diff --git a/docs/tutorials/Manifest.toml b/docs/tutorials/Manifest.toml
new file mode 100644
index 00000000000..ae15ab9abf8
--- /dev/null
+++ b/docs/tutorials/Manifest.toml
@@ -0,0 +1,3333 @@
+# This file is machine-generated - editing it directly is not advised
+
+julia_version = "1.11.5"
+manifest_format = "2.0"
+project_hash = "4aba04f9a57fbcfaaee36c8bb9263b033e0ea1b6"
+
+[[deps.ADTypes]]
+git-tree-sha1 = "f7304359109c768cf32dc5fa2d371565bb63b68a"
+uuid = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
+version = "1.21.0"
+weakdeps = ["ChainRulesCore", "ConstructionBase", "EnzymeCore"]
+
+ [deps.ADTypes.extensions]
+ ADTypesChainRulesCoreExt = "ChainRulesCore"
+ ADTypesConstructionBaseExt = "ConstructionBase"
+ ADTypesEnzymeCoreExt = "EnzymeCore"
+
+[[deps.AbstractLattices]]
+git-tree-sha1 = "763b6f3f6bfabd72c7e262cbb5ddfd43fd5c6398"
+uuid = "398f06c4-4d28-53ec-89ca-5b2656b7603d"
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+
+[[deps.AbstractTrees]]
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+uuid = "1520ce14-60c1-5f80-bbc7-55ef81b5835c"
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+
+[[deps.Accessors]]
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+version = "0.1.44"
+
+ [deps.Accessors.extensions]
+ AxisKeysExt = "AxisKeys"
+ IntervalSetsExt = "IntervalSets"
+ LinearAlgebraExt = "LinearAlgebra"
+ StaticArraysExt = "StaticArrays"
+ StructArraysExt = "StructArrays"
+ TestExt = "Test"
+ UnitfulExt = "Unitful"
+
+ [deps.Accessors.weakdeps]
+ AxisKeys = "94b1ba4f-4ee9-5380-92f1-94cde586c3c5"
+ IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+ LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
+ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+ StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
+ Unitful = "1986cc42-f94f-5a68-af5c-568840ba703d"
+
+[[deps.Adapt]]
+deps = ["LinearAlgebra", "Requires"]
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+
+ [deps.Adapt.extensions]
+ AdaptSparseArraysExt = "SparseArrays"
+ AdaptStaticArraysExt = "StaticArrays"
+
+[[deps.AliasTables]]
+deps = ["PtrArrays", "Random"]
+git-tree-sha1 = "9876e1e164b144ca45e9e3198d0b689cadfed9ff"
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+[[deps.ArgCheck]]
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+[[deps.ArgTools]]
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+
+[[deps.ArnoldiMethod]]
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+[[deps.ArrayInterface]]
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+
+ [deps.ArrayInterface.extensions]
+ ArrayInterfaceAMDGPUExt = "AMDGPU"
+ ArrayInterfaceBandedMatricesExt = "BandedMatrices"
+ ArrayInterfaceBlockBandedMatricesExt = "BlockBandedMatrices"
+ ArrayInterfaceCUDAExt = "CUDA"
+ ArrayInterfaceCUDSSExt = ["CUDSS", "CUDA"]
+ ArrayInterfaceChainRulesCoreExt = "ChainRulesCore"
+ ArrayInterfaceChainRulesExt = "ChainRules"
+ ArrayInterfaceGPUArraysCoreExt = "GPUArraysCore"
+ ArrayInterfaceMetalExt = "Metal"
+ ArrayInterfaceReverseDiffExt = "ReverseDiff"
+ ArrayInterfaceSparseArraysExt = "SparseArrays"
+ ArrayInterfaceStaticArraysCoreExt = "StaticArraysCore"
+ ArrayInterfaceTrackerExt = "Tracker"
+
+ [deps.ArrayInterface.weakdeps]
+ AMDGPU = "21141c5a-9bdb-4563-92ae-f87d6854732e"
+ BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+ BlockBandedMatrices = "ffab5731-97b5-5995-9138-79e8c1846df0"
+ CUDA = "052768ef-5323-5732-b1bb-66c8b64840ba"
+ CUDSS = "45b445bb-4962-46a0-9369-b4df9d0f772e"
+ ChainRules = "082447d4-558c-5d27-93f4-14fc19e9eca2"
+ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ GPUArraysCore = "46192b85-c4d5-4398-a991-12ede77f4527"
+ Metal = "dde4c033-4e86-420c-a63e-0dd931031962"
+ ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
+ SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+ StaticArraysCore = "1e83bf80-4336-4d27-bf5d-d5a4f845583c"
+ Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"
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+ ArrayLayoutsSparseArraysExt = "SparseArrays"
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+[[deps.Artifacts]]
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+
+ [deps.BangBang.extensions]
+ BangBangChainRulesCoreExt = "ChainRulesCore"
+ BangBangDataFramesExt = "DataFrames"
+ BangBangStaticArraysExt = "StaticArrays"
+ BangBangStructArraysExt = "StructArrays"
+ BangBangTablesExt = "Tables"
+ BangBangTypedTablesExt = "TypedTables"
+
+ [deps.BangBang.weakdeps]
+ ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+ DataFrames = "a93c6f00-e57d-5684-b7b6-d8193f3e46c0"
+ StaticArrays = "90137ffa-7385-5640-81b9-e52037218182"
+ StructArrays = "09ab397b-f2b6-538f-b94a-2f83cf4a842a"
+ Tables = "bd369af6-aec1-5ad0-b16a-f7cc5008161c"
+ TypedTables = "9d95f2ec-7b3d-5a63-8d20-e2491e220bb9"
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+ BlockArraysBandedMatricesExt = "BandedMatrices"
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+ [deps.BlockArrays.weakdeps]
+ Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"
+ BandedMatrices = "aae01518-5342-5314-be14-df237901396f"
+
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+ [deps.BracketingNonlinearSolve.extensions]
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+ BracketingNonlinearSolveForwardDiffExt = "ForwardDiff"
+
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+ MetisExt = "Metis"
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diff --git a/docs/tutorials/Project.toml b/docs/tutorials/Project.toml
new file mode 100644
index 00000000000..c1c9fb6af68
--- /dev/null
+++ b/docs/tutorials/Project.toml
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+[deps]
+JSON = "682c06a0-de6a-54ab-a142-c8b1cf79cde6"
+LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
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+SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
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diff --git a/docs/tutorials/time-evolution.ipynb b/docs/tutorials/time-evolution.ipynb
new file mode 100644
index 00000000000..3af95068e95
--- /dev/null
+++ b/docs/tutorials/time-evolution.ipynb
@@ -0,0 +1,1135 @@
+{
+ "cells": [
+ {
+ "cell_type": "markdown",
+ "id": "8d86bf32",
+ "metadata": {},
+ "source": [
+ "---\n",
+ "title: Simulate time evolution of the transverse-field Ising model\n",
+ "description: Use Qiskit.jl to simulate time evolution of the transverse-field Ising model on IBM Quantum hardware\n",
+ "---\n",
+ "\n",
+ "{/* cspell:ignore Néel spdiagm Runge Kutta tspan saveat siteinds Neel maxdim tensornetworkstate println countmap clims xlabel ylabel colorbar */}"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "65550e2a",
