From bf9a1c49816681cdf33d75b3155f6ebd0c19a1cf Mon Sep 17 00:00:00 2001 From: "Vincent R. Pascuzzi" Date: Fri, 24 Apr 2026 13:01:01 -0700 Subject: [PATCH 1/6] Update tutorial template and details, remove serverless This commit update the tutorial to use the latest template. Additionally, we add details about the training dataset and reference to further background for the inquisitive reader so as to not overwhelm the text with group theory. This addition is to address #4929. Finally, we remove the bit on serverless for two primary reasons: 1. the workload is small and can be easily performed on a laptop, 2. serverless nodes appear to not have the necessary modules installed (e.g., pandas) It is suggested to include serverless in an SQD-type tutorial or standalone. Closes #4929. --- docs/tutorials/quantum-kernel-training.ipynb | 218 ++++++++++--------- 1 file changed, 115 insertions(+), 103 deletions(-) diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index 2d07485ef08..a30eaa21fbd 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -12,7 +12,36 @@ "\n", "\n", "# Quantum kernel training\n", - "*Usage estimate: under one minute on an Eagle r3 processor (NOTE: This is an estimate only. Your runtime might vary.)*" + "*Usage estimate: under one minute on a Heron r3 processor (NOTE: This is an estimate only. Your runtime might vary.)*" + ] + }, + { + "cell_type": "markdown", + "id": "bd3bec67", + "metadata": {}, + "source": [ + "## Learning outcomes\n", + "After completing this tutorial, you can expect to understand the following information:\n", + "\n", + " * kernel methods and their uses\n", + " * quantum kernels and how they can provide enhanced feature spaces\n", + " * quantum kernel circuit construction\n", + " * how to train a quantum kernel using a `Qiskit pattern`: map, optimize, execute, and post-process\n" + ] + }, + { + "cell_type": "markdown", + "id": "ba36136c", + "metadata": {}, + "source": [ + "## Prerequisites\n", + "It is recommended that you familiarize yourself with quantum kernels, why they are important and how they are used in practice.\n", + "\n", + " * [Covariant quantum kernels for data with group structure](https://arxiv.org/abs/2105.03406) (paper)\n", + " * [Introduction to Quantum Kernels and Support Vector Machines](https://www.youtube.com/watch?v=GVhCOTzAkCM) (video)\n", + " * [Quantum Kernels in Practice](https://www.youtube.com/watch?v=LmQcSxgINis) (video)\n", + "\n", + "It is also useful to have a basic understanding of group theory." ] }, { @@ -21,8 +50,22 @@ "metadata": {}, "source": [ "## Background\n", - "\n", - "This tutorial shows how to build a `Qiskit pattern` for evaluating entries into a quantum kernel matrix used for binary classification. For more information on `Qiskit patterns` and how `Qiskit Serverless` can be used to deploy them to the cloud for managed execution, visit our [docs page on IBM Quantum® Platform](/docs/guides/serverless)." + "Kernel methods are commonplace in machine learning applications.\n", + "In this context, \"kernel\" refers to the kernel matrix or individual entries therein.\n", + "In general, a kernel is a similarity measure between data encoded in a high-dimensional _feature space_ and can be utilized, for example, in classification tasks with support vector machines.\n", + "\n", + "Quantum kernel methods are those which use quantum computers to estimate a kernel.\n", + "It is known that quantum computers can encode data in quantum-enhanced feature spaces, effectively replacing classical analogs.\n", + "For $\\vec{x} \\in \\mathbb{R}$ and $\\Psi(\\vec{x}) \\in \\mathbb{R}^{d'}$, typically with $d' >d$, $\\Psi(\\vec{x})$ is a feature map, $\\vec{x} \\mapsto \\Psi(\\vec{x})$.\n", + "The goal of $\\Psi(\\vec{x})$ is to make categories of data separated by a hyperplane.\n", + "Taking the vectors in the feature-mapped space as arguments, kernel function $K(\\vec{x}, \\vec{y}) = \\langle{\\Psi(\\vec{x}) | \\Psi(\\vec{y}) \\rangle{}}$ returns their inner product: $K: \\mathbb{R}^d \\rightarrow$ $\\mathbb{R}^d$.\n", + "Classically, feature maps of interest are those in which the kernel function can be easily evaluated;\n", + "i.e., when the inner product in the feature-mapped space can be written in terms of the original data vectors and $\\Psi(\\vec{x})$ and $\\Psi(\\vec{y})$ do not need to be constructed.\n", + "In the case of quantum kernels, feature mapping is performed by a quantum circuit, and the kernel is estimated using the measurement probabilities sampled from the circuit.\n", + "\n", + "\n", + "In this lesson we will examine the depths of pre-coded encoding circuits that use substantial entanglement and compare those to depths of circuits we code by hand. This is not to advocate for one method over another. You may find that pre-coded circuits are too deep, and that the entanglement in the custom-built circuit is insufficient to be useful. Again, these are shown only to enable your exploration.\n", + "This tutorial shows how to build a `Qiskit pattern` for evaluating entries into a quantum kernel matrix used for binary classification." ] }, { @@ -33,8 +76,9 @@ "## Requirements\n", "\n", "Before starting this tutorial, be sure you have the following installed:\n", - "- Qiskit SDK v1.0 or later, with [visualization](/docs/api/qiskit/visualization) support\n", - "- Qiskit Runtime v0.22 or later (`pip install qiskit-ibm-runtime`)" + "- Qiskit SDK v2.3.1 or later, with [visualization](/docs/api/qiskit/visualization) support\n", + "- Qiskit Runtime v0.44.0 or later (`pip install qiskit-ibm-runtime`)\n", + "- Qiskit IBM Catalog v0.14.0 or later (`pip install qiskit-ibm-catalog`)" ] }, { @@ -47,7 +91,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": null, "id": "4405f2da-ce6e-4b97-960a-bb04730cfb6d", "metadata": {}, "outputs": [ @@ -55,11 +99,17 @@ "name": "stdout", "output_type": "stream", "text": [ + "--2026-04-23 18:53:41-- https://raw.githubusercontent.com/qiskit-community/prototype-quantum-kernel-training/main/data/dataset_graph7.csv\n", + "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.109.133, 185.199.110.133, 185.199.111.133, ...\n", + "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.109.133|:443... connected.\n", + "HTTP request sent, awaiting response... 