{ "cells": [ { "cell_type": "markdown", "id": "0", "metadata": {}, "source": [ "# Getting started: setting up your first quantum simulation problem\n", "\n", "To get familiar with the main concepts of QruiseML, you can work through this example notebook. We'll briefly explain how to define a drive and Hamiltonian, set up and solve a quantum problem, and plot the results. \n", "\n", "## Defining the Hamiltonian\n", "\n", "We describe the dynamics of a quantum system using a Hamiltonian of the form\n", "\n", "$$\n", "H_{\\text{total}} (t; p) = H_0 + H(t; p),\n", "$$\n", "\n", "where $H_0$ and $H(t, p)$ are the stationary and time-dependent parts, respectively, and $p$ represents the drive parameter set $p$.\n", "\n", "\n", "### Time-dependent drive functions\n", "\n", "The time-dependent part is constructed by combining drive functions with quantum operators. A drive function is a time-dependent control field applied to the system, which determines the evolution of the quantum state.\n", "\n", "For example, we could use a sinusoidal drive of the form\n", "\n", "$$\n", "f(t; \\{a, \\omega, \\phi\\}) = a \\sin(\\omega t + \\phi),\n", "$$\n", "\n", "where $a$ is the amplitude, $\\omega$ the frequency, and $\\phi$ the phase.\n", "\n", "In QruiseML, drive functions are defined as annotated Python functions. This means that each input parameter, as well as the function output, must have a type annotation. These annotations must use the types defined in the [`types`](../src/qruise/toolset/types.py) module in QruiseML.\n", "\n", "For example, we can define a sine drive and a cosine drive, where the inputs and the output are all 64-bit floating-point numbers:" ] }, { "cell_type": "code", "execution_count": 1, "id": "1", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:56.967675Z", "iopub.status.busy": "2026-08-20T10:23:56.967461Z", "iopub.status.idle": "2026-08-20T10:23:58.235643Z", "shell.execute_reply": "2026-08-20T10:23:58.234753Z" } }, "outputs": [], "source": [ "import numpy as np\n", "from qruise.toolset.types import Float64\n", "\n", "\n", "# define sine drive\n", "def f(t: Float64, a: Float64, w: Float64, p: Float64) -> Float64:\n", " return a * np.sin(w * t + p)\n", "\n", "\n", "# define cosine drive\n", "def g(t: Float64, a: Float64, w: Float64, p: Float64) -> Float64:\n", " return a * np.cos(w * t + p)" ] }, { "cell_type": "markdown", "id": "2", "metadata": {}, "source": [ "### Drive parameters and channels\n", "\n", "Next, we define the parameter values associated with each drive function. \n", "\n", "When working with multiple drives in QruiseML, we need to specify which parameters belong to which drive channel. This ensures that parameters with the same name — such as `a`, `w`, and `p` — are associated with the correct drive channel. We can do this by creating a `Parameters` object with two drive channels, `\"d1\"` and `\"d2\"`:" ] }, { "cell_type": "code", "execution_count": 2, "id": "3", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:58.238529Z", "iopub.status.busy": "2026-08-20T10:23:58.238176Z", "iopub.status.idle": "2026-08-20T10:23:58.254578Z", "shell.execute_reply": "2026-08-20T10:23:58.253720Z" } }, "outputs": [], "source": [ "from qruise.toolset import Parameters\n", "\n", "ps = Parameters(\n", " {\"d1\": {\"a\": 1.0, \"w\": 2.0, \"p\": 0.01}, \"d2\": {\"a\": 0.5, \"w\": 1.8, \"p\": -0.3}}\n", ")" ] }, { "cell_type": "markdown", "id": "4", "metadata": {}, "source": [ "We then use the `Drive` class to associate the parameters of each drive function (`f` and `g`) with their corresponding channel (`\"d1\"` and `\"d2\"`):" ] }, { "cell_type": "code", "execution_count": 3, "id": "5", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:58.256521Z", "iopub.status.busy": "2026-08-20T10:23:58.256345Z", "iopub.status.idle": "2026-08-20T10:23:58.536301Z", "shell.execute_reply": "2026-08-20T10:23:58.535371Z" } }, "outputs": [], "source": [ "from qruise.toolset import Drive\n", "\n", "drv1 = Drive(\"d1\", f)\n", "drv2 = Drive(\"d2\", g)" ] }, { "cell_type": "markdown", "id": "6", "metadata": {}, "source": [ "### Constructing the Hamiltonian \n", "\n", "The Hamiltonian is constructed in a similar way to `QuTiP`. We define the stationary part, `H0`, and the time-dependent part, which consists of pairs of drives ($d_n$) and quantum operators ($A_n$), e.g. \n", "\n", "$$\n", "(d_1, A_1), (d_2, A_2), \\cdots, (d_N, A_N).