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update of week 15
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‎doc/pub/week15/html/week15-bs.html‎

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end of tocinfo -->
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<body>
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<a href="#" class="dropdown-toggle" data-toggle="dropdown">Contents <b class="caret"></b></a>
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<ul class="dropdown-menu">
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<!-- navigation toc: --> <li><a href="#plan-for-the-week-of-may-5-9" style="font-size: 80%;">Plan for the week of May 5-9</a></li>
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<!-- navigation toc: --> <li><a href="#quantum-svms" style="font-size: 80%;">Quantum SVMs</a></li>
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<!-- navigation toc: --> <li><a href="#quantum-svms-short-reminder-from-last-week" style="font-size: 80%;">Quantum SVMs, short reminder from last week</a></li>
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<!-- navigation toc: --> <li><a href="#how-qsvm-works" style="font-size: 80%;">How QSVM works</a></li>
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<!-- navigation toc: --> <li><a href="#basic-steps-data-encoding-quantum-feature-mapping" style="font-size: 80%;">Basic steps: Data Encoding (Quantum Feature Mapping)</a></li>
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<!-- navigation toc: --> <li><a href="#basic-steps-quantum-kernel" style="font-size: 80%;">Basic steps: Quantum Kernel</a></li>
@@ -369,6 +377,8 @@
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<!-- navigation toc: --> <li><a href="#applications-and-examples" style="font-size: 80%;">Applications and examples</a></li>
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<!-- navigation toc: --> <li><a href="#additional-applications-and-examples" style="font-size: 80%;">Additional applications and examples</a></li>
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<!-- navigation toc: --> <li><a href="#more-on-applications" style="font-size: 80%;">More on applications</a></li>
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<!-- navigation toc: --> <li><a href="#references-of-interest" style="font-size: 80%;">References of interest</a></li>
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<!-- navigation toc: --> <li><a href="#plans-for-the-week-of-may-12-16" style="font-size: 80%;">Plans for the week of May 12-16</a></li>
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</ul>
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</li>
@@ -411,18 +421,18 @@ <h2 id="plan-for-the-week-of-may-5-9" class="anchor">Plan for the week of May 5-
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<li> Variational Quantum Circuits (VQCs)</li>
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<li> Quantum neural networks (QNNs)</li>
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<ul>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_self">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.pdf" target="_self">Whiteboard notes</a> --></li>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be" target="_self">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMay7.pdf" target="_self">Whiteboard notes</a> --></li>
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</ul>
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</ol>
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</div>
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</div>
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<!-- !split -->
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<h2 id="quantum-svms" class="anchor">Quantum SVMs </h2>
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<h2 id="quantum-svms-short-reminder-from-last-week" class="anchor">Quantum SVMs, short reminder from last week </h2>
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<p>The idea of a classical SVM is that we have a set of points
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that are in either one group or another and we want to find a line that
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</div>
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<!-- A. Abbas et al., &#8220;The power of quantum neural networks,&#8221; Nature Comput. Sci. 1, 403&#8211;409 (2021) . -->
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<!-- E. Anschuetz and B. Kiani, &#8220;Quantum variational algorithms are swamped with traps,&#8221; Nat. Commun. 13, 7760 (2022) . -->
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<!-- J. Zhang et al. (Wells Fargo Quantum Research), arXiv:2412.12484 (2024) &#8211; discusses QNN architectures and variationa#l circuits . -->
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<!-- J. Millet et al., &#8220;Variational quantum circuits for machine learning: an application for detecting weak signals,&#8221; Ap#pl. Sci. 11, 6427 (2021) . -->
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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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<!-- !split -->
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<h2 id="references-of-interest" class="anchor">References of interest </h2>
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<ol>
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<li> A. Abbas et al., <b>The power of quantum neural networks</b>, Nature Comput. Sci. 1, 403&#8211;409 (2021).</li>
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<li> E. Anschuetz and B. Kiani, <b>Quantum variational algorithms are swamped with traps</b>, Nat. Commun. 13, 7760 (2022) .</li>
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<li> J. Millet et al., <b>Variational quantum circuits for machine learning: an application for detecting weak signals</b>, Appl. Sci. 11, 6427 (2021) .</li>
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<li> M. Zhao et al., <b>A tutorial on quantum machine learning and quantum neural networks</b>, arXiv:2504.16131 (2025) .</li>
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<li> D. M. Houshmand, <b>Quantum Machine Learning Lecture Notes</b>, (online, 2023) . (Tutorial using PennyLane QNNs.)</li>
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<li> PennyLane documentation and tutorials: <a href="https://pennylane.a" target="_self"><tt>https://pennylane.a</tt></a>&#12297; (for code examples and parameter-shift rules).</li>
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</ol>
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<!-- !split -->
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<h2 id="plans-for-the-week-of-may-12-16" class="anchor">Plans for the week of May 12-16 </h2>
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<ol>
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<li> Discussion of quantum neural networks</li>
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<li> Start discussion fo Boltzmann machines, classical and quantum mechanical ones.</li>
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</ol>
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<!-- ------------------- end of main content --------------- -->
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</div> <!-- end container -->
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<!-- include javascript, jQuery *first* -->