200 OK\n", + "Length: 49405 (48K) [text/plain]\n", + "Saving to: ‘dataset_graph7.csv’\n", "\n", + "dataset_graph7.csv 100%[===================>] 48.25K --.-KB/s in 0.009s \n", "\n", - "\u001b7\u001b[1A\u001b[1G\u001b[27G[Files: 0 Bytes: 0 [0 B/s] Re]\u001b8\u001b7\u001b[2A\u001b[1G\u001b[27G[https://raw.githubusercontent.]\u001b8\u001b7\u001b[1S\u001b[3A\u001b[1G\u001b[0JSaving 'dataset_graph7.csv.1'\n", - "\u001b8\u001b7\u001b[2A\u001b[1Gdataset_graph7.csv.1 100% [=============================>] 20.25K --.-KB/s\u001b8\u001b7\u001b[1S\u001b[3A\u001b[1G\u001b[0JHTTP response 200 [https://raw.githubusercontent.com/qiskit-community/prototype-quantum-kernel-training/main/data/dataset_graph7.csv]\n", - "\u001b8\u001b7\u001b[2A\u001b[1Gdataset_graph7.csv.1 100% [=============================>] 20.25K --.-KB/s\u001b8\u001b7\u001b[1A\u001b[1G\u001b[27G[Files: 1 Bytes: 20.25K [93.33]\u001b8\u001b[m\u001b[m\u001b[m\u001b[m" + "2026-04-23 18:53:42 (5.26 MB/s) - ‘dataset_graph7.csv’ saved [49405/49405]\n", + "\n" ] } ], @@ -74,14 +124,11 @@ "\n", "\n", "from qiskit.circuit import Parameter, ParameterVector, QuantumCircuit\n", - "from qiskit.circuit.library import UnitaryOverlap\n", + "from qiskit.circuit.library import unitary_overlap\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "\n", "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler\n", "\n", - "# from qiskit_serverless import IBMServerlessClient, QiskitFunction\n", - "from qiskit_ibm_catalog import QiskitServerless, QiskitFunction\n", - "\n", "\n", "def visualize_counts(res_counts, num_qubits, num_shots):\n", " \"\"\"Visualize the outputs from the Qiskit Sampler primitive.\"\"\"\n", @@ -122,29 +169,41 @@ "id": "6ddce42e-a365-451d-972d-24c1306ac47b", "metadata": {}, "source": [ - "## Step 1: Map classical inputs to a quantum problem\n", + "## Step 1: Map problem to quantum circuits and operators\n", "\n", "* Input: Training dataset.\n", "* Output: Abstract circuit for calculating a kernel matrix entry.\n", "\n", - "Create the quantum circuit used to evaluate one entry in the kernel matrix. We use the input data to determine the rotation angles for the circuit's parametrized gates. We will use data samples `x1=14` and `x2=19`.\n", + "The binary classification problem we aim to solve here is referred to as \"[_labeling cosets with error_](https://arxiv.org/abs/2105.03406).\" The input training dataset contains a group structure, consisting of two cosets formed by a group and subgroup.\n", + "The group is taken to be $G = SU(2)^{\\otimes n}$ for qubits, which is the special unitary group of \n", + "$2 \\times 2$ matrices and has wide applicability in nature; e.g., the Standard Model of particle physics.\n", + "We take the (graph-stabilizer) subgroup $S_\\text{graph} < G$ with $S_\\text{graph} = \\langle \\{ X_i \\otimes _{k:(k,i) \\in \\mathcal{E}} Z_k\\} _{i \\in \\mathcal{V}} \\} \\rangle$ for a graph with edges $\\mathcal{E}$ and vertices $\\mathcal{V}$.\n", + "Note that the stabilizers fix a stabilizer state such that $D_s | \\psi \\rangle = | \\psi \\rangle,~ \\forall s \\in S_\\text{graph}$.\n", + "Finally, we define two left-cosets $C_\\pm = c_\\pm S_\\text{graph}$ by drawing two $c_\\pm \\in G$ at random.\n", + "\n", + "For more details about the dataset and how it is generated, see [this notebook](https://github.com/qiskit-community/prototype-quantum-kernel-training/blob/main/docs/background/qkernels_and_data_w_group_structure.ipynb) from the [Quantum Kernel Training Toolkit](https://github.com/qiskit-community/prototype-quantum-kernel-training/tree/main).\n", + "\n", + "We create the quantum circuit used to evaluate one entry in the kernel matrix.\n", + "The input data is used to determine the rotation angles for the circuit's parametrized gates.\n", + "For simpliciyt, we will use data samples `x1=14` and `x2=19`.\n", "\n", "***Note: The dataset used in this tutorial can be downloaded [here](https://github.com/qiskit-community/prototype-quantum-kernel-training/blob/main/data/dataset_graph7.csv).***" ] }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 2, "id": "70d6faff-9a56-44bb-b26f-f573a8c90889", "metadata": {}, "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "\"Output" + "
" ] }, - "execution_count": 3, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -178,7 +237,7 @@ "unitary2 = fm.assign_parameters(list(X_train[x2]) + [np.pi / 2])\n", "\n", "# Create the overlap circuit\n", - "overlap_circ = UnitaryOverlap(unitary1, unitary2)\n", + "overlap_circ = unitary_overlap(unitary1, unitary2)\n", "overlap_circ.measure_all()\n", "overlap_circ.draw(\"mpl\", scale=0.6, style=\"iqp\")" ] @@ -188,7 +247,7 @@ "id": "158d8cec-1d92-4105-ac64-6f801dec4259", "metadata": {}, "source": [ - "## Step 2: Optimize problem for quantum hardware execution\n", + "## Step 2: Optimize for target hardware\n", "\n", "* Input: Abstract circuit, not optimized for a particular backend\n", "* Output: Target circuit and observable, optimized for the selected QPU\n", @@ -198,26 +257,35 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "id": "49607b34-9723-493d-85da-bd97c1351104", "metadata": {}, "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Using backend: ibm_fez\n" + ] + }, { "data": { + "image/png": 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", "text/plain": [ - "\"Output" + "
" ] }, - "execution_count": 4, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "service = QiskitRuntimeService()\n", + "service = QiskitRuntimeService(name=\"solutions_demo_premium\")\n", "backend = service.least_busy(\n", " operational=True, simulator=False, min_num_qubits=overlap_circ.num_qubits\n", ")\n", + "print(f\"Using backend: {backend.name}\")\n", "pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n", "overlap_ibm = pm.run(overlap_circ)\n", "overlap_ibm.draw(\"mpl\", scale=0.6, idle_wires=False, fold=-1, style=\"iqp\")" @@ -228,7 +296,7 @@ "id": "9359b92c-a130-44d1-ba11-752f8f4935a0", "metadata": {}, "source": [ - "## Step 3: Execute using Qiskit primitives\n", + "## Step 3: Execute on target hardware\n", "\n", "* Input: Target circuit\n", "* Output: Quasi-probability distribution\n", @@ -240,14 +308,15 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": null, "id": "d2f4f6cf-067e-4d53-aa04-7ca9c803d3e1", "metadata": {}, "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "\"Output" + "