+ "metadata": {},
+ "source": [
+ "# Simulate time evolution of the transverse-field Ising model\n",
+ "\n",
+ "## Learning outcomes\n",
+ "1. Learn how to transpile and run quantum circuits on the hardware using Julia\n",
+ "2. Learn how to post-process measurement outcomes to compute expectation values\n",
+ "3. Learn how to benchmark hardware results against classical simulation to quantify the combined effects of Trotter approximation error and hardware noise"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "727912c7",
+ "metadata": {},
+ "source": [
+ "## Background\n",
+ "\n",
+ "Julia is a dynamic programming language designed primarily for numerical and scientific computing. Its high-performance numerical computing capabilities make it a natural fit for quantum simulation workflows. In this tutorial, we will show how Julia is used for both classical pre- and post-processing (e.g., building Hamiltonians, running ODE solvers, computing expectation values) and for orchestrating quantum hardware jobs, eliminating the need to switch between languages or environments.\n",
+ "\n",
+ "To interface with IBM Quantum hardware from Julia, this tutorial uses two packages from the Qiskit ecosystem: `Qiskit.jl` wraps the Qiskit C library and provides circuit construction and transpilation functionality in Julia; `QiskitIBMRuntimeC.jl` connects to IBM Quantum hardware through the Qiskit IBM Runtime service, enabling job submission and result retrieval directly from Julia.\n",
+ "\n",
+ "In this tutorial, we consider the trotterized evolution of the transverse-field Ising model on a 1D chain with nearest-neighbor interactions:\n",
+ "\n",
+ "$$\n",
+ " H = \\sum_{\\langle i,j\\rangle}J_{ij}Z_iZ_j + \\sum_i h_i X_i\n",
+ "$$\n",
+ "\n",
+ "To implement the time evolution $e^{-iH\\tau}$, we divide the time interval $\\tau$ into $r$ steps and define $\\Delta\\tau=\\tau/r$. The second-order Trotter-Suzuki decomposition gives:\n",
+ "$$\n",
+ " e^{-iH\\Delta\\tau}\\approx \\prod_i e^{-ih_i X_i\\Delta\\tau/2 } \\prod_{\\langle i,j\\rangle} e^{-iJ_{ij}Z_iZ_j\\Delta\\tau} \\prod_i e^{-ih_iX_i\\Delta\\tau/2}\n",
+ "$$\n",
+ "\n",
+ "For circuit construction, each Trotter step is implemented as a sequence of single-qubit $R_x$ rotations and two-qubit $R_{ZZ}$ gates. The circuit begins by preparing the Néel state $|0101\\cdots\\rangle$ using X gates on alternating qubits. Each subsequent Trotter step applies: (1) $R_x(h_i\\Delta\\tau/2)$ on every qubit, (2) $R_{ZZ}(2J_{ij}\\Delta\\tau)$ on each neighboring pair along the chain, and (3) $R_x(h_i\\Delta\\tau/2)$ again on every qubit. The total circuit depth grows linearly with the number of Trotter steps $r$."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "020f72af",
+ "metadata": {},
+ "source": [
+ "## Requirements\n",
+ "\n",
+ "Note that this tutorial requires macOS or Linux — Qiskit.jl is not currently supported on Windows (tracked in [this open issue](https://github.com/Qiskit/Qiskit.jl/issues/15)).\n",
+ "\n",
+ "To get started, install Julia, following the instructions on the [Julia download page](https://julialang.org/downloads/).\n",
+ "\n",
+ "Then, run the following command in a terminal to install the Julia package `IJulia.jl` into the global environment; this will allow us to use the Julia programming language inside the Jupyter notebook.\n",
+ "\n",
+ "```\n",
+ "julia -e 'using Pkg; Pkg.add(\"IJulia\")'\n",
+ "```\n",
+ "\n",
+ "This tutorial also comes with two additional files: `Project.toml` and `Manifest.toml`. The project file describes the project at a high level — for example, the `[deps]` section lists all dependencies. The manifest file records the exact state of those dependencies, allowing you to reproduce the same project environment. See the [Julia documentation](https://pkgdocs.julialang.org/v1/toml-files/) for more on these files.\n",
+ "\n",
+ "We will use Julia's built-in package manager to set up the project environment. We run the code cell below to activate the environment defined by the `Project.toml` and `Manifest.toml` files in the current directory."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "940631f3",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\u001b[32m\u001b[1m Activating\u001b[22m\u001b[39m project at `~/Documents/ibm-quantum-engineering-and-enablement/tutorials/julia-tutorial`\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Activate the project environment and list installed packages\n",
+ "using Pkg\n",
+ "Pkg.activate(\".\")"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a519f88d",
+ "metadata": {},
+ "source": [
+ "The cell below installs all dependencies listed in `Project.toml`, with versions pinned as specified in Manifest.toml. The following packages will be installed:\n",
+ "\n",
+ "For quantum circuit construction and execution:\n",
+ "* `Qiskit.jl`\n",
+ "* `QiskitIBMRuntimeC.jl`\n",
+ "\n",
+ "For classical simulation:\n",
+ "* `OrdinaryDiffEq.jl`\n",
+ "* `TensorNetworkQuantumSimulator.jl`\n",
+ "\n",
+ "For post-processing results and visualization:\n",
+ "* `StatsBase.jl`\n",
+ "* `JSON.jl`\n",
+ "* `Plots.jl`"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "df94a35c",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stderr",
+ "output_type": "stream",
+ "text": [
+ "\u001b[33m\u001b[1m┌ \u001b[22m\u001b[39m\u001b[33m\u001b[1mWarning: \u001b[22m\u001b[39mThe project dependencies or compat requirements have changed since the manifest was last resolved.\n",
+ "\u001b[33m\u001b[1m│ \u001b[22m\u001b[39mIt is recommended to `Pkg.resolve()` or consider `Pkg.update()` if necessary.\n",
+ "\u001b[33m\u001b[1m└ \u001b[22m\u001b[39m\u001b[90m@ Pkg.API ~/.julia/juliaup/julia-1.11.5+0.aarch64.apple.darwin14/share/julia/stdlib/v1.11/Pkg/src/API.jl:1206\u001b[39m\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Download and install all packages specified in Project.toml\n",
+ "Pkg.instantiate()"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a13bff0e",
+ "metadata": {},
+ "source": [
+ "Up to this point, we have set up the Julia project environment to run the notebook. In order to run the workflow on IBM's quantum processing unit, an IBM Quantum account and API token are also required to instantiate Service from Qiskit IBM Runtime. Follow the \"Install and authenticate\" steps in the [IBM Quantum getting started guide](https://quantum.cloud.ibm.com/docs/en/guides/hello-world) to generate your API token and find your instance CRN — the account setup steps apply regardless of programming language."
