diff --git a/exercises/cv_submissions/cv_tutorial_feiyang_chen.ipynb b/exercises/cv_submissions/cv_tutorial_feiyang_chen.ipynb new file mode 100644 index 0000000..741c815 --- /dev/null +++ b/exercises/cv_submissions/cv_tutorial_feiyang_chen.ipynb @@ -0,0 +1,398 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "title-intro", + "metadata": {}, + "source": [ + "# A short introduction to continuous-variable states\n", + "\n", + "**Feiyang Chen**\n", + "\n", + "In a qubit system the basis has two states, $|0\\rangle$ and $|1\\rangle$. A harmonic oscillator instead has the infinite basis $|0\\rangle, |1\\rangle, |2\\rangle, \\ldots$. This notebook uses a finite cutoff and QuTiP to look at four simple states: the vacuum state, a one-photon state, a coherent state, and a squeezed vacuum state." + ] + }, + { + "cell_type": "markdown", + "id": "quadratures", + "metadata": {}, + "source": [ + "## Quadratures\n", + "\n", + "The states $|n\\rangle$ are number states, also called Fock states. The annihilation operator $a$ lowers the photon number by one, while $a^\\dagger$ raises it:\n", + "\n", + "$$a|n\\rangle=\\sqrt{n}|n-1\\rangle, \\qquad a^\\dagger|n\\rangle=\\sqrt{n+1}|n+1\\rangle.$$\n", + "\n", + "The number operator is $\\hat n=a^\\dagger a$. From $a$ and $a^\\dagger$, we define two quadratures\n", + "\n", + "$$x = \\frac{a+a^\\dagger}{\\sqrt{2}}, \\qquad p = \\frac{a-a^\\dagger}{i\\sqrt{2}}.$$\n", + "\n", + "They are similar to position and momentum. In the units used here, they obey $[x,p]=i$ and the uncertainty relation $\\Delta x\\,\\Delta p \\geq 1/2$." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "imports", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:39.093617Z", + "iopub.status.busy": "2026-08-08T16:23:39.093341Z", + "iopub.status.idle": "2026-08-08T16:23:40.235038Z", + "shell.execute_reply": "2026-08-08T16:23:40.234283Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "from qutip import basis, coherent, destroy, expect, squeeze, wigner" + ] + }, + { + "cell_type": "markdown", + "id": "three-states", + "metadata": {}, + "source": [ + "## Four states\n", + "\n", + "The vacuum state $|0\\rangle$ has no photons, but its quadratures still have quantum uncertainty. The state $|1\\rangle$ contains exactly one photon. A coherent state $|\\alpha\\rangle$ is a displaced vacuum state and is often used as a simple model of laser light. A squeezed vacuum state reduces the uncertainty of one quadrature while increasing the uncertainty of the other." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "make-states", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:40.237033Z", + "iopub.status.busy": "2026-08-08T16:23:40.236723Z", + "iopub.status.idle": "2026-08-08T16:23:40.241607Z", + "shell.execute_reply": "2026-08-08T16:23:40.240983Z" + } + }, + "outputs": [], + "source": [ + "# The harmonic oscillator is infinite-dimensional, so we keep 30 basis states.\n", + "N = 30\n", + "\n", + "vacuum = basis(N, 0)\n", + "one_photon = basis(N, 1)\n", + "coherent_state = coherent(N, 2.0)\n", + "squeezed_vacuum = squeeze(N, 0.7) * vacuum\n", + "\n", + "states = [vacuum, one_photon, coherent_state, squeezed_vacuum]\n", + "state_names = [\"Vacuum\", \"One-photon state\", \"Coherent state\", \"Squeezed vacuum\"]" + ] + }, + { + "cell_type": "markdown", + "id": "energy-level-text", + "metadata": {}, + "source": [ + "## Energy levels and Fock states\n", + "\n", + "For a harmonic oscillator, the energy of the Fock state $|n\\rangle$ is\n", + "\n", + "$$E_n=\\hbar\\omega\\left(n+\\frac{1}{2}\\right).$$\n", + "\n", + "The levels are equally spaced. The finite cutoff $N=30$ means that the calculation keeps the states from $|0\\rangle$ to $|29\\rangle$." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "energy-level-plot", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:40.243267Z", + "iopub.status.busy": "2026-08-08T16:23:40.243047Z", + "iopub.status.idle": "2026-08-08T16:23:40.429189Z", + "shell.execute_reply": "2026-08-08T16:23:40.428640Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# We set hbar*omega = 1 and draw the first six energy levels.\n", + "level_numbers = np.arange(6)\n", + "energies = level_numbers + 0.5\n", + "\n", + "fig, ax = plt.subplots(figsize=(5, 4))\n", + "for n, energy in zip(level_numbers, energies):\n", + " ax.hlines(energy, 0, 1.5, color=\"tab:blue\")\n", + " ax.text(1.58, energy, f\"|{n}>\", va=\"center\")\n", + "\n", + "ax.set_xlim(-0.1, 2.0)\n", + "ax.set_ylim(0, 6.2)\n", + "ax.set_xticks([])\n", + "ax.set_ylabel(r\"Energy $E_n / (\\hbar\\omega)$\")\n", + "ax.set_title(\"First six harmonic-oscillator energy levels\")\n", + "ax.spines[[\"top\", \"right\", \"bottom\"]].set_visible(False)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "photon-distribution-text", + "metadata": {}, + "source": [ + "## Photon-number distributions\n", + "\n", + "For a pure state $|\\psi\\rangle$, the probability of measuring $n$ photons is\n", + "\n", + "$$P(n)=|\\langle n|\\psi\\rangle|^2.$$\n", + "\n", + "For a coherent state, this is the Poisson distribution\n", + "\n", + "$$P(n)=e^{-|\\alpha|^2}\\frac{|\\alpha|^{2n}}{n!}.$$\n", + "\n", + "The following bar charts show the first twelve photon-number probabilities." + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "photon-distribution-plot", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:40.430864Z", + "iopub.status.busy": "2026-08-08T16:23:40.430634Z", + "iopub.status.idle": "2026-08-08T16:23:40.705153Z", + "shell.execute_reply": "2026-08-08T16:23:40.704432Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def photon_probabilities(state):\n", + " amplitudes = state.full().flatten()\n", + " return np.abs(amplitudes) ** 2\n", + "\n", + "fig, axes = plt.subplots(2, 2, figsize=(9, 6), sharex=True, sharey=True)\n", + "axes = axes.flatten()\n", + "photon_numbers = np.arange(12)\n", + "\n", + "for ax, name, state in zip(axes, state_names, states):\n", + " probabilities = photon_probabilities(state)\n", + " ax.bar(photon_numbers, probabilities[:12], width=0.75)\n", + " ax.set_title(name)\n", + " ax.set_xlabel(\"Photon number n\")\n", + " ax.set_xticks(photon_numbers[::2])\n", + "\n", + "axes[0].set_ylabel(\"Probability P(n)\")\n", + "axes[2].set_ylabel(\"Probability P(n)\")\n", + "fig.suptitle(\"Photon-number distributions\")\n", + "fig.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "photon-observations", + "metadata": {}, + "source": [ + "The vacuum has only the zero-photon outcome, while the one-photon state has only the $n=1$ outcome. The coherent state has a distribution over several photon numbers. The squeezed vacuum contains only even photon numbers in this ideal model." + ] + }, + { + "cell_type": "markdown", + "id": "wigner-text", + "metadata": {}, + "source": [ + "## Wigner functions\n", + "\n", + "A Wigner function $W(x,p)$ represents a state in phase space. It is called a quasi-probability distribution because it can become negative. The vacuum, coherent and squeezed states have non-negative Gaussian Wigner functions. The one-photon state is non-Gaussian and has a negative region. QuTiP calculates the Wigner function on a grid of $x$ and $p$ values." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "wigner-plots", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:40.707035Z", + "iopub.status.busy": "2026-08-08T16:23:40.706794Z", + "iopub.status.idle": "2026-08-08T16:23:41.200860Z", + "shell.execute_reply": "2026-08-08T16:23:41.200144Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "x_values = np.linspace(-5, 5, 150)\n", + "p_values = np.linspace(-5, 5, 150)\n", + "wigner_functions = [wigner(state, x_values, p_values) for state in states]\n", + "maximum = max(np.max(np.abs(values)) for values in wigner_functions)\n", + "levels = np.linspace(-maximum, maximum, 