\int_{-\\infty}^{\\infty} |\\psi(x)|^2\\,dx = 1\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "193f4b6d-a45a-4b9d-9297-fbd1c762a3c2", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8,5))\n", + "\n", + "for n in range(5):\n", + "\n", + " psi = (\n", + " eval_hermite(n,x)\n", + " *np.exp(-x**2/2)\n", + " /\n", + " np.sqrt((2**n)*factorial(n)*np.sqrt(np.pi))\n", + " )\n", + "\n", + " plt.plot(x,np.abs(psi)**2,label=f\"$|{n}>$\")\n", + "\n", + "plt.title(\"Probability Densities\")\n", + "plt.xlabel(\"$x$\")\n", + "plt.ylabel(r\"$|\\psi(x)|^2$\")\n", + "plt.grid(alpha=.3)\n", + "plt.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "6ba6b22e-d177-4096-89f6-e767444dbe2a", + "metadata": {}, + "source": [ + "# Phase Space\n", + "\n", + "Instead of visualising states in position space, quantum optics usually represents them in phase space.\n", + "\n", + "A point in phase space consists of two continuous variables, $(X,P)$, the quadratures. These are analogous to the classical position and momentum variables.\n", + "\n", + "Classically, a particle can be described by a single point in phase space.\n", + "\n", + " As for quantum mechanics, this is impossible because of the Heisenberg uncertainty relation, $ \\Delta X\\,\\Delta P \\geq \\frac{1}{2}$.\n", + "\n", + "Instead, every quantum state occupies a finite area in phase space." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "43cfa1a2-ad26-4c51-8c74-651f433c1ed8", + "metadata": { + "tags": [] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig=plt.figure(figsize=(6,6))\n", + "\n", + "circle=plt.Circle((0,0),1.0,fill=False,lw=3)\n", + "\n", + "plt.gca().add_patch(circle)\n", + "\n", + "plt.axhline(0,color='black')\n", + "plt.axvline(0,color='black')\n", + "\n", + "plt.xlabel(r\"$X$\")\n", + "plt.ylabel(r\"$P$\")\n", + "\n", + "plt.title(\"A Minimum-Uncertainty State\")\n", + "\n", + "plt.axis(\"equal\")\n", + "plt.grid(alpha=0.2)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "72565e09-b9bf-41fc-abcf-ebb396f43846", + "metadata": {}, + "source": [ + "# The Wigner Function\n", + "\n", + "The Wigner function is a quasi-probability distribution in phase space.\n", + "\n", + "Unlike ordinary probability distributions, it may become negative, revealing non-classical behaviour.\n", + "\n", + "For a density matrix $\\rho$, its Wigner function is $W(x, p)$. The Wigner function contains the same information as the density matrix, so it can completely describe the quantum state.\n", + "\n", + "Gaussian states have Gaussian Wigner functions.\n", + "\n", + "Non-Gaussian states, such as Schrödinger cat states, display oscillations and negative regions in their Wigner functions, which belong to quantum behaviour." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "88e5a243", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from qutip import *\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "N=30\n", + "\n", + "vacuum=basis(N,0)\n", + "\n", + "x=np.linspace(-5,5,200)\n", + "\n", + "W=wigner(vacuum,x,x)\n", + "\n", + "plt.figure(figsize=(6,5))\n", + "\n", + "plt.contourf(x,x,W,100,cmap=\"RdBu_r\")\n", + "\n", + "plt.xlabel(r\"$X$\")\n", + "plt.ylabel(r\"$P$\")\n", + "plt.colorbar()\n", + "\n", + "plt.title(\"Vacuum Wigner Function\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "cb2dd0c7", + "metadata": {}, + "source": [ + "# Coherent States\n", + "\n", + "The coherent state are often used to describe classical-like electromagnetic fields. For example, an ideal laser field is well approximated by a coherent state. However, it is still a quantum state. Even though it behaves in many ways like a classical field, it still contains unavoidable quantum fluctuations.\n", + "\n", + "These fluctuations correspond to the finite width of its Wigner function.\n", + "\n", + "A coherent state is denoted by $|\\alpha\\rangle$, where $\\alpha$ is a complex number, $\\alpha = |\\alpha|e^{i\\phi}$.\n", + "\n", + "The magnitude $|\\alpha|$ determines the amplitude of the field, while the phase $\\phi$ determines its position around the origin in phase space.