‎doc/pub/week15/html/week15-reveal.html‎

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@@ -201,18 +201,20 @@ <h2 id="plan-for-the-week-of-may-5-9">Plan for the week of May 5-9 </h2>
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<p><li> Variational Quantum Circuits (VQCs)</li>
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<p><li> Quantum neural networks (QNNs)</li>
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<ul>
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<p><li> Training QNNs and Loss Landscapes</li>
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<p><li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.pdf" target="_blank">Whiteboard notes</a> --></li>
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<p><li> Training QNNs and Loss Landscapes</li>
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<p><li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMay7.pdf" target="_blank">Whiteboard notes</a> --></li>
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</ul>
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<p>
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</ol>
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</div>
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</section>
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<section>
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<h2 id="quantum-svms">Quantum SVMs </h2>
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<h2 id="quantum-svms-short-reminder-from-last-week">Quantum SVMs, short reminder from last week </h2>
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<p>The idea of a classical SVM is that we have a set of points
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that are in either one group or another and we want to find a line that
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<p>Small-scale QML experiments have been run on IBM, Google, and IonQ devices. These serve as proof-of-concept for the hybrid model.</p>
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</div>
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</section>
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<section>
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<h2 id="references-of-interest">References of interest </h2>
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<ol>
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<p><li> A. Abbas et al., <b>The power of quantum neural networks</b>, Nature Comput. Sci. 1, 403&#8211;409 (2021).</li>
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<p><li> E. Anschuetz and B. Kiani, <b>Quantum variational algorithms are swamped with traps</b>, Nat. Commun. 13, 7760 (2022) .</li>
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<p><li> J. Millet et al., <b>Variational quantum circuits for machine learning: an application for detecting weak signals</b>, Appl. Sci. 11, 6427 (2021) .</li>
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<p><li> M. Zhao et al., <b>A tutorial on quantum machine learning and quantum neural networks</b>, arXiv:2504.16131 (2025) .</li>
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<p><li> D. M. Houshmand, <b>Quantum Machine Learning Lecture Notes</b>, (online, 2023) . (Tutorial using PennyLane QNNs.)</li>
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<p><li> PennyLane documentation and tutorials: <a href="https://pennylane.a" target="_blank"><tt>https://pennylane.a</tt></a>&#12297; (for code examples and parameter-shift rules).</li>
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</ol>
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</section>
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<!-- A. Abbas et al., &#8220;The power of quantum neural networks,&#8221; Nature Comput. Sci. 1, 403&#8211;409 (2021) . -->
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<!-- E. Anschuetz and B. Kiani, &#8220;Quantum variational algorithms are swamped with traps,&#8221; Nat. Commun. 13, 7760 (2022) . -->
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<!-- J. Zhang et al. (Wells Fargo Quantum Research), arXiv:2412.12484 (2024) &#8211; discusses QNN architectures and variationa#l circuits . -->
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<!-- J. Millet et al., &#8220;Variational quantum circuits for machine learning: an application for detecting weak signals,&#8221; Ap#pl. Sci. 11, 6427 (2021) . -->
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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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<section>
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<h2 id="plans-for-the-week-of-may-12-16">Plans for the week of May 12-16 </h2>
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<ol>
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<p><li> Discussion of quantum neural networks</li>
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<p><li> Start discussion fo Boltzmann machines, classical and quantum mechanical ones.</li>
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</ol>
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</section>
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‎doc/pub/week15/html/week15-solarized.html‎