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "613853a6",
+ "metadata": {},
+ "source": [
+ "## Setup"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "4ea0efac",
+ "metadata": {},
+ "outputs": [],
+ "source": [
+ "using Qiskit\n",
+ "using QiskitIBMRuntimeC\n",
+ "using StatsBase\n",
+ "using OrdinaryDiffEq\n",
+ "using SparseArrays\n",
+ "using LinearAlgebra\n",
+ "using TensorNetworkQuantumSimulator\n",
+ "using Dates\n",
+ "using JSON\n",
+ "using Plots\n",
+ "using Plots.PlotMeasures"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "5016929d",
+ "metadata": {},
+ "source": [
+ "We will also define the following utility function which returns the value of the bit in a bitstring `v` at position `i`. For example, with `v = 6` (binary `110`),\n",
+ "- `bit_at(6, 1)` returns `0`,\n",
+ "- `bit_at(6, 2)` returns `1`,\n",
+ "- `bit_at(6, 3)` returns `1`.\n",
+ "\n",
+ "This follows Qiskit's little endian convention, i.e., the position `i` is indexed from the least-significant (the \"rightmost\") bit."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "143aecbe",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "bit_at"
+ ]
+ },
+ "execution_count": 26,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "\"\"\"\n",
+ " bit_at(v::Integer, i::Integer) = (v >> (i-1)) & 1\n",
+ "\n",
+ "Return the value of the bit at position `i` in `v`.\n",
+ "\"\"\"\n",
+ "bit_at(v::Integer, i::Integer) = (v >> (i-1)) & 1"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "6a17088d",
+ "metadata": {},
+ "source": [
+ "## Small-scale simulator example\n",
+ "\n",
+ "We consider a 1D chain of $N$ qubits, described by the transverse-field Ising model above. For the system of interest, we specify below the system size `N`, the Trotter step size `δt`, and the total number of Trotter steps `r_max`. The total evolution time is `δt * r_max`. Note that Julia supports Unicode identifiers such as `δt`; in the notebook or Julia REPL, type `\\delta` followed by Tab to enter `δ`. For a full reference, see the [Julia Unicode input documentation](https://docs.julialang.org/en/v1/manual/unicode-input/).\n",
+ "\n",
+ "### Exact solution\n",
+ "To establish a baseline for comparing results from the quantum hardware, we first demonstrate the classical simulation workflow for a small-scale problem. We build the Ising Hamiltonian as a sparse matrix, then obtain the exact time evolution by numerically integrating the Schrödinger equation using `ODEProblem` from `OrdinaryDiffEq.jl`. This approach scales exponentially in the number of qubits $N$. It requires storing the full $2^N$-dimensional state vector. For $N=20$ the Hilbert space already has over one million dimensions, making it impractical for larger systems."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "aa6b4db3",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "1048576×1048576 SparseMatrixCSC{ComplexF64, Int64} with 22020096 stored entries:\n",
+ "⎡⣿⣿⣾⢦⡀⠳⣄⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎤\n",
+ "⎢⠺⣟⢻⣶⣿⡂⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⢤⡈⠻⠻⠿⣧⣤⣠⡈⠳⠄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠙⢦⡀⠀⣻⣿⣿⣙⣦⡀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠙⢦⡈⠳⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠙⢦⡀⠀⠀⠁⠀⠈⠈⠉⣿⣿⣾⢦⡀⠳⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠺⣟⢻⣶⣿⡂⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⢤⡈⠻⠻⠿⣧⣤⣠⡈⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⡀⠀⣻⣿⣿⣙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⡈⠳⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⎥\n",
+ "⎢⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢦⡈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⣿⣿⣯⠀⠈⠳⣄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡈⠋⠛⢻⣶⣦⣦⡈⠓⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠨⣿⠿⣧⣽⡦⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⢦⠈⠳⡿⣿⣿⣀⡀⡀⠀⢀⠀⠀⠈⠳⣄⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⢦⡈⠳⣄⠀⠀⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠈⠻⣍⣿⣿⣯⠀⠈⠳⣄⠀⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠐⢦⡈⠋⠛⢻⣶⣦⣦⡈⠓⎥\n",
+ "⎢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠙⢦⡀⠨⣿⠿⣧⣽⡦⎥\n",
+ "⎣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠙⢦⠈⠳⡿⣿⣿⎦"
+ ]
+ },
+ "execution_count": 4,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "N = 20\n",
+ "δt = 0.05 # Trotter step size\n",
+ "r_max = 10 # total number of Trotter steps\n",
+ "\n",
+ "h = fill(1.0, N)\n",
+ "J = fill(1.0, N-1)\n",
+ "\n",
+ "function build_ising_hamiltonian(h::Vector, J::Vector, n::Int)\n",
+ " dim = 2^n\n",
+ "\n",
+ " # diagonal ZZ terms\n",
+ " diag_terms = zeros(Float64, dim)\n",
+ " for i in 1:n-1\n",
+ " for b in 0:dim-1\n",
+ " bi = bit_at(b, i) # bit at position i\n",
+ " bi_next = bit_at(b, i+1) # bit at position i + 1\n",
+ " diag_terms[b+1] += J[i] * (1-2bi) * (1-2bi_next)\n",
+ " end\n",
+ " end\n",
+ " H = spdiagm(0 => complex(diag_terms))\n",
+ "\n",
+ " # off-diagonal local X terms\n",
+ " for i in 1:n\n",
+ " mask = 1 << (i-1)\n",
+ " cols = [xor(b, mask) + 1 for b in 0:dim-1]\n",
+ " H += h[i] * sparse(1:dim, cols, ones(ComplexF64, dim), dim, dim)\n",
+ " end\n",
+ " return H\n",
+ "end\n",
+ "\n",
+ "H_ising = build_ising_hamiltonian(h, J, N)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "bbe38420",
+ "metadata": {},
+ "source": [
+ "We define the right-hand side of the Schrödinger equation in the in-place form `schrodinger!(dψ, ψ, H, t)`, which computes $d\\psi/dt = -iH\\psi$ using a sparse matrix-vector multiplication. We then set up an `ODEProblem` with the Néel state as the initial condition and solve it over the time span $[0, r \\cdot \\delta t]$, saving the state at each time step $\\delta t$. The solver used is `Tsit5()`, a standard explicit 4th/5th-order Runge-Kutta method suitable for non-stiff problems."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "959f77e9",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "retcode: Success\n",
+ "Interpolation: 1st order linear\n",
+ "t: 11-element Vector{Float64}:\n",
+ " 0.0\n",
+ " 0.05\n",
+ " 0.1\n",
+ " 0.15\n",
+ " 0.2\n",
+ " 0.25\n",
+ " 0.3\n",
+ " 0.35\n",
+ " 0.4\n",
+ " 0.45\n",
+ " 0.5\n",
+ "u: 11-element Vector{Vector{ComplexF64}}:\n",
+ " [0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im … 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im, 0.0 + 0.0im]\n",
+ " [-8.447198152606215e-14 + 8.551269476709602e-30im, 8.452613704293039e-14 - 1.798092880310424e-12im, -1.083059452476694e-16 + 3.807165445547495e-15im, -8.452616757829304e-14 - 1.2684837509562956e-15im, 1.6905229445367383e-13 - 1.7942825729563814e-12im, 3.686879554841385e-11 + 5.3942753560200465e-12im, -8.441779547549441e-14 - 5.078648506287416e-15im, 8.452616758772015e-14 - 1.7980927376219225e-12im, -1.0836194633904448e-16 + 3.8093089835689296e-15im, -8.439610286431264e-14 - 6.349847282668091e-15im … -8.420097996175948e-14 - 8.886670419764126e-15im, 1.6905232499846317e-13 - 1.794282572013269e-12im, -5.4155517237564695e-17 + 3.810165765655752e-15im, -8.447198662231154e-14 - 5.080792111641971e-15im, 1.6247166441264587e-16 + 6.4275606486265795e-18im, -1.0836194596930011e-16 + 3.809308983571259e-15im, -8.447197643886808e-14 - 3.810164822661854e-15im, 1.6905229954179186e-13 - 1.7942827156449086e-12im, -5.4155516867796697e-17 + 3.808022070471655e-15im, -8.447198152606218e-14 - 6.199887719107612e-29im]\n",