\n", "$$\n", "\n", "Let's construct the Hamiltonian\n", "\n", "$$\n", "H_{\\text{total}} (t; p) = \\sigma_z + d_1 \\sigma_x + d_2 \\sigma_y, \n", "$$\n", "\n", "where $\\sigma_{x,y,z}$ are Pauli operators. We instantiate this using the `Hamiltonian` class by passing the stationary part of the Hamiltonian together with a list\n", "of `(drive, operator)` pairs defining the time-dependent terms:" ] }, { "cell_type": "code", "execution_count": 4, "id": "7", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:58.538425Z", "iopub.status.busy": "2026-08-20T10:23:58.538249Z", "iopub.status.idle": "2026-08-20T10:23:58.543554Z", "shell.execute_reply": "2026-08-20T10:23:58.542743Z" } }, "outputs": [], "source": [ "import qutip as qt\n", "from qruise.toolset import Hamiltonian\n", "\n", "# define Pauli operators\n", "sx = qt.sigmax()\n", "sy = qt.sigmay()\n", "sz = qt.sigmaz()\n", "\n", "# define Hamiltonian\n", "H = Hamiltonian(sz, [(drv1, sx), (drv2, sy)])" ] }, { "cell_type": "markdown", "id": "8", "metadata": {}, "source": [ "## Defining the quantum simulation problem\n", "\n", "Now that we've defined our Hamiltonian, we can start setting up a quantum simulation problem. In QruiseML, we use the `Problem` class to group together the equations and parameters that govern the system. To instantiate the `Problem`, we need:\n", "\n", "- the equation that governs the dynamics (e.g. `\"Schroedinger\"` or `\"Master Equation\"`)\n", "- the Hamiltonian (`H`)\n", "- the initial qubit state (`u0`)\n", "- the time interval of the simulation (`t0` to `tfinal`)\n", "- the pulse parameters (`ps`)\n", "\n", "---\n", "\n", "**Note:** If you select `\"Master Equation\"`, the absence or presence of collapse operators (`c_ops`) determines whether the von Neumann or Lindblad equation is used.\n", "\n", "---\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "9", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:58.545475Z", "iopub.status.busy": "2026-08-20T10:23:58.545307Z", "iopub.status.idle": "2026-08-20T10:23:58.552462Z", "shell.execute_reply": "2026-08-20T10:23:58.551673Z" } }, "outputs": [], "source": [ "from qruise.toolset import Problem\n", "\n", "t0 = 0.0 # start time\n", "tfinal = 1.0 # end time\n", "ts = np.linspace(t0, tfinal, 100) # to save the result at these timestamps\n", "u0 = qt.basis(2, 0) # initial qubit state |0>\n", "\n", "prob = Problem(\"Schroedinger\", H, u0, (t0, tfinal), ps)" ] }, { "cell_type": "markdown", "id": "10", "metadata": {}, "source": [ "## Starting a session and solving the problem\n", "\n", "The `Problem` object defines the quantum system we want to simulate,\n", "but it does not run the simulation itself. To do this, we need to create a `Session` and initialise the `Problem` object within it using `qsprob_init`. The session prepares the problem for numerical simulation and manages the solver execution." ] }, { "cell_type": "code", "execution_count": 6, "id": "11", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:23:58.554413Z", "iopub.status.busy": "2026-08-20T10:23:58.554235Z", "iopub.status.idle": "2026-08-20T10:24:10.531676Z", "shell.execute_reply": "2026-08-20T10:24:10.530605Z" } }, "outputs": [], "source": [ "from qruise.toolset.session import Session\n", "\n", "sess = Session()\n", "sess.qsprob_init(prob)" ] }, { "cell_type": "markdown", "id": "12", "metadata": {}, "source": [ "To compute the system time evolution, we use the `evolve` method to solve the quantum simulation problem numerically. \n", "\n", "In the implementation below, `\"Tsit5\"` specifies the ODE algorithm, `reltol`\n", "and `abstol` the numerical tolerances, and `saveat` the times at which the result is stored. Other solver options can also be passed as keyword arguments." ] }, { "cell_type": "code", "execution_count": 7, "id": "13", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:24:10.534190Z", "iopub.status.busy": "2026-08-20T10:24:10.533985Z", "iopub.status.idle": "2026-08-20T10:24:17.115688Z", "shell.execute_reply": "2026-08-20T10:24:17.114889Z" } }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "\r", "\u001b[KODE [ ] 0%\r", "\u001b[KODE [########################################] 100%\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " Size: 6kB\n", "Dimensions: (time: 100, state: 2)\n", "Coordinates:\n", " * time (time) float64 800B 0.0 0.0101 0.0202 ... 