\n", + "\n", + "A coherent state can also be written as a superposition of Fock states:\n", + "$$\n", + "|\\alpha\\rangle =e^{-|\\alpha|^2/2}\\sum_{n=0}^{\\infty} \\frac{\\alpha^n}{\\sqrt{n!}}|n\\rangle\n", + "$$\n", + "\n", + "This equation shows that a coherent state is not a state with a definite photon number. Instead, it is a superposition containing $|0\\rangle,\\ |1\\rangle,\\ |2\\rangle,\\ldots$ with different probabilities.\n", + "\n", + "Increasing $|\\alpha|$ increases the coherent state average photon number and moves the coherent state farther from the origin in phase space." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "f41d648f", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "alpha=2\n", + "\n", + "coh=coherent(30,alpha)\n", + "\n", + "W=wigner(coh,x,x)\n", + "\n", + "plt.figure(figsize=(6,5))\n", + "\n", + "plt.contourf(x,x,W,100,cmap=\"RdBu_r\")\n", + "\n", + "plt.xlabel(\"$X$\")\n", + "plt.ylabel(\"$P$\")\n", + "\n", + "plt.title(r\"Coherent State ($\\alpha=2$)\")\n", + "\n", + "plt.colorbar()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "9ef626bd", + "metadata": {}, + "source": [ + "# Squeezed States\n", + "\n", + "The vacuum state has equal uncertainty in both quadratures,\n", + "\n", + "$$\n", + "\\Delta X = \\Delta P = \\frac{1}{\\sqrt{2}}\n", + "$$\n", + "\n", + "The Heisenberg uncertainty principle requires that\n", + "\n", + "$$\n", + "\\Delta X \\Delta P \\geq \\frac{1}{2}\n", + "$$\n", + "\n", + "A squeezed state redistributes this uncertainty. One quadrature becomes more precisely known while the uncertainty in the conjugate quadrature increases. \n", + "\n", + "Unlike coherent states, squeezed states have no classical comparison and are considered genuinely quantum." + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "203c154b", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from qutip import squeeze, basis, wigner\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "N = 30\n", + "\n", + "r = 0.8\n", + "\n", + "vacuum = basis(N, 0)\n", + "\n", + "psi = squeeze(N, r) * vacuum\n", + "\n", + "x = np.linspace(-5, 5, 200)\n", + "\n", + "W = wigner(psi, x, x)\n", + "\n", + "fig, ax = plt.subplots(figsize=(6,5))\n", + "\n", + "contour = ax.contourf(\n", + " x,\n", + " x,\n", + " W,\n", + " levels=100,\n", + " cmap=\"RdBu_r\"\n", + ")\n", + "\n", + "ax.set_xlabel(r\"$X$\")\n", + "ax.set_ylabel(r\"$P$\")\n", + "ax.set_title(\"Squeezed Vacuum State\")\n", + "\n", + "fig.colorbar(contour)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "4a423f7a", + "metadata": {}, + "source": [ + "Compared to the vacuum and coherent states, the Wigner function has become elliptical.\n", + "\n", + "The state has reduced uncertainty in one quadrature and increased uncertainty in the other while maintaining the minimum uncertainty product required by quantum mechanics." + ] + }, + { + "cell_type": "markdown", + "id": "e9a0e6e0", + "metadata": {}, + "source": [ + "# Gaussian Operations\n", + "\n", + "A Gaussian operation is any transformation that maps a Gaussian state to another Gaussian state. In other words, if the Wigner function of a state is initially Gaussian, it remains Gaussian after the transformation. These operations are implemented experimentally using optical components such as mirrors, beam splitters or phase shifters.\n", + "\n", + "Mathematically, Gaussian operations correspond to symple transformations in phase space. Rather than changing the Hilbert space itself, they transform the quadrature operators $\\hat{X}$ and $\\hat{P}$.\n", + "\n", + "The most important Gaussian operations are:\n", + "\n", + "## Displacement\n", + "\n", + "The displacement operator translates a quantum state through phase space without changing its shape.\n", + "\n", + "It is defined as\n", + "\n", + "$$\n", + "\\hat{D}(\\alpha)\n", + "=\n", + "\\exp\\!\\left(\n", + "\\alpha \\hat{a}^{\\dagger}\n", + "-\n", + "\\alpha^{*}\\hat{a}\n", + "\\right)\n", + "$$\n", + "\n", + "where $\\alpha$ is a complex number describing the displacement as previously described.