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‎doc/pub/week15/html/week15-bs.html‎

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2,
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None,
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'training-svm-with-precomputed-quantum-kernels'),
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('Example: Kernel SVM in PennyLane',
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2,
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None,
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'example-kernel-svm-in-pennylane'),
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('Discussion of Implementation',
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2,
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None,
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2,
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None,
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'steps-in-quantum-kernel-svm'),
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('The Iris data and classical SVM',
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2,
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None,
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'the-iris-data-and-classical-svm'),
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('Iris Dataset', 2, None, 'iris-dataset'),
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('Qiskit implementation', 2, None, 'qiskit-implementation'),
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('Credit data classification',
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<!-- navigation toc: --> <li><a href="#defining-quantum-feature-maps-in-pennylane" style="font-size: 80%;">Defining Quantum Feature Maps in PennyLane</a></li>
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<!-- navigation toc: --> <li><a href="#computing-quantum-kernel-matrices" style="font-size: 80%;">Computing Quantum Kernel Matrices</a></li>
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<!-- navigation toc: --> <li><a href="#training-svm-with-precomputed-quantum-kernels" style="font-size: 80%;">Training SVM with Precomputed Quantum Kernels</a></li>
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<!-- navigation toc: --> <li><a href="#example-kernel-svm-in-pennylane" style="font-size: 80%;">Example: Kernel SVM in PennyLane</a></li>
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<!-- navigation toc: --> <li><a href="#discussion-of-implementation" style="font-size: 80%;">Discussion of Implementation</a></li>
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<!-- navigation toc: --> <li><a href="#pennylane-implementations" style="font-size: 80%;">PennyLane implementations</a></li>
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<!-- navigation toc: --> <li><a href="#steps-in-quantum-kernel-svm" style="font-size: 80%;">Steps in Quantum Kernel SVM</a></li>
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<!-- navigation toc: --> <li><a href="#the-iris-data-and-classical-svm" style="font-size: 80%;">The Iris data and classical SVM</a></li>
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<!-- navigation toc: --> <li><a href="#iris-dataset" style="font-size: 80%;">Iris Dataset</a></li>
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<!-- navigation toc: --> <li><a href="#qiskit-implementation" style="font-size: 80%;">Qiskit implementation</a></li>
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<!-- navigation toc: --> <li><a href="#credit-data-classification" style="font-size: 80%;">Credit data classification</a></li>
@@ -1342,67 +1342,6 @@ <h2 id="training-svm-with-precomputed-quantum-kernels" class="anchor">Training S
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<p>It is also possible to integrate PennyLane&#8217;s differentiable capabilities by defining a parameterized kernel and optimizing parameters via gradient descent, but here we keep a fixed feature map.</p>
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<!-- !split -->
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<h2 id="example-kernel-svm-in-pennylane" class="anchor">Example: Kernel SVM in PennyLane </h2>
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<p>Below is a compact example that ties it together for a toy 2D dataset:</p>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="inner_cell">
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<div class="highlight" style="background: #f8f8f8">
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<pre style="line-height: 125%;"><span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pennylane</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">qml</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">pennylane</span> <span style="color: #008000; font-weight: bold">import</span> numpy <span style="color: #008000; font-weight: bold">as</span> np
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn</span> <span style="color: #008000; font-weight: bold">import</span> svm
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<span style="color: #408080; font-style: italic"># Example dataset</span>
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X_train <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0.1</span>, <span style="color: #666666">0.2</span>], [<span style="color: #666666">1.1</span>, <span style="color: #666666">-0.4</span>], [<span style="color: #666666">0.0</span>, <span style="color: #666666">0.9</span>], [<span style="color: #666666">1.0</span>, <span style="color: #666666">0.5</span>]])
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Y_train <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([<span style="color: #666666">+1</span>, <span style="color: #666666">+1</span>, <span style="color: #666666">-1</span>, <span style="color: #666666">-1</span>])
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X_test <span style="color: #666666">=</span> np<span style="color: #666666">.</span>array([[<span style="color: #666666">0.2</span>, <span style="color: #666666">0.1</span>], [<span style="color: #666666">0.9</span>, <span style="color: #666666">0.0</span>]])