81)\n", + "\n", + "fig, axes = plt.subplots(2, 2, figsize=(8, 7), sharex=True, sharey=True)\n", + "axes = axes.flatten()\n", + "\n", + "for ax, name, values in zip(axes, state_names, wigner_functions):\n", + " image = ax.contourf(x_values, p_values, values, levels=levels, cmap=\"RdBu_r\")\n", + " ax.set_title(name)\n", + " ax.set_xlabel(\"x\")\n", + " ax.set_aspect(\"equal\")\n", + "\n", + "axes[0].set_ylabel(\"p\")\n", + "axes[2].set_ylabel(\"p\")\n", + "fig.colorbar(image, ax=axes, label=\"W(x, p)\", shrink=0.82)\n", + "fig.suptitle(\"Wigner functions in phase space\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "wigner-observations", + "metadata": {}, + "source": [ + "The vacuum is circular and centred at the origin. The one-photon state is also centred at the origin, but its negative central region distinguishes it from the Gaussian states. The coherent state has the same circular shape as the vacuum but is displaced. The squeezed state is narrower in one direction and wider in the other." + ] + }, + { + "cell_type": "markdown", + "id": "uncertainty-text", + "metadata": {}, + "source": [ + "## Quadrature uncertainty\n", + "\n", + "The Wigner plots show the shape visually. We can also calculate the variances $\\Delta x^2$ and $\\Delta p^2$ directly." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "uncertainty-code", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-08T16:23:41.202959Z", + "iopub.status.busy": "2026-08-08T16:23:41.202675Z", + "iopub.status.idle": "2026-08-08T16:23:41.315918Z", + "shell.execute_reply": "2026-08-08T16:23:41.315065Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Vacuum var(x) = 0.500, var(p) = 0.500\n", + "One-photon state var(x) = 1.500, var(p) = 1.500\n", + "Coherent state var(x) = 0.500, var(p) = 0.500\n", + "Squeezed vacuum var(x) = 0.123, var(p) = 2.028\n" + ] + }, + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "a = destroy(N)\n", + "x_operator = (a + a.dag()) / np.sqrt(2)\n", + "p_operator = (a - a.dag()) / (1j * np.sqrt(2))\n", + "\n", + "def variance(state, operator):\n", + " mean = expect(operator, state)\n", + " mean_square = expect(operator * operator, state)\n", + " return np.real(mean_square - mean**2)\n", + "\n", + "variances_x = []\n", + "variances_p = []\n", + "\n", + "for name, state in zip(state_names, states):\n", + " variance_x = variance(state, x_operator)\n", + " variance_p = variance(state, p_operator)\n", + " variances_x.append(variance_x)\n", + " variances_p.append(variance_p)\n", + " print(f\"{name:18s} var(x) = {variance_x:.3f}, var(p) = {variance_p:.3f}\")\n", + "\n", + "positions = np.arange(len(state_names))\n", + "width = 0.36\n", + "\n", + "fig, ax = plt.subplots(figsize=(9, 4))\n", + "ax.bar(positions - width / 2, variances_x, width, label=r\"$\\Delta x^2$\")\n", + "ax.bar(positions + width / 2, variances_p, width, label=r\"$\\Delta p^2$\")\n", + "ax.set_xticks(positions, state_names)\n", + "ax.set_ylabel(\"Variance\")\n", + "ax.set_title(\"Quadrature variances\")\n", + "ax.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "summary", + "metadata": {}, + "source": [ + "## Summary\n", + "\n", + "The photon-number basis and the Wigner function give two different views of the same state. The photon-number distribution describes possible counting outcomes, while the Wigner function shows the state in phase space. The negative region of the one-photon Wigner function is a sign of non-Gaussian behaviour. The squeezed state is a simple example where reducing uncertainty in one quadrature necessarily increases it in the other.\n", + "\n", + "### References\n", + "\n", + "- J. B. Brask, [*Gaussian states and operations: a quick reference*](https://arxiv.org/abs/2102.05748).\n", + "- [QuTiP documentation](https://qutip.readthedocs.io/)." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "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 +}