" ] }, "metadata": {}, @@ -255,21 +324,17 @@ } ], "source": [ - "num_shots = 10_000\n", - "\n", - "## Evaluate the problem using statevector-based primitives from Qiskit\n", - "# from qiskit.primitives import StatevectorSampler\n", - "\n", - "# sampler = StatevectorSampler()\n", - "# results = sampler.run([overlap_circ]).result()\n", - "# counts = results[0].data.meas.get_int_counts()\n", - "\n", "# Evaluate the problem using a QPU via Qiskit IBM Runtime\n", - "\n", "sampler = Sampler(mode=backend)\n", - "results = sampler.run([overlap_ibm]).result()\n", + "# Add tag to the job for reference\n", + "sampler.options.environment.job_tags = [\"quantum-kernel-training-demo\"]\n", + "\n", + "# Execute and get counts\n", + "num_shots = 10_000\n", + "results = sampler.run([overlap_ibm], shots=num_shots).result()\n", "counts = results[0].data.meas.get_int_counts()\n", "\n", + "# Plot counts\n", "visualize_counts(counts, num_qubits, num_shots)" ] }, @@ -278,17 +343,17 @@ "id": "1b750103-c369-4651-9092-db0385294c46", "metadata": {}, "source": [ - "## Step 4: Post-process and return result in desired classical format\n", + "## Step 4: Post-process results\n", "\n", "* Input: Probability distribution\n", "* Output: A single kernel matrix element\n", "\n", - "Calculate the probability of measuring |0> on the overlap circuit, and populate the kernel matrix in the position corresponding to the samples represented by this particular overlap circuit (row 15, column 20). In this visualization, darker red indicates fidelities closer to 1.0. To fill out the entire kernel matrix, we need to run a quantum experiment for each entry." + "Calculate the probability of measuring $|0 \\rangle$ on the overlap circuit, and populate the kernel matrix in the position corresponding to the samples represented by this particular overlap circuit (row 15, column 20). In this visualization, darker red indicates fidelities closer to 1.0. To fill out the entire kernel matrix, we need to run a quantum experiment for each entry." ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 5, "id": "8efcb466-3110-4e60-82a6-185f0dca1771", "metadata": {}, "outputs": [ @@ -296,7 +361,7 @@ "name": "stdout", "output_type": "stream", "text": [ - "Fidelity: 0.1279\n" + "Fidelity: 0.2949\n" ] } ], @@ -315,78 +380,25 @@ "![kernel_matrix.png](/docs/images/tutorials/quantum-kernel-training/kernel_matrix.avif)" ] }, - { - "cell_type": "markdown", - "id": "5b0397d6-6673-45cb-9d38-7e9faadba4a1", - "metadata": {}, - "source": [ - "## Deploy the Qiskit pattern to the cloud\n", - "\n", - "To do this, move the source code above to a file, `./source/generate_kernel_entry.py`, wrap the code in a script which takes inputs returns the final solution, and finally upload it to a remote cluster using the `QiskitFunction` class from `Qiskit Serverless`. For guidance on specifying external dependencies, passing input arguments, and more, check out the [Qiskit Serverless guides](https://qiskit.github.io/qiskit-serverless/getting_started/index.html).\n", - "\n", - "The input to the Pattern is a pair of data samples, `x1` and `x2`. The output is the fidelity between the two samples. This value will be used to populate the kernel matrix entry corresponding to these two samples." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "8ce74c3c-4212-4c75-ae55-1394813c89a6", - "metadata": {}, - "outputs": [], - "source": [ - "serverless = QiskitServerless()\n", - "\n", - "kernel_entry_pattern = QiskitFunction(\n", - " title=\"generate-kernel-entry\",\n", - " entrypoint=\"generate_kernel_entry.py\",\n", - " working_dir=\"./source/\",\n", - ")\n", - "\n", - "serverless.upload(kernel_entry_pattern)" - ] - }, - { - "cell_type": "markdown", - "id": "f5b1e64a-881e-459e-a425-7876e56d73de", - "metadata": {}, - "source": [ - "## Run the Qiskit pattern as a managed service\n", - "\n", - "Once we have uploaded the pattern to the cloud, we can easily run it using the `IBMServerlessProvider` client. For simplicity, we will use an exact quantum simulator in the cloud environment, so the fidelity we calculate will be exact." - ] - }, - { - "cell_type": "code", - "execution_count": null, - "id": "c70725fe-57e9-42ed-a0a4-daf0222ddc3a", - "metadata": {}, - "outputs": [], - "source": [ - "generate_kernel_entry = serverless.load(\"generate-kernel-entry\")\n", - "job = generate_kernel_entry.run(\n", - " sample1=list(X_train[x1]), sample2=list(X_train[x2])\n", - ")\n", - "\n", - "kernel_matrix[x1, x2] = job.result()[\"fidelity\"]\n", - "print(f\"fidelity: {kernel_matrix[x1, x2]}\")" - ] - }, { "cell_type": "markdown", "id": "6847b837", "metadata": {}, "source": [ - "## Tutorial survey\n", + "## Next steps\n", "\n", - "Please take this short survey to provide feedback on this tutorial. Your insights will help us improve our content offerings and user experience.\n", + "If you've found this work interesting, you might be interested in the following material:\n", "\n", - "[Link to survey](https://your.feedback.ibm.com/jfe/form/SV_6xsFvUYV1pNHCqW)" + " * [Quantum Kernel Training Toolkit](https://github.com/qiskit-community/prototype-quantum-kernel-training/tree/main)\n", + " * [Quantum Kernel Training for Machine Learning Applications](https://qiskit-community.github.io/qiskit-machine-learning/tutorials/08_quantum_kernel_trainer.html)\n", + " * [Introduction to Quantum Machine Learning](https://quantum.cloud.ibm.com/learning/en/courses/quantum-machine-learning/introduction)\n", + " * [Quantum Machine Learning from IBM Research](https://research.ibm.com/topics/quantum-machine-learning)" ] } ], "metadata": { "kernelspec": { - "display_name": "Python 3", + "display_name": "py312-qae", "language": "python", "name": "python3" }, @@ -400,7 +412,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3" + "version": "3.12.3" } }, "nbformat": 4, From 171dbfd950942752438178810a6048f170dc2193 Mon Sep 17 00:00:00 2001 From: Henry Zou Date: Thu, 30 Apr 2026 17:25:28 -0400 Subject: [PATCH 2/6] tox -e fix --- docs/tutorials/quantum-kernel-training.ipynb | 17 +++++++---------- ...9607b34-9723-493d-85da-bd97c1351104-0.avif | Bin 8764 -> 0 bytes ...9607b34-9723-493d-85da-bd97c1351104-1.avif | Bin 0 -> 8447 bytes ...0d6faff-9a56-44bb-b26f-f573a8c90889-0.avif | Bin 6810 -> 7094 bytes ...2f4f6cf-067e-4d53-aa04-7ca9c803d3e1-0.avif | Bin 6022 -> 6213 bytes 5 files changed, 7 insertions(+), 10 deletions(-) delete mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/49607b34-9723-493d-85da-bd97c1351104-0.avif create mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/49607b34-9723-493d-85da-bd97c1351104-1.avif diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index a30eaa21fbd..0faf7823dd2 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -26,7 +26,7 @@ " * kernel methods and their uses\n", " * quantum kernels and how they can provide enhanced feature spaces\n", " * quantum kernel circuit construction\n", - " * how to train a quantum kernel using a `Qiskit pattern`: map, optimize, execute, and post-process\n" + " * how to train a quantum kernel using a `Qiskit pattern`: map, optimize, execute, and post-process" ] }, { @@ -175,7 +175,7 @@ "* Output: Abstract circuit for calculating a kernel matrix entry.\n", "\n", "The binary classification problem we aim to solve here is referred to as \"[_labeling cosets with error_](https://arxiv.org/abs/2105.03406).\" The input training dataset contains a group structure, consisting of two cosets formed by a group and subgroup.\n", - "The group is taken to be $G = SU(2)^{\\otimes n}$ for qubits, which is the special unitary group of \n", + "The group is taken to be $G = SU(2)^{\\otimes n}$ for qubits, which is the special unitary group of\n", "$2 \\times 2$ matrices and has wide applicability in nature; e.g., the Standard Model of particle physics.\n", "We take the (graph-stabilizer) subgroup $S_\\text{graph} < G$ with $S_\\text{graph} = \\langle \\{ X_i \\otimes _{k:(k,i) \\in \\mathcal{E}} Z_k\\} _{i \\in \\mathcal{V}} \\} \\rangle$ for a graph with edges $\\mathcal{E}$ and vertices $\\mathcal{V}$.\n", "Note that the stabilizers fix a stabilizer state such that $D_s | \\psi \\rangle = | \\psi \\rangle,~ \\forall s \\in S_\\text{graph}$.\n", @@ -198,9 +198,8 @@ "outputs": [ { "data": { - "image/png": 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", "text/plain": [ - "
" + "\"Output" ] }, "execution_count": 2, @@ -270,9 +269,8 @@ }, { "data": { - "image/png": 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", "text/plain": [ - "
" + "\"Output" ] }, "execution_count": 3, @@ -314,9 +312,8 @@ "outputs": [ { "data": { - "image/png": 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zrk_-`9`39=fgBjPN=cjbXN=|Zr_rP74N{=AM7zv0$iG!+P7L|pe>1MN?Ruyn44>)^ zsN8y`mur=?Y~~r%nj9Q8EPR}QAJVO;nYot2LN~aK<&hmrsUp`8e%ZSim)c5!tJb|A zO$OaFgL2eb{X<%4>*_W;o)RwprV8Kd!y_{U5rEy30S_O>xjU@6mMYp3MDM$lM0kBGDYJRWkqUFG3RBlSO4n`#s}dF&m^500wpdHX?D` z2??oo`P8|RQ(CR+po&nT&>FmzoE!g4hMg7}GON0la$E@+$jcD$2~0 zp$Ykm`$C_Za{-}a1$5I`1rI6;NE5R*A3kzw2T>(b6t|}9P3<_xh*YY)L45)43Z5zO z>@7w==Qv(z>)eyxOVfk0Y@KllFmX8W?rt?%(?nS$J{`}^vG6HVCx!R?s82+zk~COA D|Kk^* From 95c401a77a735aa5ba216850ba2af0666a813b3b Mon Sep 17 00:00:00 2001 From: Henry Zou Date: Thu, 30 Apr 2026 17:30:48 -0400 Subject: [PATCH 3/6] cspell and typo fix --- docs/tutorials/quantum-kernel-training.ipynb | 3 ++- 1 file changed, 2 insertions(+), 1 deletion(-) diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index 0faf7823dd2..a0a1982fe4d 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -10,6 +10,7 @@ "description: Build a Qiskit pattern for evaluating entries into a quantum kernel matrix used for binary classification.\n", "---\n", "\n", + "{/* cspell:ignore mapsto forall */}\n", "\n", "# Quantum kernel training\n", "*Usage estimate: under one minute on a Heron r3 processor (NOTE: This is an estimate only. Your runtime might vary.)*" @@ -185,7 +186,7 @@ "\n", "We create the quantum circuit used to evaluate one entry in the kernel matrix.\n", "The input data is used to determine the rotation angles for the circuit's parametrized gates.\n", - "For simpliciyt, we will use data samples `x1=14` and `x2=19`.\n", + "For simplicity, we will use data samples `x1=14` and `x2=19`.\n", "\n", "***Note: The dataset used in this tutorial can be downloaded [here](https://github.com/qiskit-community/prototype-quantum-kernel-training/blob/main/data/dataset_graph7.csv).***" ] From 788e3eca20b1ad642291c3a0e6098ed243a2a00c Mon Sep 17 00:00:00 2001 From: Henry Zou Date: Wed, 20 May 2026 12:00:28 -0400 Subject: [PATCH 4/6] Apply review feedback Structure - Wrap existing pattern under `## Small-scale simulator example` using `StatevectorSampler` from `qiskit.primitives`, demoting the four step headings to `###` and renaming them to the template wording ("Map classical inputs to a quantum problem", "Optimize problem for quantum hardware execution", "Execute using Qiskit primitives", "Post-process and return result in desired classical format"). - Add `## Large-scale hardware example` that reruns the same 7-qubit instance on a real QPU, with an explanation of why we don't scale further (O(N^2) kernel-matrix entries, depth growth from `unitary_overlap`, fidelity at depth, total QPU time). Compress Steps 1-4 into a single - Reformat `## Next steps` with the `` wrapper used across recent tutorials. Code - Drop the named credential: `QiskitRuntimeService(name="solutions_demo_premium")` -> `QiskitRuntimeServic - Set `sampler.options.environment.job_tags = ["TUT_QKT"]` per the TUT-XYZ tagging convent - Replace `!wget` with `urllib.request.urlretrieve(...)` so setup works on macOS without `brew install wget`. Content - Remove the stray Backgrd vs. hand-coded encoding circuits (the comparison was never performed). - Remove `Qiskit IBM Catalog v0.14.0 or later` from Requirements (unused). - Drop "and observable" from the Step 2 Output description (only a transpiled circuit is produced). --- docs/tutorials/quantum-kernel-training.ipynb | 243 +++++++++++------- ...9607b34-9723-493d-85da-bd97c1351104-1.avif | Bin 8447 -> 0 bytes ...2f4f6cf-067e-4d53-aa04-7ca9c803d3e1-0.avif | Bin 6213 -> 0 bytes ...2f4f6cf-067e-4d53-aa04-7ca9c803d3e1-1.avif | Bin 0 -> 6164 bytes .../extracted-outputs/step3-small-code-0.avif | Bin 0 -> 6236 bytes 5 files changed, 149 insertions(+), 94 deletions(-) delete mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/49607b34-9723-493d-85da-bd97c1351104-1.avif delete mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/d2f4f6cf-067e-4d53-aa04-7ca9c803d3e1-0.avif create mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/d2f4f6cf-067e-4d53-aa04-7ca9c803d3e1-1.avif create mode 100644 public/docs/images/tutorials/quantum-kernel-training/extracted-outputs/step3-small-code-0.avif diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index a0a1982fe4d..faca2b090a3 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -64,8 +64,6 @@ "i.e., when the inner product in the feature-mapped space can be written in terms of the original data vectors and $\\Psi(\\vec{x})$ and $\\Psi(\\vec{y})$ do not need to be constructed.