0.9798 0.9899 1.0\n", " * state (state) ' '|1>'\n", "Data variables:\n", " qstates (time, state) complex128 3kB (1+0j) ... (0.13077861932833706-...\n", " population (time, state) float64 2kB 1.0 0.0 1.0 ... 0.2461 0.753 0.247" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ds[\"population\"] = np.abs(ds[\"qstates\"]) ** 2 # calculate the population\n", "\n", "ds = ds.rename({\"row\": \"state\"}) # rename the dimension \"row\" to \"states\"\n", "ds = ds.assign_coords(state=[r\"|0>\", r\"|1>\"]) # assign labels to the dimensions\n", "ds" ] }, { "cell_type": "markdown", "id": "16", "metadata": {}, "source": [ "`xarray` provides different backends to conveniently plot the result. For example, we can use `hvplot` with the native `matplotlib` backend to plot the population of each state:" ] }, { "cell_type": "code", "execution_count": 9, "id": "17", "metadata": { "execution": { "iopub.execute_input": "2026-08-20T10:24:17.136178Z", "iopub.status.busy": "2026-08-20T10:24:17.136012Z", "iopub.status.idle": "2026-08-20T10:24:20.646368Z", "shell.execute_reply": "2026-08-20T10:24:20.645532Z" } }, "outputs": [ { "data": { "text/html": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/javascript": [ "(function(root) {\n", " function now() {\n", " return new Date();\n", " }\n", "\n", " const force = true;\n", " const version = '3.9.0'.replace('rc', '-rc.').replace('.dev', '-dev.');\n", " const reloading = false;\n", " const Bokeh = root.Bokeh;\n", " const BK_RE = /^https:\\/\\/cdn\\.bokeh\\.org\\/bokeh\\/(release|dev)\\/bokeh-/;\n", " const PN_RE = /^https:\\/\\/cdn\\.holoviz\\.org\\/panel\\/[^/]+\\/dist\\/panel/i;\n", "\n", " // Set a 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Map();\n", " }\n", " if (NewBokeh.version !== Bokeh.version) {\n", " Bokeh[NewBokeh.version] = NewBokeh;\n", " Bokeh.versions.set(NewBokeh.version, NewBokeh);\n", " }\n", " root.Bokeh = Bokeh;\n", " }\n", " });\n", " }\n", " }\n", " // Give older versions of the autoload script a head-start to ensure\n", " // they initialize before we start loading newer version.\n", " setTimeout(load_or_wait, 100)\n", "}(window));" ], "application/vnd.holoviews_load.v0+json": "(function(root) {\n function now() {\n return new Date();\n }\n\n const force = true;\n const version = '3.9.0'.replace('rc', '-rc.').replace('.dev', '-dev.');\n const reloading = false;\n const Bokeh = root.Bokeh;\n const BK_RE = /^https:\\/\\/cdn\\.bokeh\\.org\\/bokeh\\/(release|dev)\\/bokeh-/;\n const PN_RE = /^https:\\/\\/cdn\\.holoviz\\.org\\/panel\\/[^/]+\\/dist\\/panel/i;\n\n // Set a timeout for this load but only if we are not already initializing\n if (typeof (root._bokeh_timeout) === \"undefined\" || (force || !root._bokeh_is_initializing)) {\n root._bokeh_timeout = Date.now() + 5000;\n root._bokeh_failed_load = false;\n }\n\n function run_callbacks() {\n try {\n root._bokeh_onload_callbacks.forEach(function(callback) {\n if (callback != null)\n callback();\n });\n } finally {\n delete root._bokeh_onload_callbacks;\n }\n console.debug(\"Bokeh: all callbacks have finished\");\n }\n\n function load_libs(css_urls, js_urls, js_modules, js_exports, Bokeh, callback) {\n if (css_urls == null) css_urls = [];\n if (js_urls == null) js_urls = [];\n if (js_modules == null) js_modules = [];\n if (js_exports == null) js_exports = {};\n\n root._bokeh_onload_callbacks.push(callback);\n\n if (root._bokeh_is_loading > 0) {\n // Don't load bokeh if it is still initializing\n console.debug(\"Bokeh: BokehJS is being loaded, scheduling callback at\", now());\n return null;\n } else if (js_urls.length === 0 && js_modules.length === 0 && Object.keys(js_exports).length === 0) {\n // There is nothing to load\n 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= encodeURI(url)\n if (existing_stylesheets.indexOf(escaped) !