\n", + "\n", + "Applying the displacement operator to the vacuum state produces a coherent state,\n", + "\n", + "$$\n", + "|\\alpha\\rangle\n", + "=\n", + "\\hat{D}(\\alpha)|0\\rangle\n", + "$$\n", + "\n", + "In phase space, the Gaussian Wigner function simply moves away from the origin while maintaining its circular shape. \n", + "\n", + "## Rotation (Phase Shift)\n", + "\n", + "A phase shift rotates the state within phase space.\n", + "\n", + "The corresponding operator is\n", + "\n", + "$$\n", + "\\hat{R}(\\theta)\n", + "=\n", + "e^{-i\\theta\\hat{a}^{\\dagger}\\hat{a}}\n", + "$$\n", + "\n", + "where $\\theta$ is the rotation angle.\n", + "\n", + "The quadrature operators transform according to\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "X' &= X\\cos\\theta - P\\sin\\theta,\\\\\n", + "P' &= X\\sin\\theta + P\\cos\\theta\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "For coherent states this simply changes the optical phase while preserving the state's uncertainty.\n", + "\n", + "For squeezed states, the squeezing ellipse rotates without changing its size.\n", + "\n", + "\n", + "## Squeezing\n", + "\n", + "Squeezing redistributes quantum uncertainty between the two quadratures.\n", + "\n", + "The squeezing operator is\n", + "\n", + "$$\n", + "\\hat{S}(r)\n", + "=\n", + "\\exp\\!\\left[\n", + "\\frac{r}{2}\n", + "\\left(\n", + "\\hat{a}^{2}\n", + "-\n", + "\\hat{a}^{\\dagger 2}\n", + "\\right)\n", + "\\right]\n", + "$$\n", + "\n", + "where $r$ is the squeezing parameter.\n", + "\n", + "After squeezing,\n", + "\n", + "$$\n", + "\\Delta X\n", + "<\n", + "\\frac{1}{\\sqrt{2}}\n", + "$$\n", + "\n", + "while\n", + "\n", + "$$\n", + "\\Delta P\n", + ">\n", + "\\frac{1}{\\sqrt{2}}\n", + "$$\n", + "\n", + "The uncertainty product remains constrained by the Heisenberg uncertainty relation,\n", + "\n", + "$$\n", + "\\Delta X\\,\\Delta P\n", + "\\ge\n", + "\\frac{1}{2}\n", + "$$\n", + "\n", + "# Hilbert Space Cut Off\n", + "\n", + "Unlike qubits, the harmonic oscillator possesses an infinite-dimensional Hilbert space.\n", + "\n", + "The Fock basis is therefore\n", + "\n", + "$$\n", + "|0\\rangle,\n", + "|1\\rangle,\n", + "|2\\rangle,\n", + "\\ldots\n", + "$$\n", + "\n", + "and continues indefinitely.\n", + "\n", + "Since computers cannot represent infinitely many basis states, numerical simulations must truncate the Hilbert space at some maximum photon number,\n", + "\n", + "$$\n", + "N_{\\mathrm{cutoff}}\n", + "$$\n", + "\n", + "The approximation becomes\n", + "\n", + "$$\n", + "|0\\rangle,\n", + "|1\\rangle,\n", + "\\ldots,\n", + "|N_{\\mathrm{cutoff}}-1\\rangle\n", + "$$\n", + "\n", + "For states with only a few photons, this approximation works extremely well.\n", + "\n", + "However, coherent and squeezed states possess probability amplitudes across infinitely many Fock states.\n", + "\n", + "If the cutoff is chosen too small, the simulated state no longer accurately represents the true physical state." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "5f819f0e", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, axes = plt.subplots(\n", + " 3,\n", + " 1,\n", + " figsize=(8, 9),\n", + " sharex=True\n", + ")\n", + "\n", + "states = [\n", + " basis(N, 4),\n", + " coherent(N, 2),\n", + " squeeze(N, 1) * basis(N, 0)\n", + "]\n", + "\n", + "titles = [\n", + " \"Fock |4⟩\",\n", + " \"Coherent |α=2⟩\",\n", + " \"Squeezed Vacuum r = 1\"\n", + "]\n", + "\n", + "for ax, state, title in zip(axes, states, titles):\n", + "\n", + " P = np.abs(state.full().flatten())**2\n", + "\n", + " ax.bar(np.arange(N), P)\n", + "\n", + " ax.set_title(title)\n", + "\n", + "fig.suptitle(\"Photon Number Distributions\", fontsize=16)\n", + "fig.supylabel(\"Probability\", fontsize=12)\n", + "\n", + "axes[-1].set_xticks(np.arange(0, 21, 1))\n", + "axes[-1].set_xlim(-0.5, 20.5)\n", + "axes[-1].set_xlabel(\"Photon number\")\n", + "\n", + "plt.tight_layout()\n", + "\n", + "# Leave space for the main title\n", + "plt.subplots_adjust(top=0.93)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "d81ba979", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "msc-sciqis (3.13.14.final.0)", + "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": "3.13.14" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}