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<span style="color: #408080; font-style: italic"># Define device and feature map</span>
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dev <span style="color: #666666">=</span> qml<span style="color: #666666">.</span>device(<span style="color: #BA2121">&quot;default.qubit&quot;</span>, wires<span style="color: #666666">=2</span>)
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<span style="color: #AA22FF">@qml</span><span style="color: #666666">.</span>qnode(dev)
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<span style="color: #008000; font-weight: bold">def</span> <span style="color: #0000FF">kernel_circuit</span>(x1, x2):
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qml<span style="color: #666666">.</span>templates<span style="color: #666666">.</span>AngleEmbedding(x1, wires<span style="color: #666666">=</span>[<span style="color: #666666">0</span>,<span style="color: #666666">1</span>])
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qml<span style="color: #666666">.</span>adjoint(qml<span style="color: #666666">.</span>templates<span style="color: #666666">.</span>AngleEmbedding)(x2, wires<span style="color: #666666">=</span>[<span style="color: #666666">0</span>,<span style="color: #666666">1</span>])
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<span style="color: #008000; font-weight: bold">return</span> qml<span style="color: #666666">.</span>probs(wires<span style="color: #666666">=</span>[<span style="color: #666666">0</span>,<span style="color: #666666">1</span>])[<span style="color: #666666">0</span>]
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kernel <span style="color: #666666">=</span> <span style="color: #008000; font-weight: bold">lambda</span> a, b: kernel_circuit(a, b)
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<span style="color: #408080; font-style: italic"># Compute kernel matrices</span>
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K_train <span style="color: #666666">=</span> qml<span style="color: #666666">.</span>kernels<span style="color: #666666">.</span>kernel_matrix(X_train, X_train, kernel_function<span style="color: #666666">=</span>kernel)
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K_test <span style="color: #666666">=</span> qml<span style="color: #666666">.</span>kernels<span style="color: #666666">.</span>kernel_matrix(X_test, X_train, kernel_function<span style="color: #666666">=</span>kernel)
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<span style="color: #408080; font-style: italic"># Train SVM</span>
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clf <span style="color: #666666">=</span> svm<span style="color: #666666">.</span>SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">&#39;precomputed&#39;</span>)
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clf<span style="color: #666666">.</span>fit(K_train, Y_train)
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predictions <span style="color: #666666">=</span> clf<span style="color: #666666">.</span>predict(K_test)
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<span style="color: #008000">print</span>(<span style="color: #BA2121">&quot;Predicted labels:&quot;</span>, predictions)
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</pre>
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</div>
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<div class="output_subarea output_stream output_stdout output_text">
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<p>This code snippet demonstrates defining a quantum kernel via
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AngleEmbedding and using it with scikit-learn. In a real application,
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one would use more data points and possibly include more sophisticated
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feature maps.
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</p>
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<!-- !split -->
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<h2 id="discussion-of-implementation" class="anchor">Discussion of Implementation </h2>
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<li> New data is classified using the trained SVM model with the quantum kernel.</li>
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</ul>
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</ol>
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<!-- !split -->
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<h2 id="the-iris-data-and-classical-svm" class="anchor">The Iris data and classical SVM </h2>
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<!-- code=python (!bc pycod) typeset with pygments style "default" -->
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<div class="cell border-box-sizing code_cell rendered">
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<div class="input">
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<div class="inner_cell">
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<div class="highlight" style="background: #f8f8f8">
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<pre style="line-height: 125%;"><span style="color: #408080; font-style: italic"># import the required packages</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">numpy</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">np</span>
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">pandas</span> <span style="color: #008000; font-weight: bold">as</span> <span style="color: #0000FF; font-weight: bold">pd</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.model_selection</span> <span style="color: #008000; font-weight: bold">import</span> train_test_split
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.svm</span> <span style="color: #008000; font-weight: bold">import</span> SVC
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.datasets</span> <span style="color: #008000; font-weight: bold">import</span> load_iris
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.metrics</span> <span style="color: #008000; font-weight: bold">import</span> accuracy_score,classification_report,f1_score