== -1) {\n on_load()\n continue;\n }\n const element = document.createElement(\"link\");\n element.onload = on_load;\n element.onerror = on_error;\n element.rel = \"stylesheet\";\n element.type = \"text/css\";\n element.href = url;\n console.debug(\"Bokeh: injecting link tag for BokehJS stylesheet: \", url);\n document.body.appendChild(element);\n } var existing_scripts = []\n const scripts = document.getElementsByTagName('script')\n for (let i = 0; i < scripts.length; i++) {\n var script = scripts[i]\n if (script.src != null) {\n existing_scripts.push(script.src)\n }\n }\n for (let i = 0; i < js_urls.length; i++) {\n const url = js_urls[i];\n const escaped = encodeURI(url)\n const shouldSkip = skip.includes(escaped) || existing_scripts.includes(escaped)\n const isBokehOrPanel = BK_RE.test(escaped) || PN_RE.test(escaped)\n const missingOrBroken = Bokeh == null || Bokeh.Panel == null || (Bokeh.version != version && 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document.head.appendChild(element);\n }\n for (const name in js_exports) {\n const url = js_exports[name];\n const escaped = encodeURI(url)\n if (skip.indexOf(escaped) >= 0 || root[name] != null) {\n if (!window.requirejs) {\n on_load();\n }\n continue;\n }\n var element = document.createElement('script');\n element.onerror = on_error;\n element.async = false;\n element.type = \"module\";\n console.debug(\"Bokeh: injecting script tag for BokehJS library: \", url);\n element.textContent = `\n import ${name} from \"${url}\"\n window.${name} = ${name}\n window._bokeh_on_load()\n `\n document.head.appendChild(element);\n }\n if (!js_urls.length && !js_modules.length) {\n on_load()\n }\n };\n\n function inject_raw_css(css) {\n const element = document.createElement(\"style\");\n element.appendChild(document.createTextNode(css));\n document.body.appendChild(element);\n }\n\n const js_urls = 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root._bokeh_is_loading = 0;\n console.log(\"Bokeh: BokehJS was loaded multiple times but one version failed to initialize.\");\n load_or_wait();\n } else if (root._bokeh_is_initializing || (typeof root._bokeh_is_initializing === \"undefined\" && root._bokeh_onload_callbacks !== undefined)) {\n setTimeout(load_or_wait, 100);\n } else {\n root._bokeh_is_initializing = true;\n root._bokeh_onload_callbacks = [];\n const bokeh_loaded = Bokeh != null && ((Bokeh.version === version && Bokeh.Panel) || (Bokeh.versions?.has(version) && Bokeh.versions.get(version)?.Panel));\n if (!reloading && !bokeh_loaded) {\n if (root.Bokeh) {\n root.Bokeh = undefined;\n }\n console.debug(\"Bokeh: BokehJS not loaded, scheduling load and callback at\", now());\n }\n load_libs(css_urls, js_urls, js_modules, js_exports, Bokeh, function() {\n console.debug(\"Bokeh: BokehJS plotting callback run at\", now());\n run_inline_js();\n if (Bokeh != undefined && !reloading) {\n const NewBokeh = root.Bokeh;\n if 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\n", "" ], "text/plain": [ ":NdOverlay [state]\n", " :Curve [time] (population)" ] }, "execution_count": 9, "metadata": { "application/vnd.holoviews_exec.v0+json": { "id": "6033504c-7cd7-4a59-aeb5-27d09d3f2d14" } }, "output_type": "execute_result" } ], "source": [ "import hvplot.xarray\n", "\n", "ds.hvplot.line(x=\"time\", y=\"population\", by=\"state\", xlabel=\"time [arb. u.]\")" ] }, { "cell_type": "markdown", "id": "18", "metadata": {}, "source": [ "Great, you just simulated your first quantum system in QruiseML! You can now explore the other notebooks for more advanced examples covering different quantum platforms and QruiseML features." ] } ], "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": "3.11.16" } }, "nbformat": 4, "nbformat_minor": 5 }