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end of tocinfo -->
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<body>
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<li> Variational Quantum Circuits (VQCs)</li>
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<li> Quantum neural networks (QNNs)</li>
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<ul>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.pdf" target="_blank">Whiteboard notes</a> --></li>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMay7.pdf" target="_blank">Whiteboard notes</a> --></li>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-svms">Quantum SVMs </h2>
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<h2 id="quantum-svms-short-reminder-from-last-week">Quantum SVMs, short reminder from last week </h2>
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<p>The idea of a classical SVM is that we have a set of points
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that are in either one group or another and we want to find a line that
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<!-- A. Abbas et al., &#8220;The power of quantum neural networks,&#8221; Nature Comput. Sci. 1, 403&#8211;409 (2021) . -->
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<!-- E. Anschuetz and B. Kiani, &#8220;Quantum variational algorithms are swamped with traps,&#8221; Nat. Commun. 13, 7760 (2022) . -->
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<!-- J. Zhang et al. (Wells Fargo Quantum Research), arXiv:2412.12484 (2024) &#8211; discusses QNN architectures and variationa#l circuits . -->
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<!-- J. Millet et al., &#8220;Variational quantum circuits for machine learning: an application for detecting weak signals,&#8221; Ap#pl. Sci. 11, 6427 (2021) . -->
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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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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="references-of-interest">References of interest </h2>
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<ol>
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<li> A. Abbas et al., <b>The power of quantum neural networks</b>, Nature Comput. Sci. 1, 403&#8211;409 (2021).</li>
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<li> E. Anschuetz and B. Kiani, <b>Quantum variational algorithms are swamped with traps</b>, Nat. Commun. 13, 7760 (2022) .</li>
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<li> J. Millet et al., <b>Variational quantum circuits for machine learning: an application for detecting weak signals</b>, Appl. Sci. 11, 6427 (2021) .</li>
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<li> M. Zhao et al., <b>A tutorial on quantum machine learning and quantum neural networks</b>, arXiv:2504.16131 (2025) .</li>
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<li> D. M. Houshmand, <b>Quantum Machine Learning Lecture Notes</b>, (online, 2023) . (Tutorial using PennyLane QNNs.)</li>
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<li> PennyLane documentation and tutorials: <a href="https://pennylane.a" target="_blank"><tt>https://pennylane.a</tt></a>&#12297; (for code examples and parameter-shift rules).</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="plans-for-the-week-of-may-12-16">Plans for the week of May 12-16 </h2>
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<ol>
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<li> Discussion of quantum neural networks</li>
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<li> Start discussion fo Boltzmann machines, classical and quantum mechanical ones.</li>
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</ol>
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<!-- ------------------- end of main content --------------- -->
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<center style="font-size:80%">
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<!-- copyright --> &copy; 1999-2025, Morten Hjorth-Jensen. Released under CC Attribution-NonCommercial 4.0 license

‎doc/pub/week15/html/week15.html‎

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end of tocinfo -->
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<body>
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<li> Variational Quantum Circuits (VQCs)</li>
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<li> Quantum neural networks (QNNs)</li>
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<ul>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be/OZdyky8UYdk" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2024/NotesMay8.pdf" target="_blank">Whiteboard notes</a> --></li>
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<li> Training QNNs and Loss Landscapes</li>
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<li> Implementing QNNs with PennyLane
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<!-- o <a href="https://youtu.be" target="_blank">Video of lecture at</a> -->
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<!-- o <a href="https://github.com/CompPhysics/QuantumComputingMachineLearning/blob/gh-pages/doc/HandWrittenNotes/2025/NotesMay7.pdf" target="_blank">Whiteboard notes</a> --></li>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="quantum-svms">Quantum SVMs </h2>
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<h2 id="quantum-svms-short-reminder-from-last-week">Quantum SVMs, short reminder from last week </h2>
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<p>The idea of a classical SVM is that we have a set of points
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that are in either one group or another and we want to find a line that
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<!-- A. Abbas et al., &#8220;The power of quantum neural networks,&#8221; Nature Comput. Sci. 1, 403&#8211;409 (2021) . -->
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<!-- E. Anschuetz and B. Kiani, &#8220;Quantum variational algorithms are swamped with traps,&#8221; Nat. Commun. 13, 7760 (2022) . -->
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<!-- J. Zhang et al. (Wells Fargo Quantum Research), arXiv:2412.12484 (2024) &#8211; discusses QNN architectures and variationa#l circuits . -->
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<!-- J. Millet et al., &#8220;Variational quantum circuits for machine learning: an application for detecting weak signals,&#8221; Ap#pl. Sci. 11, 6427 (2021) . -->
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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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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="references-of-interest">References of interest </h2>
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<ol>
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<li> A. Abbas et al., <b>The power of quantum neural networks</b>, Nature Comput. Sci. 1, 403&#8211;409 (2021).</li>
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<li> E. Anschuetz and B. Kiani, <b>Quantum variational algorithms are swamped with traps</b>, Nat. Commun. 13, 7760 (2022) .</li>
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<li> J. Millet et al., <b>Variational quantum circuits for machine learning: an application for detecting weak signals</b>, Appl. Sci. 11, 6427 (2021) .</li>
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<li> M. Zhao et al., <b>A tutorial on quantum machine learning and quantum neural networks</b>, arXiv:2504.16131 (2025) .</li>
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<li> D. M. Houshmand, <b>Quantum Machine Learning Lecture Notes</b>, (online, 2023) . (Tutorial using PennyLane QNNs.)</li>
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<li> PennyLane documentation and tutorials: <a href="https://pennylane.a" target="_blank"><tt>https://pennylane.a</tt></a>&#12297; (for code examples and parameter-shift rules).</li>
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</ol>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="plans-for-the-week-of-may-12-16">Plans for the week of May 12-16 </h2>
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<ol>
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<li> Discussion of quantum neural networks</li>
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<li> Start discussion fo Boltzmann machines, classical and quantum mechanical ones.</li>
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</ol>
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<!-- ------------------- end of main content --------------- -->
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