+ " [-8.542585712438249e-11 + 1.9929101268716206e-26im, 8.569125285284879e-11 - 8.635067812751866e-10im, -5.306424302864609e-13 + 8.328123827513827e-12im, -8.569214822372148e-11 - 2.769424302035447e-12im, 1.7138310559601293e-10 - 8.551423278653412e-10im, 8.39199218333215e-9 + 2.5904823474669143e-9im, -8.515956647862476e-11 - 1.1132244075358072e-11im, 8.569215079628697e-11 - 8.63505140242374e-10im, -5.322892899226488e-13 + 8.353003341597956e-12im, -8.505251313504091e-11 - 1.3933172316791102e-11im … -8.409229768005623e-11 - 1.9470241911381096e-11im, 1.71384003543064e-10 - 8.551422499844646e-10im, -2.6539582878806465e-13 + 8.362903008236219e-12im, -8.542600827593182e-11 - 1.1157129107141602e-11im, 7.963431233947527e-13 + 7.43870020751736e-14im, -5.322891894826147e-13 + 8.353003344887579e-12im, -8.542570845011376e-11 - 8.36282528772974e-12im, 1.7138325452216785e-10 - 8.551439688989101e-10im, -2.653957284666945e-13 + 8.338010545110564e-12im, -8.542585712438258e-11 + 2.627361551401706e-26im]\n",
+ " [-4.303405333965998e-9 - 5.193630550605571e-24im, 4.335919445889365e-9 - 2.830382424300664e-8im, -6.498069885582034e-11 + 6.504076362362121e-10im, -4.336205744540504e-9 - 2.1550356498433456e-10im, 8.672032579234898e-9 - 2.764630624190242e-8im, 1.7283135071236338e-7 + 8.490403097958473e-8im, -4.270605352165285e-9 - 8.727078958709279e-10im, 4.336208182705919e-9 - 2.8303506579709142e-8im, -6.551064529705039e-11 + 6.553146447470977e-10im, -4.257311049335466e-9 - 1.09442154260546e-9im … -4.138721218175993e-9 - 1.5250366228861508e-9im, 8.672321329580106e-9 - 2.764626391998368e-8im, -3.25142054699411e-11 + 6.572493036705701e-10im, -4.303454890254258e-9 - 8.776178471225664e-10im, 9.759641300111312e-11 + 1.4585132876705085e-11im, -6.551055131286663e-11 + 6.55314650464077e-10im, -4.303358140965984e-9 - 6.572072678851363e-10im, 8.67208001005786e-9 - 2.764662390651905e-8im, -3.25141119233684e-11 + 6.523352973843646e-10im, -4.303405333965988e-9 + 2.8545025130761877e-24im]\n",
+ " [-6.083199966007407e-8 - 9.540245785861004e-23im, 6.16722818774796e-8 - 2.958810995196636e-7im, -1.6782947014076044e-9 + 1.24288974064075e-8im, -6.168600513165e-8 - 4.097156349668386e-9im, 1.233539699746149e-7 - 2.832024612353697e-7im, 1.252933004842736e-6 + 8.873816782202638e-7im, -5.997803315172046e-8 - 1.6765068984299418e-8im, 6.168622745316284e-8 - 2.958701102717921e-7im, -1.7039157218198832e-9 + 1.2603072756863413e-8im, -5.962792484875573e-8 - 2.1082486711325728e-8im … -5.652866530611903e-8 - 2.9260908273130446e-8im, 1.233679180212103e-7 - 2.8319964249863656e-7im, -8.402905669842858e-10 + 1.2670885091139626e-8im, -6.083445670086162e-8 - 1.6939435453712348e-8im, 2.523714073069501e-9 + 5.135457980423157e-10im, -1.7039072937245032e-9 + 1.260307346580212e-8im, -6.082975996233972e-8 - 1.2668103038228729e-8im, 1.2335623124766002e-7 - 2.8321345064677676e-7im, -8.40282217405561e-10 + 1.2496247175220009e-8im, -6.083199966007414e-8 + 8.196459109639649e-23im]\n",
+ " [-4.1925039215386654e-7 + 2.677460600678109e-22im, 4.285318172936476e-7 - 1.6047893295112335e-6im, -1.8522719720643802e-8 + 1.0858038020469898e-7im, -4.2877562523585216e-7 - 3.5548593734905984e-8im, 8.572335916432149e-7 - 1.4927112809364224e-6im, 4.848221310265979e-6 + 4.810699752103751e-6im, -4.0972627660257283e-7 - 1.4748177040290743e-7im, 4.2878203032358745e-7 - 1.6046384831470835e-6im, -1.8982996464234093e-8 + 1.1105352498078254e-7im, -4.057614080752629e-7 - 1.8615483937396652e-7im … -3.710180491512003e-7 - 2.569903126546681e-7im, 8.574839228294255e-7 - 1.4926466432762158e-6im, -9.281659171705513e-9 + 1.1200067005267184e-7im, -4.1929599616947026e-7 - 1.4995915650948877e-7im, 2.7901633489406097e-8 + 7.215569826549181e-9im, -1.8982758758906585e-8 + 1.1105355018381482e-7im, -4.192111181964125e-7 - 1.1193739241623215e-7im, 8.572734830263881e-7 - 1.4928621331129255e-6im, -9.281425139782206e-9 + 1.0951702287304549e-7im, -4.192503921538662e-7 + 2.661345043815625e-23im]\n",
+ " [-1.7817651554513163e-6 - 4.180501251498204e-22im, 1.8402335629865725e-6 - 5.568890720784772e-6im, -1.1656437057998571e-7 + 5.63053819766895e-7im, -1.8425103652721044e-6 - 1.8270531202207626e-7im, 3.682088247811752e-6 - 4.978997351832734e-6im, 1.1824907850927261e-5 + 1.6678485694702425e-5im, -1.7210354017969e-6 - 7.715388675442235e-7im, 1.8425994685783273e-6 - 5.567762625020958e-6im, -1.209233455197462e-7 + 5.823643699480997e-7im, -1.6952491076773805e-6 - 9.78610899497098e-7im … -1.4722034878691387e-6 - 1.3416293435467407e-6im, 3.6844566640986107e-6 - 4.978247294205355e-6im, -5.847155042780926e-8 + 5.896070272308257e-7im, -1.7822151187493028e-6 - 7.908966120354e-7im, 1.7601746209747826e-7 + 5.5595988528799426e-8im, -1.209201267760062e-7 + 5.823647800580671e-7im, -1.7814044723225213e-6 - 5.888803302922145e-7im, 3.6824574441818106e-6 - 4.980125542149313e-6im, -5.846840753528626e-8 + 5.701761719748441e-7im, -1.781765155451315e-6 + 8.623497000558872e-22im]\n",
+ " [-5.271556176203792e-6 - 7.49861285367763e-21im, 5.515281172948297e-6 - 1.377059415567794e-5im, -4.852845888355539e-7 + 1.9836337932952575e-6im, -5.528622145891747e-6 - 6.363949532395746e-7im, 1.1040309690470572e-5 - 1.1654162722487635e-5im, 1.915715819195639e-5 + 4.117210952884277e-5im, -5.0146169282898706e-6 - 2.7478986873213113e-6im, 5.5293581250209145e-6 - 1.3765189822055999e-5im, -5.112684948147294e-7 + 2.081245160683002e-6im, -4.902764641122375e-6 - 3.507285521843372e-6im … -3.9507324874193736e-6 - 4.765869677224743e-6im, 1.1054416732747048e-5 - 1.1648824840323625e-5im, -2.437498364252954e-7 + 2.1169241933748807e-6im, -5.274376086001212e-6 - 2.845828783634021e-6im, 7.353223852567491e-7 + 2.7647107507387665e-7im, -5.112427791560938e-7 + 2.081248969040159e-6im, -5.269486324617225e-6 - 2.1118185275908083e-6im, 1.1042449053634926e-5 - 1.1659567933855285e-5im, -2.4372499674447915e-7 + 2.018470625295779e-6im, -5.271556176203793e-6 + 1.7209000235047736e-20im]\n",
+ " [-1.1618646186431486e-5 + 5.233521846484844e-21im, 1.2350171711697867e-5 - 2.574554532195816e-5im, -1.4543215666068316e-6 + 5.123970161431332e-6im, -1.2404477846976538e-5 - 1.620365060187081e-6im, 2.4741267389821994e-5 - 2.015652026305624e-5im, 1.9141869485564655e-5 + 7.674672015038458e-5im, -1.0833508462252628e-5 - 7.193477030308175e-6im, 1.2408545868337687e-5 - 2.5727362734969932e-5im, -1.562305741475959e-6 + 5.474798582528361e-6im, -1.0480946680993082e-5 - 9.255154022783992e-6im … -7.538345968459838e-6 - 1.2435897348750635e-5im, 2.479987472814011e-5 - 2.013047817105541e-5im, -7.316555787305937e-7 + 5.599068773640798e-6im, -1.1631089870058428e-5 - 7.54576342467153e-6im, 2.214269432895923e-6 + 9.741574698716366e-7im, -1.562169208445682e-6 + 5.474821495984485e-6im, -1.1610434114128265e-5 - 5.574545959458894e-6im, 2.4749858042645256e-5 - 2.0174708129239346e-5im, -7.315255252662917e-7 + 5.24421553420276e-6im, -1.1618646186431457e-5 + 2.1495938600676603e-21im]\n",