\n", "In the case of quantum kernels, feature mapping is performed by a quantum circuit, and the kernel is estimated using the measurement probabilities sampled from the circuit.\n", "\n", - "\n", - "In this lesson we will examine the depths of pre-coded encoding circuits that use substantial entanglement and compare those to depths of circuits we code by hand. This is not to advocate for one method over another. You may find that pre-coded circuits are too deep, and that the entanglement in the custom-built circuit is insufficient to be useful. Again, these are shown only to enable your exploration.\n", "This tutorial shows how to build a `Qiskit pattern` for evaluating entries into a quantum kernel matrix used for binary classification." ] }, @@ -78,8 +76,7 @@ "\n", "Before starting this tutorial, be sure you have the following installed:\n", "- Qiskit SDK v2.3.1 or later, with [visualization](/docs/api/qiskit/visualization) support\n", - "- Qiskit Runtime v0.44.0 or later (`pip install qiskit-ibm-runtime`)\n", - "- Qiskit IBM Catalog v0.14.0 or later (`pip install qiskit-ibm-catalog`)" + "- Qiskit Runtime v0.44.0 or later (`pip install qiskit-ibm-runtime`)" ] }, { @@ -95,29 +92,10 @@ "execution_count": null, "id": "4405f2da-ce6e-4b97-960a-bb04730cfb6d", "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "--2026-04-23 18:53:41-- https://raw.githubusercontent.com/qiskit-community/prototype-quantum-kernel-training/main/data/dataset_graph7.csv\n", - "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.109.133, 185.199.110.133, 185.199.111.133, ...\n", - "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.109.133|:443... connected.\n", - "HTTP request sent, awaiting response... 200 OK\n", - "Length: 49405 (48K) [text/plain]\n", - "Saving to: ‘dataset_graph7.csv’\n", - "\n", - "dataset_graph7.csv 100%[===================>] 48.25K --.-KB/s in 0.009s \n", - "\n", - "2026-04-23 18:53:42 (5.26 MB/s) - ‘dataset_graph7.csv’ saved [49405/49405]\n", - "\n" - ] - } - ], + "outputs": [], "source": [ - "!wget https://raw.githubusercontent.com/qiskit-community/prototype-quantum-kernel-training/main/data/dataset_graph7.csv\n", - "\n", "# General Imports and helper functions\n", + "import urllib.request\n", "\n", "import pandas as pd\n", "import numpy as np\n", @@ -126,10 +104,17 @@ "\n", "from qiskit.circuit import Parameter, ParameterVector, QuantumCircuit\n", "from qiskit.circuit.library import unitary_overlap\n", + "from qiskit.primitives import StatevectorSampler\n", "from qiskit.transpiler.preset_passmanagers import generate_preset_pass_manager\n", "\n", "from qiskit_ibm_runtime import QiskitRuntimeService, Sampler\n", "\n", + "# Download the dataset (portable across platforms)\n", + "urllib.request.urlretrieve(\n", + " \"https://raw.githubusercontent.com/qiskit-community/prototype-quantum-kernel-training/main/data/dataset_graph7.csv\",\n", + " \"dataset_graph7.csv\",\n", + ")\n", + "\n", "\n", "def visualize_counts(res_counts, num_qubits, num_shots):\n", " \"\"\"Visualize the outputs from the Qiskit Sampler primitive.\"\"\"\n", @@ -165,12 +150,22 @@ " return X_train" ] }, + { + "cell_type": "markdown", + "id": "small-scale-intro", + "metadata": {}, + "source": [ + "## Small-scale simulator example\n", + "\n", + "In this section, we walk through the four steps of the `Qiskit pattern` on a 7-qubit instance of the labeling-cosets-with-error problem and evaluate a single kernel matrix entry using the `StatevectorSampler` primitive from Qiskit. A statevector simulator is exact (up to shot noise) and lets us see the method end-to-end without consuming QPU time. We then repeat the same instance on real hardware in the [Large-scale hardware example](#large-scale-hardware-example) section." + ] + }, { "cell_type": "markdown", "id": "6ddce42e-a365-451d-972d-24c1306ac47b", "metadata": {}, "source": [ - "## Step 1: Map problem to quantum circuits and operators\n", + "### Step 1: Map classical inputs to a quantum problem\n", "\n", "* Input: Training dataset.\n", "* Output: Abstract circuit for calculating a kernel matrix entry.\n", @@ -244,137 +239,194 @@ }, { "cell_type": "markdown", - "id": "158d8cec-1d92-4105-ac64-6f801dec4259", + "id": "step2-small-md", + "metadata": {}, + "source": [ + "### Step 2: Optimize problem for quantum hardware execution\n", + "\n", + "* Input: Abstract circuit, not optimized for a particular backend.\n", + "* Output: Target circuit, optimized for the selected QPU.\n", + "\n", + "For the statevector simulator path used in this section, no backend-specific optimization is required: the abstract circuit can be sampled directly. We exercise this step in the [Large-scale hardware example](#large-scale-hardware-example) below, where the circuit is transpiled against a real QPU using `generate_preset_pass_manager` with `optimization_level=3`." + ] + }, + { + "cell_type": "markdown", + "id": "step3-small-md", "metadata": {}, "source": [ - "## Step 2: Optimize for target hardware\n", + "### Step 3: Execute using Qiskit primitives\n", "\n", - "* Input: Abstract circuit, not optimized for a particular backend\n", - "* Output: Target circuit and observable, optimized for the selected QPU\n", + "* Input: Abstract circuit.\n", + "* Output: Quasi-probability distribution.