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iris <span style="color: #666666">=</span> load_iris()
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dataset<span style="color: #666666">=</span>pd<span style="color: #666666">.</span>DataFrame(iris<span style="color: #666666">.</span>data,columns<span style="color: #666666">=</span>iris<span style="color: #666666">.</span>feature_names)
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dataset[<span style="color: #BA2121">&quot;target&quot;</span>]<span style="color: #666666">=</span>iris<span style="color: #666666">.</span>target
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dataset
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features<span style="color: #666666">=</span> dataset[dataset<span style="color: #666666">.</span>columns[<span style="color: #666666">1</span>:<span style="color: #666666">4</span>]]
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target<span style="color: #666666">=</span>dataset[<span style="color: #BA2121">&quot;target&quot;</span>]
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<span style="color: #408080; font-style: italic"># split the data into training set and testing set </span>
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X_train,X_test,Y_train,Y_test<span style="color: #666666">=</span>train_test_split(features,target,test_size<span style="color: #666666">=0.25</span>,random_state<span style="color: #666666">=42</span>)
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<span style="color: #408080; font-style: italic"># Scale the data</span>
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<span style="color: #008000; font-weight: bold">from</span> <span style="color: #0000FF; font-weight: bold">sklearn.preprocessing</span> <span style="color: #008000; font-weight: bold">import</span> MinMaxScaler
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minmax<span style="color: #666666">=</span>MinMaxScaler()
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X_train<span style="color: #666666">=</span>minmax<span style="color: #666666">.</span>fit_transform(X_train)
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X_test<span style="color: #666666">=</span>minmax<span style="color: #666666">.</span>transform(X_test)
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X_test<span style="color: #666666">=</span>np<span style="color: #666666">.</span>clip(X_test,<span style="color: #666666">0</span>,<span style="color: #666666">1</span>)
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<span style="color: #008000; font-weight: bold">import</span> <span style="color: #0000FF; font-weight: bold">time</span>
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start_time<span style="color: #666666">=</span>time<span style="color: #666666">.</span>time()
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svm_model<span style="color: #666666">=</span>SVC(kernel<span style="color: #666666">=</span><span style="color: #BA2121">&quot;rbf&quot;</span>)
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svm_model<span style="color: #666666">.</span>fit(X_train, Y_train)
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end_time<span style="color: #666666">=</span>time<span style="color: #666666">.</span>time()
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<span style="color: #008000">print</span>(end_time<span style="color: #666666">-</span>start_time)
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predictions <span style="color: #666666">=</span> svm_model<span style="color: #666666">.</span>predict(X_test)
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<span style="color: #408080; font-style: italic"># Calculate accuracy and other metrics</span>
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predictions<span style="color: #666666">=</span>svm_model<span style="color: #666666">.</span>predict(X_test)
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accuracy<span style="color: #666666">=</span>accuracy_score(Y_test,predictions)
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<span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;the accuracy is: </span><span style="color: #BB6688; font-weight: bold">{</span>accuracy<span style="color: #BB6688; font-weight: bold">:</span><span style="color: #BA2121">.2f</span><span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">%&quot;</span>)
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f1score<span style="color: #666666">=</span>f1_score(Y_test,predictions,average<span style="color: #666666">=</span><span style="color: #BA2121">&#39;macro&#39;</span>)
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<span style="color: #008000">print</span>(<span style="color: #BA2121">f&quot;the f1-score is:</span><span style="color: #BB6688; font-weight: bold">{</span>f1score<span style="color: #BB6688; font-weight: bold">:</span><span style="color: #BA2121">.2f</span><span style="color: #BB6688; font-weight: bold">}</span><span style="color: #BA2121">%&quot;</span>)
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<span style="color: #008000">print</span>(classification_report(Y_test,predictions))
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</pre>
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<!-- !split -->
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<h2 id="iris-dataset" class="anchor">Iris Dataset </h2>
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<!-- M. Zhao et al., &#8220;A tutorial on quantum machine learning and quantum neural networks,&#8221; arXiv:2504.16131 (2025) . -->
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<!-- D. M. Houshmand, Quantum Machine Learning Lecture Notes, (online, 2023) . (Tutorial using PennyLane QNNs.) -->
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<!-- PennyLane documentation and tutorials: &#12296;https://pennylane.ai&#12297; (for code examples and parameter-shift rules). -->
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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<!-- include javascript, jQuery *first* -->

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