+ " [-1.9810892562955863e-5 + 2.6563290838882735e-21im, 2.1471103943211705e-5 - 3.756889823565732e-5im, -3.2945107550531108e-6 + 1.013804349590116e-5im, -2.1634260467349484e-5 - 3.147801224677167e-6im, 4.3069770508492815e-5 - 2.621309035844639e-5im, 4.771848300292048e-6 + 0.00011142181244930624im, -1.799025340359317e-5 - 1.4466183637177169e-5im, 2.16504459545483e-5 - 3.7523595478996604e-5im, -3.6270994457264773e-6 + 1.1085999584280634e-5im, -1.7140754048084706e-5 - 1.8804196986586844e-5im … -1.021469258325402e-5 - 2.4909710894472004e-5im, 4.325038734181345e-5 - 2.6119885929391285e-5im, -1.6606955241263973e-6 + 1.1409217134286393e-5im, -1.9852053608017645e-5 - 1.541896070874341e-5im, 5.050201856207086e-6 + 2.5698844144095232e-6im, -3.6265818903201203e-6 + 1.1086096022793172e-5im, -1.97869872654681e-5 - 1.1323100777445457e-5im, 4.309515374843075e-5 - 2.6258415326241147e-5im, -1.6602113802557154e-6 + 1.0447225917844316e-5im, -1.9810892562955852e-5 + 1.6983937095323886e-21im]\n",
+ " [-2.6605214427338516e-5 - 6.180799465720513e-20im, 2.9531446475580105e-5 - 4.3337099198844914e-5im, -5.793846580656099e-6 + 1.5720190535815128e-5im, -2.9906142754527473e-5 - 4.767705782738602e-6im, 5.936891953776828e-5 - 2.5156729741187773e-5im, -2.1872711224392463e-5 + 0.00012741205276715139im, -2.331232564161358e-5 - 2.288276752511159e-5im, 2.9954542216375753e-5 - 4.325107358148504e-5im, -6.580704817067804e-6 + 1.7709282874923144e-5im, -2.1701730895550637e-5 - 3.014284801145639e-5im … -8.925842492154665e-6 - 3.921199970948722e-5im, 5.979719796491406e-5 - 2.4901895630642944e-5im, -2.927566307844948e-6 + 1.8356788062284654e-5im, -2.671116254264494e-5 - 2.4883818971586353e-5im, 8.96796918836386e-6 + 5.238539136970021e-6im, -6.579244391007846e-6 + 1.7709579495160987e-5im, -2.6552409636898105e-5 - 1.8126698440020543e-5im, 5.942603691652531e-5 - 2.524282365146583e-5im, -2.9262320482414796e-6 + 1.6330559522508323e-5im, -2.660521442733849e-5 - 5.198273955187834e-20im]"
+ ]
+ },
+ "execution_count": 5,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# initial state |0101...01⟩\n",
+ "ψ0 = zeros(ComplexF64, 2^N)\n",
+ "neel_index = sum(1 << (i-1) for i in 1:2:N)\n",
+ "ψ0[neel_index + 1] = 1.0\n",
+ "\n",
+ "function schrodinger!(dψ, ψ, H, t)\n",
+ " mul!(dψ, H, ψ)\n",
+ " dψ .*= -im\n",
+ "end\n",
+ "\n",
+ "tspan = (0.0, r_max * δt)\n",
+ "prob = ODEProblem(schrodinger!, ψ0, tspan, H_ising)\n",
+ "sol = solve(prob, Tsit5(), saveat=δt)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "8054932d",
+ "metadata": {},
+ "source": [
+ "From the solution which describes the state vector $\\psi(t)$, we can obtain the magnetization per site, expressed as the single-qubit $\\langle Z\\rangle$ expectation values as a function of time. We will compare this with the results obtained from the trotterized circuits."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "27b209db",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11×20 Matrix{Float64}:\n",
+ " -1.0 1.0 -1.0 1.0 … 1.0 -1.0 1.0\n",
+ " -0.995009 0.995022 -0.995022 0.995022 0.995022 -0.995022 0.995009\n",
+ " -0.980214 0.98041 -0.98041 0.98041 0.98041 -0.98041 0.980214\n",
+ " -0.955737 0.956712 -0.956712 0.956712 0.956712 -0.956712 0.955737\n",
+ " -0.922329 0.92532 -0.925321 0.925321 0.925321 -0.92532 0.922329\n",
+ " -0.880651 0.887676 -0.887679 0.887679 … 0.887679 -0.887676 0.880651\n",
+ " -0.831446 0.845337 -0.84535 0.84535 0.84535 -0.845337 0.831446\n",
+ " -0.775847 0.800169 -0.800211 0.800211 0.800211 -0.800169 0.775847\n",
+ " -0.714946 0.753787 -0.753898 0.753898 0.753898 -0.753787 0.714946\n",
+ " -0.649935 0.707714 -0.707977 0.707978 0.707977 -0.707714 0.649935\n",
+ " -0.579691 0.660741 -0.661309 0.661309 … 0.661309 -0.660741 0.579691"
+ ]
+ },
+ "execution_count": 6,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function z_expval_from_state(ψ, qubit::Int, n::Int)\n",
+ " s = 0.0\n",
+ " for b in 0:2^n-1\n",
+ " bit = bit_at(b, qubit)\n",
+ " s += (1 - 2bit) * abs2(ψ[b+1])\n",
+ " end\n",
+ " return s\n",
+ "end\n",
+ "\n",
+ "classical_magnetizations = [z_expval_from_state(sol.u[r+1], q, N)\n",
+ " for r in 0:r_max, q in 1:N]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "c3568ea2",
+ "metadata": {},
+ "source": [
+ "### Small-scale simulation of the Trotterized circuits\n",
+ "\n",
+ "In the following, we show the classical simulation of the noiseless circuits using tensor network methods supported by `TensorNetworkQuantumSimulator.jl`. This allows us to validate our circuit construction and provides a baseline to compare with results from the quantum hardware.\n",
+ "\n",
+ "We first define the lattice as a 1D chain graph using `named_grid((N,))`, where each vertex is a tuple `(i,)`. We then specify the circuit gates as a list of tuples `(gate_name, qubit_indices, gate_parameter)`, which serves as the input format for the tensor network simulator."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "47e7b661",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "make_trotter_circuit_tn (generic function with 1 method)"
+ ]
+ },
+ "execution_count": 7,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# 1D chain graph — vertices are named (1,), (2,), ..., (N,)\n",
+ "g = named_grid((N,))\n",
+ "s = siteinds(\"S=1/2\", g)\n",
+ "\n",
+ "function make_trotter_circuit_tn(h::Vector, J::Vector, n::Int, δt::Float64, n_trotter_steps::Int)\n",
+ " circuit = []\n",
+ "\n",
+ " # Neel state initialization\n",
+ " append!(circuit, [(\"X\", [(i,)]) for i in 1:2:n])\n",
+ "\n",
+ " for _ in 1:n_trotter_steps\n",
+ " # first half X rotation\n",
+ " append!(circuit, [(\"Rx\", [(i,)], h[i]* δt / 2) for i in 1:n])\n",
+ " # ZZ interactions\n",
+ " append!(circuit, [(\"Rzz\", [(i,), (i+1,)], 2 * J[i] * δt) for i in 1:n-1])\n",
+ " # second half X rotation\n",
+ " append!(circuit, [(\"Rx\", [(i,)], h[i] * δt / 2) for i in 1:n])\n",
+ " end\n",
+ "\n",
+ " return circuit\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "2425014b",
+ "metadata": {},
+ "source": [
+ "We use the belief propagation algorithm for tensor network contraction. This method is efficient for circuits with limited entanglement, but its accuracy degrades as entanglement grows with circuit depth. The `maxdim` and `cutoff` parameters control the trade-off between accuracy and computational cost. Similarly, we compute the magnetization at each site to compare later."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5e3ea2c3",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "fidelity at trotter step 0 was 1.0\n",
+ "fidelity at trotter step 1 was 1.0\n",
+ "fidelity at trotter step 2 was 1.0\n",