\n", "\n", - "Use the `generate_preset_pass_manager` function from Qiskit to specify an optimization routine for our circuit with respect to the QPU on which we plan to run the experiment. We set `optimization_level=3` , which means we will use the preset pass manager which provides the highest level of optimization." + "Use the `StatevectorSampler` primitive from Qiskit to reconstruct a quasi-probability distribution of states yielded from sampling the circuit. For the task of generating a kernel matrix, we are particularly interested in the probability of measuring the |0> state." ] }, { "cell_type": "code", "execution_count": 3, - "id": "49607b34-9723-493d-85da-bd97c1351104", + "id": "step3-small-code", "metadata": {}, "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "Using backend: ibm_fez\n" - ] - }, { "data": { "text/plain": [ - "\"Output" + "\"Output" ] }, - "execution_count": 3, "metadata": {}, - "output_type": "execute_result" + "output_type": "display_data" } ], "source": [ - "service = QiskitRuntimeService(name=\"solutions_demo_premium\")\n", - "backend = service.least_busy(\n", - " operational=True, simulator=False, min_num_qubits=overlap_circ.num_qubits\n", - ")\n", - "print(f\"Using backend: {backend.name}\")\n", - "pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n", - "overlap_ibm = pm.run(overlap_circ)\n", - "overlap_ibm.draw(\"mpl\", scale=0.6, idle_wires=False, fold=-1, style=\"iqp\")" + "sampler = StatevectorSampler()\n", + "\n", + "# Execute and get counts\n", + "num_shots = 10_000\n", + "results = sampler.run([overlap_circ], shots=num_shots).result()\n", + "counts = results[0].data.meas.get_int_counts()\n", + "\n", + "# Plot counts\n", + "visualize_counts(counts, num_qubits, num_shots)" ] }, { "cell_type": "markdown", - "id": "9359b92c-a130-44d1-ba11-752f8f4935a0", + "id": "step4-small-md", "metadata": {}, "source": [ - "## Step 3: Execute on target hardware\n", + "### Step 4: Post-process and return result in desired classical format\n", "\n", - "* Input: Target circuit\n", - "* Output: Quasi-probability distribution\n", + "* Input: Probability distribution.\n", + "* Output: A single kernel matrix element.\n", "\n", - "Use the `Sampler` primitive from Qiskit Runtime to reconstruct a quasi-probability distribution of states yielded from sampling the circuit. For the task of generating a kernel matrix, we are particularly interested in the probability of measuring the |0> state.\n", - "\n", - "For this demo, we will run on a QPU with `qiskit-ibm-runtime` primitives. To run on `qiskit` statevector-based primitives, replace the block of code using Qiskit IBM® Runtime primitives with the commented block." + "Calculate the probability of measuring $|0 \\rangle$ on the overlap circuit, and populate the kernel matrix in the position corresponding to the samples represented by this particular overlap circuit (row 15, column 20)." ] }, { "cell_type": "code", - "execution_count": null, - "id": "d2f4f6cf-067e-4d53-aa04-7ca9c803d3e1", + "execution_count": 4, + "id": "step4-small-code", "metadata": {}, "outputs": [ { - "data": { - "text/plain": [ - "\"Output" - ] - }, - "metadata": {}, - "output_type": "display_data" + "name": "stdout", + "output_type": "stream", + "text": [ + "Fidelity (simulator): 0.8261\n" + ] } ], "source": [ - "# Evaluate the problem using a QPU via Qiskit IBM Runtime\n", - "sampler = Sampler(mode=backend)\n", - "# Add tag to the job for reference\n", - "sampler.options.environment.job_tags = [\"quantum-kernel-training-demo\"]\n", - "\n", - "# Execute and get counts\n", - "num_shots = 10_000\n", - "results = sampler.run([overlap_ibm], shots=num_shots).result()\n", - "counts = results[0].data.meas.get_int_counts()\n", - "\n", - "# Plot counts\n", - "visualize_counts(counts, num_qubits, num_shots)" + "kernel_matrix[x1, x2] = counts.get(0, 0.0) / num_shots\n", + "print(f\"Fidelity (simulator): {kernel_matrix[x1, x2]}\")" ] }, { "cell_type": "markdown", - "id": "1b750103-c369-4651-9092-db0385294c46", + "id": "large-scale-intro", "metadata": {}, "source": [ - "## Step 4: Post-process results\n", - "\n", - "* Input: Probability distribution\n", - "* Output: A single kernel matrix element\n", + "## Hardware example\n", "\n", - "Calculate the probability of measuring $|0 \\rangle$ on the overlap circuit, and populate the kernel matrix in the position corresponding to the samples represented by this particular overlap circuit (row 15, column 20). In this visualization, darker red indicates fidelities closer to 1.0. To fill out the entire kernel matrix, we need to run a quantum experiment for each entry." + "A quantum kernel matrix has $\\mathcal{O}(N^2)$ entries for $N$ training samples, and each entry requires running an overlap circuit whose two-qubit-gate depth grows with the size of the feature map. As a result, scaling this tutorial to a larger problem has two compounding costs: the QPU time per kernel matrix grows quadratically with $N$, and the depth of `unitary_overlap` (which composes the feature map with its adjoint) erodes fidelity at the system size and connectivity of current hardware. To keep the demo short and to make a clean comparison, we therefore run the **same** 7-qubit instance from the small-scale example on a real QPU and compare the fidelity of a single kernel matrix entry against the simulator value computed above." ] }, { "cell_type": "code", "execution_count": 5, - "id": "8efcb466-3110-4e60-82a6-185f0dca1771", + "id": "d2f4f6cf-067e-4d53-aa04-7ca9c803d3e1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ - "Fidelity: 0.2949\n" + "Using backend: ibm_pittsburgh\n" + ] + }, + { + "data": { + "text/plain": [ + "\"Output" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Fidelity (hardware): 0.7517\n" ] } ], "source": [ - "# Calculate the fidelity, or the probability to measure 0\n", + "# ------------------------------ Step 1 ------------------------------\n", + "# Prepare training data\n", + "X_train = get_training_data()\n", + "\n", + "# Empty kernel matrix\n", + "num_samples = np.shape(X_train)[0]\n", + "kernel_matrix = np.full((num_samples, num_samples), np.nan)\n", + "\n", + "# Prepare feature map for computing overlap\n", + "num_features = np.shape(X_train)[1]\n", + "num_qubits = int(num_features / 2)\n", + "entangler_map = [[0, 2], [3, 4], [2, 5], [1, 4], [2, 3], [4, 6]]\n", + "fm = QuantumCircuit(num_qubits)\n", + "training_param = Parameter(\"θ\")\n", + "feature_params = ParameterVector(\"x\", num_qubits * 2)\n", + "fm.ry(training_param, fm.qubits)\n", + "for cz in entangler_map:\n", + " fm.cz(cz[0], cz[1])\n", + "for i in range(num_qubits):\n", + " fm.rz(-2 * feature_params[2 * i + 1], i)\n", + " fm.rx(-2 * feature_params[2 * i], i)\n", + "\n", + "# Assign