From b5d24d4417a220d94366cbdb38fc6cc7e6d2335c Mon Sep 17 00:00:00 2001 From: Danyang Chen Date: Mon, 23 Mar 2026 10:59:16 -0500 Subject: [PATCH] add branch analysis plotting --- .../hilbertspace/ipynb/branch_analysis.ipynb | 2450 ++++++++++++++++- 1 file changed, 2439 insertions(+), 11 deletions(-) diff --git a/docs/source/guide/hilbertspace/ipynb/branch_analysis.ipynb b/docs/source/guide/hilbertspace/ipynb/branch_analysis.ipynb index 003a8bc..8b1efda 100644 --- a/docs/source/guide/hilbertspace/ipynb/branch_analysis.ipynb +++ b/docs/source/guide/hilbertspace/ipynb/branch_analysis.ipynb @@ -2,13 +2,14 @@ "cells": [ { "cell_type": "code", - "execution_count": 2, + "execution_count": 1, "metadata": { "nbsphinx": "hidden" }, "outputs": [], "source": [ - "import scqubits as scq" + "import scqubits as scq\n", + "import matplotlib.pyplot as plt" ] }, { @@ -24,7 +25,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "metadata": {}, "outputs": [], "source": [ @@ -32,15 +33,15 @@ "N_tmon, N_res = 10, 50 \n", "\n", "tmon = scq.Transmon(\n", - " EJ = 20, \n", - " EC = 0.3, \n", + " EJ = 15, \n", + " EC = 0.4, \n", " ng = 0.25, \n", " ncut = 100,\n", " truncated_dim = N_tmon,\n", ")\n", "\n", "res = scq.Oscillator(\n", - " E_osc = 5,\n", + " E_osc = 6.68,\n", " l_osc = 1,\n", " truncated_dim = N_res,\n", ")\n", @@ -92,15 +93,16 @@ "metadata": {}, "outputs": [], "source": [ - "hilbertspace.generate_lookup(\n", - " ordering = 'LX'\n", - ")" + "hilbertspace.generate_lookup(ordering = 'LX')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ + "## Examine the Branch Analysis Results\n", + "\n", + "### Retrieve the bare index of an eigenstate \n", "The labeling of an eigenstate can be accessed by lookup functions described in section \"Spectrum lookup: converting between bare and dressed indices\" on page [Composite Hilbert Spaces & QuTiP](./hilbertspace.ipynb). For example, the $8^{\\text{th}}$ eigenstate is corresponding to the following bare product label:" ] }, @@ -112,7 +114,7 @@ { "data": { "text/plain": [ - "(2, 1)" + "(1, 2)" ] }, "execution_count": 4, @@ -124,6 +126,2432 @@ "hilbertspace.bare_index(8)" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Critical Photon Number \n", + "Following [Dumas2024], the critical photon number $n_\\text{crit}(t)$ for branch $t$ is the smallest resonator photon number $r$ such that\n", + "\n", + "$$\\langle \\overline{t, r} \\,|\\, \\hat{N}_\\text{tmon} \\,|\\, \\overline{t, r} \\rangle > t + 1,$$\n", + "\n", + "where $\\hat{N}_\\text{tmon}$ is the transmon number operator. Physically, it marks the point along branch $t$ at which the transmon is appreciably excited beyond its nominal level $t$, signaling a breakdown of the dispersive approximation.\n", + "\n", + "The following method computes the critical photon number for the branches $t=0$ and $t=1$ and returns the smallest one." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "n_crit = hilbertspace.branch_analysis_n_crit(\n", + " primary_mode = res,\n", + " branch = [0, 1],\n", + ")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Visualization\n", + "Following [Dumas2024], the full set of eigenstates can be visualized in a scatter plot where each eigenstate is positioned according to its photon-number expectation value on each subsystem. The observables used for the two axes are specified by the `x_observable` and `y_observable` arguments, both set to `'N'`. Points belonging to the same branch are connected by lines, tracing the sequence of eigenstates obtained by successively adding one photon to the resonator (the `primary_mode`)." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "data": { + "application/pdf": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(5, 3.5))\n", + "hilbertspace.plot_branch_analysis(\n", + " primary_mode = res,\n", + " x_observable = 'N',\n", + " y_observable = 'N',\n", + " fig_ax = (fig, ax)\n", + ")\n", + "ax.axvline(n_crit, color='gray', linestyle=\"--\", zorder=-1)\n", + "plt.show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -183,7 +2611,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 7, "metadata": {}, "outputs": [], "source": [