+ "fidelity at trotter step 3 was 1.0\n",
+ "fidelity at trotter step 4 was 0.9999999999999906\n",
+ "fidelity at trotter step 5 was 0.9999999999997938\n",
+ "fidelity at trotter step 6 was 0.9999999999975266\n",
+ "fidelity at trotter step 7 was 0.9999999999804221\n",
+ "fidelity at trotter step 8 was 0.9999999998846302\n",
+ "fidelity at trotter step 9 was 0.9999999994549151\n",
+ "fidelity at trotter step 10 was 0.9999999980378083\n"
+ ]
+ }
+ ],
+ "source": [
+ "apply_kwargs = (; maxdim=32, cutoff=1e-10, normalize_tensors=true)\n",
+ "tn_magnetizations = zeros(r_max+1, N)\n",
+ "fidelities = []\n",
+ "for r in 0:r_max\n",
+ " circuit = make_trotter_circuit_tn(h, J, N, δt, r)\n",
+ " # initial state\n",
+ " ψ = tensornetworkstate(ComplexF32, v -> \"↑\", g, \"S=1/2\")\n",
+ " ψ_bpc = BeliefPropagationCache(ψ)\n",
+ " ψ_bpc, errs = apply_gates(circuit, ψ_bpc; apply_kwargs)\n",
+ " fidelity = prod(1.0 .- errs)\n",
+ " println(\"fidelity at trotter step $(r) was $(fidelity)\")\n",
+ " push!(fidelities, fidelity)\n",
+ "\n",
+ " for q in 1:N\n",
+ " tn_magnetizations[r+1, q] = real(expect(ψ_bpc, [(\"Z\", [(q,)])])[1])\n",
+ " end\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "aeb0878b",
+ "metadata": {},
+ "source": [
+ "### Step 1: Map classical inputs to a quantum problem\n",
+ "\n",
+ "Now we construct the trotterized time-evolution circuit using `Qiskit.jl`. The circuit mirrors the tensor network version: it initializes the Néel state, applies $r$ Trotter steps of $R_x$ and $R_{ZZ}$ gates, and finally measures all qubits in the Z basis."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "6b680069",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048de81a00, 1)"
+ ]
+ },
+ "execution_count": 9,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function make_trotter_circuit(h::Vector, J::Vector, n::Int, δt::Float64, n_trotter_steps::Int)\n",
+ " qc = QuantumCircuit(n, n)\n",
+ "\n",
+ " # Neel state initialization\n",
+ " for i in 1:2:n\n",
+ " qc.x(i)\n",
+ " end\n",
+ "\n",
+ " # trotter evolution\n",
+ " for _ in 1:n_trotter_steps\n",
+ " for i in 1:n\n",
+ " qc.rx(h[i] * δt / 2, i)\n",
+ " end\n",
+ "\n",
+ " for i in 1:n-1\n",
+ " qc.rzz(2* J[i] * δt, i, i+1)\n",
+ " end\n",
+ "\n",
+ " for i in 1:n\n",
+ " qc.rx(h[i] * δt / 2, i)\n",
+ " end\n",
+ " end\n",
+ "\n",
+ " # measure in Z basis\n",
+ " for i in 1:n\n",
+ " qc.measure(i, i)\n",
+ " end\n",
+ " return qc\n",
+ "end\n",
+ "\n",
+ "\n",
+ "qc = make_trotter_circuit(h, J, N, δt, 1)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "7a7e4d8f",
+ "metadata": {},
+ "source": [
+ "We build a list of circuits for Trotter steps 0 through 10, corresponding to evolution times $\\tau = 0, \\delta t, 2\\delta t, \\ldots, 10\\delta t$."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "704485a7",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11-element Vector{QuantumCircuit}:\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047c8b7400, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047cd52800, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048d4b5400, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047cd85400, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047cee7a00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048d53bc00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047caeec00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048d79de00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047c93c600, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047c88c000, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000047c846600, 1)"
+ ]
+ },
+ "execution_count": 10,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# prepare a list of circuits with different trotter steps\n",
+ "qc_list = [make_trotter_circuit(h, J, N, δt, r) for r in 0:r_max]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "3b7100d9",
+ "metadata": {},
+ "source": [
+ "### Step 2: Optimize problem for quantum hardware execution\n",
+ "\n",
+ "To run on quantum hardware, the circuits must first be transpiled. This includes: selecting a set of physical qubits to map the circuit onto, recompiling the gates into the native instruction set of the backend, and optimizing the resulting circuit depth. We use `least_busy()` to automatically select the least-busy available backend, `target_from_backend()` to retrieve its native gate set and qubit connectivity, and `transpile()` to perform the compilation."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "32354a49",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "backend.name = \"ibm_pittsburgh\"\n"
+ ]
+ },
+ {
+ "data": {
+ "text/plain": [
+ "\"ibm_pittsburgh\""
+ ]
+ },
+ "execution_count": 11,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "service = Service()\n",
+ "search_results = backend_search(service)\n",
+ "backend = least_busy(search_results)\n",
+ "@show backend.name"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "14205fe7",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Qiskit.Target(Ptr{Qiskit.C.LibQiskit.QkTarget} @0x00000004ac683c60)"
+ ]
+ },
+ "execution_count": 12,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "target = target_from_backend(backend, service)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8828900e",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11-element Vector{QuantumCircuit}:\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x00000004a6f8fe00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000014b846c00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000014bd2e600, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000014aaeec00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000014bd64a00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000014ae75200, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x0000000380d6fe00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048d844a00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000048def9a00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x000000012a9d3c00, 1)\n",
+ " QuantumCircuit(Ptr{Qiskit.C.LibQiskit.QkCircuit} @0x00000004a755b200, 1)"
+ ]
+ },
+ "execution_count": 13,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "tqc_list = [transpile(qc, target)[1] for qc in qc_list]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "501e8dc5",
+ "metadata": {},
+ "source": [
+ "After transpilation, we inspect two properties of the compiled circuits. `get_circuit_layout()` returns the set of physical qubit indices selected for the circuit. `two_qubit_depth()` computes the two-qubit gate depth — the length of the longest chain of the two-qubit operations in the circuit — which is a useful indicator of noise accumulation on the hardware."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "bf4c910c",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "Set{Int64} with 20 elements:\n",
+ " 52\n",
+ " 72\n",
+ " 24\n",
+ " 17\n",
+ " 47\n",
+ " 49\n",
+ " 69\n",
+ " 3\n",