tunable parameter to known optimal value and set the data params for first two samples\n", + "x1 = 14\n", + "x2 = 19\n", + "unitary1 = fm.assign_parameters(list(X_train[x1]) + [np.pi / 2])\n", + "unitary2 = fm.assign_parameters(list(X_train[x2]) + [np.pi / 2])\n", + "\n", + "# Create the overlap circuit\n", + "overlap_circ = unitary_overlap(unitary1, unitary2)\n", + "overlap_circ.measure_all()\n", + "\n", + "# ------------------------------ Step 2 ------------------------------\n", + "service = QiskitRuntimeService()\n", + "# backend = service.least_busy(\n", + "# operational=True, simulator=False, min_num_qubits=overlap_circ.num_qubits\n", + "# )\n", + "backend = service.backend(\"ibm_pittsburgh\")\n", + "print(f\"Using backend: {backend.name}\")\n", + "pm = generate_preset_pass_manager(optimization_level=3, backend=backend)\n", + "overlap_ibm = pm.run(overlap_circ)\n", + "\n", + "# ------------------------------ Step 3 ------------------------------\n", + "sampler = Sampler(mode=backend)\n", + "sampler.options.environment.job_tags = [\"TUT_QKT\"]\n", + "\n", + "num_shots = 10_000\n", + "results = sampler.run([overlap_ibm], shots=num_shots).result()\n", + "counts = results[0].data.meas.get_int_counts()\n", + "visualize_counts(counts, num_qubits, num_shots)\n", + "\n", + "# ------------------------------ Step 4 ------------------------------\n", "kernel_matrix[x1, x2] = counts.get(0, 0.0) / num_shots\n", - "print(f\"Fidelity: {kernel_matrix[x1, x2]}\")" + "print(f\"Fidelity (hardware): {kernel_matrix[x1, x2]}\")" ] }, { - "attachments": {}, "cell_type": "markdown", "id": "dec33657-9055-4fdc-b146-dba0e5882719", "metadata": {}, "source": [ + "To fill out the entire kernel matrix, we would run a quantum experiment for each of its $N(N+1)/2$ unique entries. The figure below shows the resulting matrix for this dataset; darker red indicates fidelities closer to 1.0.\n", + "\n", "![kernel_matrix.png](/docs/images/tutorials/quantum-kernel-training/kernel_matrix.avif)" ] }, @@ -385,12 +437,15 @@ "source": [ "## Next steps\n", "\n", - "If you've found this work interesting, you might be interested in the following material:\n", + "\n", + "If you found this work interesting, you might be interested in the following material:\n", "\n", - " * [Quantum Kernel Training Toolkit](https://github.com/qiskit-community/prototype-quantum-kernel-training/tree/main)\n", - " * [Quantum Kernel Training for Machine Learning Applications](https://qiskit-community.github.io/qiskit-machine-learning/tutorials/08_quantum_kernel_trainer.html)\n", - " * [Introduction to Quantum Machine Learning](https://quantum.cloud.ibm.com/learning/en/courses/quantum-machine-learning/introduction)\n", - " * [Quantum Machine Learning from IBM Research](https://research.ibm.com/topics/quantum-machine-learning)" + " - [Quantum Kernel Training Toolkit](https://github.com/qiskit-community/prototype-quantum-kernel-training/tree/main) - the prototype repository this tutorial is based on\n", + " - [Quantum Kernel Training for Machine Learning Applications](https://qiskit-community.github.io/qiskit-machine-learning/tutorials/08_quantum_kernel_trainer.html) - a Qiskit Machine Learning tutorial showing how to train the trainable parameter\n", + " - [Introduction to Quantum Machine Learning](https://quantum.cloud.ibm.com/learning/en/courses/quantum-machine-learning/introduction) - a course on quantum machine learning\n", + " - [Quantum Machine Learning from IBM Research](https://research.ibm.com/topics/quantum-machine-learning) - an overview of QML research at IBM\n", + " - [Covariant quantum kernels for data with group structure](https://arxiv.org/abs/2105.03406) - the paper this tutorial is based on\n", + "" ] } ], diff --git 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docs/tutorials/quantum-kernel-training.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index faca2b090a3..03a8d0b92b4 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -157,7 +157,7 @@ "source": [ "## Small-scale simulator example\n", "\n", - "In this section, we walk through the four steps of the `Qiskit pattern` on a 7-qubit instance of the labeling-cosets-with-error problem and evaluate a single kernel matrix entry using the `StatevectorSampler` primitive from Qiskit. A statevector simulator is exact (up to shot noise) and lets us see the method end-to-end without consuming QPU time. We then repeat the same instance on real hardware in the [Large-scale hardware example](#large-scale-hardware-example) section." + "In this section, we walk through the four steps of the `Qiskit pattern` on a 7-qubit instance of the labeling-cosets-with-error problem and evaluate a single kernel matrix entry using the `StatevectorSampler` primitive from Qiskit. A statevector simulator is exact (up to shot noise) and lets us see the method end-to-end without consuming QPU time. We then repeat the same instance on real hardware in the hardware examplesection." ] }, { @@ -247,7 +247,7 @@ "* Input: Abstract circuit, not optimized for a particular backend.\n", "* Output: Target circuit, optimized for the selected QPU.\n", "\n", - "For the statevector simulator path used in this section, no backend-specific optimization is required: the abstract circuit can be sampled directly. We exercise this step in the [Large-scale hardware example](#large-scale-hardware-example) below, where the circuit is transpiled against a real QPU using `generate_preset_pass_manager` with `optimization_level=3`." + "For the statevector simulator path used in this section, no backend-specific optimization is required: the abstract circuit can be sampled directly. We exercise this step in the hardware example below, where the circuit is transpiled against a real QPU using `generate_preset_pass_manager` with `optimization_level=3`." ] }, { From a627a1f7da10e97a0a9b574b5008faab02c4c743 Mon Sep 17 00:00:00 2001 From: abbycross Date: Fri, 22 May 2026 10:45:39 -0400 Subject: [PATCH 6/6] Small fixes for links, IBM Style, typos --- docs/tutorials/quantum-kernel-training.ipynb | 20 ++++++++++---------- 1 file changed, 10 insertions(+), 10 deletions(-) diff --git a/docs/tutorials/quantum-kernel-training.ipynb b/docs/tutorials/quantum-kernel-training.ipynb index 03a8d0b92b4..286f46e135f 100644 --- a/docs/tutorials/quantum-kernel-training.ipynb +++ b/docs/tutorials/quantum-kernel-training.ipynb @@ -24,10 +24,10 @@ "## Learning outcomes\n", "After completing this tutorial, you can expect to understand the following information:\n", "\n", - " * kernel methods and their uses\n", - " * quantum kernels and how they can provide enhanced feature spaces\n", - " * quantum kernel circuit construction\n", - " * how to train a quantum kernel using a `Qiskit pattern`: map, optimize, execute, and post-process" + " * Kernel methods and their uses\n", + " * Quantum kernels and how they can provide enhanced feature spaces\n", + " * Quantum kernel circuit construction\n", + " * How to train a quantum kernel using a [Qiskit pattern](/docs/guides/intro-to-patterns): map, optimize, execute, and post-process" ] }, { @@ -36,7 +36,7 @@ "metadata": {}, "source": [ "## Prerequisites\n", - "It is recommended that you familiarize yourself with quantum kernels, why they are important and how they are used in practice.\n", + "It is recommended that you familiarize yourself with quantum kernels, why they are important, and how they are used in practice.\n", "\n", " * [Covariant quantum kernels for data with group structure](https://arxiv.org/abs/2105.03406) (paper)\n", " * [Introduction to Quantum Kernels and Support Vector Machines](https://www.youtube.com/watch?v=GVhCOTzAkCM) (video)\n", @@ -61,10 +61,10 @@ "The goal of $\\Psi(\\vec{x})$ is to make categories of data separated by a hyperplane.\n", "Taking the vectors in the feature-mapped space as arguments, kernel function $K(\\vec{x}, \\vec{y}) = \\langle{\\Psi(\\vec{x}) | \\Psi(\\vec{y}) \\rangle{}}$ returns their inner product: $K: \\mathbb{R}^d \\rightarrow$ $\\mathbb{R}^d$.\n", "Classically, feature maps of interest are those in which the kernel function can be easily evaluated;\n", - "i.e., when the inner product in the feature-mapped space can be written in terms of the original data vectors and $\\Psi(\\vec{x})$ and $\\Psi(\\vec{y})$ do not need to be constructed.\n", + "as in, when the inner product in the feature-mapped space can be written in terms of the original data vectors and $\\Psi(\\vec{x})$ and $\\Psi(\\vec{y})$ do not need to be constructed.\n", "In the case of quantum kernels, feature mapping is performed by a quantum circuit, and the kernel is estimated using the measurement probabilities sampled from the circuit.\n", "\n", - "This tutorial shows how to build a `Qiskit pattern` for evaluating entries into a quantum kernel matrix used for binary classification." + "This tutorial shows how to build a Qiskit pattern for evaluating entries into a quantum kernel matrix used for binary classification." ] }, { @@ -157,7 +157,7 @@ "source": [ "## Small-scale simulator example\n", "\n", - "In this section, we walk through the four steps of the `Qiskit pattern` on a 7-qubit instance of the labeling-cosets-with-error problem and evaluate a single kernel matrix entry using the `StatevectorSampler` primitive from Qiskit. A statevector simulator is exact (up to shot noise) and lets us see the method end-to-end without consuming QPU time. We then repeat the same instance on real hardware in the hardware examplesection." + "In this section, we walk through the four steps of the Qiskit pattern on a seven-qubit instance of the labeling-cosets-with-error problem and evaluate a single kernel matrix entry using the `StatevectorSampler` primitive from Qiskit. A statevector simulator is exact (up to shot noise) and shows us the method end-to-end without consuming QPU time. We then repeat the same instance on real hardware in the hardware example section." ] }, { @@ -330,7 +330,7 @@ "source": [ "## Hardware example\n", "\n", - "A quantum kernel matrix has $\\mathcal{O}(N^2)$ entries for $N$ training samples, and each entry requires running an overlap circuit whose two-qubit-gate depth grows with the size of the feature map. As a result, scaling this tutorial to a larger problem has two compounding costs: the QPU time per kernel matrix grows quadratically with $N$, and the depth of `unitary_overlap` (which composes the feature map with its adjoint) erodes fidelity at the system size and connectivity of current hardware. To keep the demo short and to make a clean comparison, we therefore run the **same** 7-qubit instance from the small-scale example on a real QPU and compare the fidelity of a single kernel matrix entry against the simulator value computed above." + "A quantum kernel matrix has $\\mathcal{O}(N^2)$ entries for $N$ training samples, and each entry requires running an overlap circuit whose two-qubit-gate depth grows with the size of the feature map. As a result, scaling this tutorial to a larger problem has two compounding costs: the QPU time per kernel matrix grows quadratically with $N$, and the depth of `unitary_overlap` (which composes the feature map with its adjoint) erodes fidelity at the system size and connectivity of current hardware. To keep the demo short and to make a clean comparison, we therefore run the **same** seven-qubit instance from the small-scale example on a real QPU and compare the fidelity of a single kernel matrix entry against the simulator value computed above." ] }, { @@ -442,7 +442,7 @@ "\n", " - [Quantum Kernel Training Toolkit](https://github.com/qiskit-community/prototype-quantum-kernel-training/tree/main) - the prototype repository this tutorial is based on\n", " - [Quantum Kernel Training for Machine Learning Applications](https://qiskit-community.github.io/qiskit-machine-learning/tutorials/08_quantum_kernel_trainer.html) - a Qiskit Machine Learning tutorial showing how to train the trainable parameter\n", - " - [Introduction to Quantum Machine Learning](https://quantum.cloud.ibm.com/learning/en/courses/quantum-machine-learning/introduction) - a course on quantum machine learning\n", + " - [Introduction to Quantum Machine Learning](/learning/courses/quantum-machine-learning/introduction) - a course on quantum machine learning\n", " - [Quantum Machine Learning from IBM Research](https://research.ibm.com/topics/quantum-machine-learning) - an overview of QML research at IBM\n", " - [Covariant quantum kernels for data with group structure](https://arxiv.org/abs/2105.03406) - the paper this tutorial is based on\n", ""