+ " 51\n",
+ " 25\n",
+ " 46\n",
+ " 71\n",
+ " 48\n",
+ " 59\n",
+ " 4\n",
+ " 50\n",
+ " 70\n",
+ " 2\n",
+ " 38\n",
+ " 26"
+ ]
+ },
+ "execution_count": 14,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "function get_circuit_layout(tqc::QuantumCircuit)\n",
+ " return Set(q for inst in tqc.data for q in inst.qubits)\n",
+ "end\n",
+ "\n",
+ "get_circuit_layout(tqc_list[2])"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "5fa03372",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "r=0: 2q depth=0\n",
+ "r=1: 2q depth=38\n",
+ "r=2: 2q depth=42\n",
+ "r=3: 2q depth=46\n",
+ "r=4: 2q depth=50\n",
+ "r=5: 2q depth=54\n",
+ "r=6: 2q depth=58\n",
+ "r=7: 2q depth=62\n",
+ "r=8: 2q depth=66\n",
+ "r=9: 2q depth=70\n",
+ "r=10: 2q depth=74\n"
+ ]
+ }
+ ],
+ "source": [
+ "function two_qubit_depth(qc::QuantumCircuit)\n",
+ " qubit_depth = Dict{Int,Int}()\n",
+ " for inst in qc.data\n",
+ " length(inst.qubits) == 2 || continue # skip non-two-qubit gates\n",
+ " d = maximum(get(qubit_depth, q, 0) for q in inst.qubits)\n",
+ " for q in inst.qubits\n",
+ " qubit_depth[q] = d + 1\n",
+ " end\n",
+ " end\n",
+ " return isempty(qubit_depth) ? 0 : maximum(values(qubit_depth))\n",
+ "end\n",
+ "\n",
+ "for (i, tqc) in enumerate(tqc_list)\n",
+ " println(\"r=$(i-1): 2q depth=$(two_qubit_depth(tqc))\")\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "37aabbc8",
+ "metadata": {},
+ "source": [
+ "### Step 3: Execute using Qiskit primitives\n",
+ "\n",
+ "Now, we can submit the transpiled circuits to the backend as `Sampler` jobs with `shots` specified."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "7bcdead5",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11-element Vector{QiskitIBMRuntimeC.Job}:\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004aa1fb0f0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004aa15e690)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b2ce070)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b2c6f10)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000012e484f70)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b27e990)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b1a5590)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b267fe0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b1a71f0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004accf53d0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000035655a9b0)"
+ ]
+ },
+ "execution_count": 16,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "shots = 1024\n",
+ "job_list = [run_sampler_job(service, backend, tqc, shots) for tqc in tqc_list]"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "cc9cc9c5",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11-element Vector{QiskitIBMRuntimeC.Job}:\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004aa1fb0f0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004aa15e690)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b2ce070)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b2c6f10)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000012e484f70)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b27e990)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b1a5590)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b267fe0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000014b1a71f0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x00000004accf53d0)\n",
+ " QiskitIBMRuntimeC.Job(Ptr{QiskitIBMRuntimeC.LibQiskitIBMRuntime.Job} @0x000000035655a9b0)"
+ ]
+ },
+ "execution_count": 17,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "job_list"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "9bca942a",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Job 1: Completed\n",
+ "Job 2: Completed\n",
+ "Job 3: Completed\n",
+ "Job 4: Completed\n",
+ "Job 5: Completed\n",
+ "Job 6: Completed\n",
+ "Job 7: Completed\n",
+ "Job 8: Completed\n",
+ "Job 9: Completed\n",
+ "Job 10: Completed\n",
+ "Job 11: Completed\n"
+ ]
+ }
+ ],
+ "source": [
+ "for (i, job) in enumerate(job_list)\n",
+ " status = get_job_status(job, service)\n",
+ " println(\"Job $i: \", status)\n",
+ "end"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "f1429d09",
+ "metadata": {},
+ "source": [
+ "As the jobs are completed, we can retrieve their results. Note that `get_job_results` function will block until the job is completed."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e8f81320",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11-element Vector{QiskitIBMRuntimeC.Samples}:\n",
+ " [\"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x54155\", \"0x55555\" … \"0x55555\", \"0x55554\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\"]\n",
+ " [\"0x55555\", \"0x55555\", \"0x55555\", \"0x14555\", \"0x55655\", \"0x55555\", \"0x55515\", \"0x55555\", \"0x55155\", \"0x55558\" … \"0x55555\", \"0x55555\", \"0x55555\", \"0x55545\", \"0x55555\", \"0x55555\", \"0x55554\", \"0x55515\", \"0x55551\", \"0x55553\"]\n",
+ " [\"0x55555\", \"0x55555\", \"0x50555\", \"0x55555\", \"0x55555\", \"0x45555\", \"0x4d555\", \"0x55555\", \"0x45555\", \"0x15555\" … \"0x55555\", \"0x55155\", \"0x55555\", \"0x55555\", \"0x15555\", \"0x55555\", \"0x55555\", \"0x75555\", \"0x55551\", \"0x555d5\"]\n",
+ " [\"0x55555\", \"0x4d555\", \"0x65555\", \"0x55555\", \"0x55551\", \"0x55551\", \"0x55545\", \"0x55555\", \"0x55555\", \"0x55555\" … \"0x55555\", \"0x65515\", \"0x55555\", \"0x55551\", \"0x55555\", \"0x55555\", \"0x4d555\", \"0x95555\", \"0x55555\", \"0x55555\"]\n",
+ " [\"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55555\", \"0x55554\", \"0x75555\", \"0x55555\", \"0x55555\", \"0x55505\" … \"0x55555\", \"0x55555\", \"0x54555\", \"0xd5555\", \"0x55555\", \"0x75555\", \"0x57545\", \"0x75555\", \"0x55755\", \"0x55554\"]\n",
+ " [\"0x55155\", \"0x54515\", \"0x55555\", \"0x55555\", \"0x75555\", \"0x55155\", \"0x75155\", \"0x75555\", \"0x75555\", \"0x55555\" … \"0x55555\", \"0x55155\", \"0x55155\", \"0x75551\", \"0x75515\", \"0x555d5\", \"0x5554d\", \"0x55555\", \"0x15455\", \"0x55575\"]\n",
+ " [\"0x55555\", \"0x5555d\", \"0x55557\", \"0x55555\", \"0x55551\", \"0x75557\", \"0x75555\", \"0x511d5\", \"0x55455\", \"0x45455\" … \"0x75555\", \"0x74555\", \"0x74f55\", \"0x75555\", \"0x55d55\", \"0x55554\", \"0x55151\", \"0x55555\", \"0x775d5\", \"0x5b555\"]\n",
+ " [\"0x55d14\", \"0x1d951\", \"0x54d55\", \"0x55555\", \"0x71555\", \"0x55345\", \"0x75545\", \"0x55551\", \"0x5595d\", \"0x75751\" … \"0x75114\", \"0x45d51\", \"0x75541\", \"0x75975\", \"0x75555\", \"0x34558\", \"0x71554\", \"0x55555\", \"0x75555\", \"0x55755\"]\n",
+ " [\"0x75554\", \"0x75551\", \"0x52565\", \"0x5a55d\", \"0x45554\", \"0x55155\", \"0x71d55\", \"0x75555\", \"0x55955\", \"0x755dd\" … \"0x7515d\", \"0x75d55\", \"0x55155\", \"0x5551d\", \"0x75d55\", \"0x75d55\", \"0xd5555\", \"0x55155\", \"0x9551d\", \"0x75751\"]\n",
+ " [\"0x77555\", \"0x55555\", \"0x55555\", \"0x7d515\", \"0x75155\", \"0x5d155\", \"0x55555\", \"0x57455\", \"0x71245\", \"0x75555\" … \"0x45955\", \"0x71755\", \"0x5411d\", \"0x7f155\", \"0x71155\", \"0x74955\", \"0x55555\", \"0x55514\", \"0x74145\", \"0xb5151\"]\n",
+ " [\"0x75155\", \"0x75574\", \"0x75755\", \"0xb9545\", \"0x54155\", \"0x5557f\", \"0x75555\", \"0x75564\", \"0x55154\", \"0x55555\" … \"0x45755\", \"0x75155\", \"0x55955\", \"0x75555\", \"0x35555\", \"0x55554\", \"0x75155\", \"0x55555\", \"0x44555\", \"0x75745\"]"
+ ]
+ },
+ "execution_count": 21,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "all_samples = [get_job_results(job, service) for job in job_list]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "64b46f68",
+ "metadata": {},
+ "source": [
+ "### Step 4: Post-process and return result in desired classical format\n",
+ "\n",
+ "The hardware returns measurement outcomes in hexadecimal format. We define `hex_to_bitstrings()` to decode each hex value into a bitstring of length $N$. The `save_counts()` function aggregates the raw samples into a bitstring-to-count dictionary using `countmap()`, then writes the result to a JSON file on disk."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "e9dd9a79",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "\"0001\""
+ ]
+ },
+ "execution_count": 22,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# from hex to bitstrings\n",
+ "function hex_to_bitstrings(s::String, n::Int)\n",
+ " val = parse(Int, replace(s, \"0x\" => \"\"), base=16)\n",
+ " join([bit_at(val, i) for i in 1:n])\n",
+ "end\n",
+ "\n",
+ "hex_to_bitstrings(\"0x8\", 4)"
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "8ad39f14",
+ "metadata": {},
+ "outputs": [
+ {
+ "name": "stdout",
+ "output_type": "stream",
+ "text": [
+ "Saved to results/counts_N=20_2026-05-29_215923.json\n"
+ ]
+ }
+ ],
+ "source": [
+ "# Save counts\n",
+ "function save_counts(all_samples::Vector{QiskitIBMRuntimeC.Samples}, N::Int; dir::String=\"results\")\n",
+ " mkpath(dir)\n",
+ " all_counts = [Dict(hex_to_bitstrings(k, N) => v for (k, v) in countmap(s)) for s in all_samples]\n",
+ "\n",
+ " date_str = Dates.format(Dates.now(), \"yyyy-mm-dd_HHMMSS\")\n",
+ " open(joinpath(dir, \"counts_N=$(N)_$(date_str).json\"), \"w\") do f\n",
+ " JSON.print(f, all_counts, 2)\n",
+ " end\n",
+ " println(\"Saved to $(joinpath(dir, \"counts_N=$(N)_$(date_str).json\"))\")\n",
+ "end\n",
+ "\n",
+ "save_counts(all_samples, N)"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "91a52002",
+ "metadata": {},
+ "source": [
+ "From the bitstring samples obtained from the quantum hardware, we compute the magnetization per site (i.e., the single-qubit $\\langle Z\\rangle$ expectation values) by averaging $(-1)^{b_i}$ over all shots, where $b_i$ is the measured bit for qubit $i$. We then plot the magnetization as a heatmap over qubits and Trotter steps, comparing the three methods side by side: exact classical simulation, noiseless tensor network simulation, and hardware execution."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "c74b479d",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "text/plain": [
+ "11×20 Matrix{Float64}:\n",
+ " -0.974609 1.0 -0.988281 1.0 … 0.996094 -0.998047 1.0\n",
+ " -0.957031 0.955078 -0.931641 0.980469 0.957031 -0.910156 0.964844\n",
+ " -0.945312 0.931641 -0.873047 0.935547 0.943359 -0.865234 0.966797\n",
+ " -0.933594 0.947266 -0.902344 0.941406 0.9375 -0.884766 0.9375\n",
+ " -0.90625 0.951172 -0.894531 0.929688 0.720703 -0.916016 0.970703\n",
+ " -0.914062 0.970703 -0.867188 0.898438 … 0.527344 -0.914062 0.962891\n",
+ " -0.876953 0.923828 -0.800781 0.898438 0.339844 -0.904297 0.964844\n",
+ " -0.8125 0.912109 -0.773438 0.875 0.246094 -0.855469 0.949219\n",
+ " -0.828125 0.931641 -0.748047 0.869141 0.148438 -0.820312 0.943359\n",
+ " -0.804688 0.929688 -0.857422 0.785156 0.0253906 -0.824219 0.933594\n",
+ " -0.753906 0.90625 -0.816406 0.818359 … -0.107422 -0.791016 0.941406"
+ ]
+ },
+ "execution_count": 24,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# Compute expectation values\n",
+ "# 0 -> 1, 1 -> -1\n",
+ "function z_expval_from_samples(samples, qubit::Int, n::Int)\n",
+ " mean((-1) ^ parse(Int, hex_to_bitstrings(s, n)[qubit]) for s in samples)\n",
+ "end\n",
+ "\n",
+ "magnetizations = [z_expval_from_samples(all_samples[i], q, N) for i in 1:length(all_samples), q in 1:N]"
+ ]
+ },
+ {
+ "cell_type": "markdown",
+ "id": "a1b2c3d4",
+ "metadata": {},
+ "source": [
+ "The three panels below show the site magnetization $\\langle Z_i \\rangle$ as a function of qubit index (x-axis) and Trotter step (y-axis). At $\\delta t = 0.05$ the total evolution time is $\\tau = r_{\\max} \\cdot \\delta t = 0.5$, which is short enough that the initial antiferromagnetic pattern has not yet decayed — all three methods show a strongly alternating pattern. The classical and tensor network results are now in close agreement, confirming that Trotter error is small at this step size. The hardware results broadly track the other two but show reduced contrast in the alternating pattern at some qubit sites, which becomes more pronounced at larger Trotter steps as the circuit depth increases."
+ ]
+ },
+ {
+ "cell_type": "code",
+ "execution_count": null,
+ "id": "cc5496cc",
+ "metadata": {},
+ "outputs": [
+ {
+ "data": {
+ "image/png": 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",
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\")
"
+ ]
+ },
+ "execution_count": 25,
+ "metadata": {},
+ "output_type": "execute_result"
+ }
+ ],
+ "source": [
+ "# plot magnetization as a function of time\n",
+ "l = @layout [a{0.3w} b{0.3w} c{0.44w}]\n",
+ "plot(\n",
+ " heatmap(classical_magnetizations, title=\"Classical\", clims=(-1,1), color=:RdBu,\n",
+ " xlabel=\"Qubit\", ylabel=\"Trotter steps\", colorbar=false),\n",
+ " heatmap(tn_magnetizations, title=\"Tensor Network\", clims=(-1,1), color=:RdBu,\n",
+ " xlabel=\"Qubit\", ylabel=\"Trotter steps\", colorbar=false),\n",
+ " heatmap(magnetizations, title=\"Hardware\", clims=(-1,1), color=:RdBu,\n",
+ " xlabel=\"Qubit\", ylabel=\"Trotter steps\", colorbar=true),\n",
+ " layout=l, size=(900,300),\n",
+ " bottom_margin=5mm, left_margin=5mm, right_margin=6mm\n",
+ ")"
+ ]
+ }
+ ],
+ "metadata": {
+ "kernelspec": {
+ "display_name": "Julia 1.11",
+ "language": "julia",
+ "name": "julia-1.11"
+ },
+ "language_info": {
+ "codemirror_mode": {
+ "name": "ipython",
+ "version": 3
+ },
+ "file_extension": ".py",
+ "mimetype": "text/x-python",
+ "name": "julia",
+ "nbconvert_exporter": "python",
+ "pygments_lexer": "ipython3",
+ "version": "3"
+ }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/qiskit_bot.yaml b/qiskit_bot.yaml
index 60531ff8260..57ade743a9c 100644
--- a/qiskit_bot.yaml
+++ b/qiskit_bot.yaml
@@ -653,6 +653,9 @@ notifications:
- "@kaelynj"
"docs/tutorials/index":
- "`@nathanearnestnoble`"
+ "docs/tutorials/time-evolution":
+ - "`@nathanearnestnoble`"
+ - "`@haimeng-zhang`"
"docs/tutorials/dc-hex-ising":
- "`@nathanearnestnoble`"
- "`@haimeng-zhang`"