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update week 16
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‎doc/pub/week16/html/week16-bs.html‎

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<!-- navigation toc: --> <li><a href="#training-of-a-qbm" style="font-size: 80%;">Training of a QBM</a></li>
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<!-- navigation toc: --> <li><a href="#more-code-examples" style="font-size: 80%;">More code examples</a></li>
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<!-- navigation toc: --> <li><a href="#summary-of-steps-in-pennylane-implementation" style="font-size: 80%;">Summary of steps in PennyLane implementation</a></li>
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<!-- navigation toc: --> <li><a href="#references-on-qbms" style="font-size: 80%;">References on QBMs</a></li>
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<p>Use an optimizer (e.g. gradient descent, Adam) with PennyLane&#8217;s gradient calculations to update parameters.</p>
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<!-- !split -->
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<h2 id="references-on-qbms" class="anchor">References on QBMs </h2>
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<div class="panel panel-default">
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<div class="panel-body">
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<!-- subsequent paragraphs come in larger fonts, so start with a paragraph -->
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<ol>
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<li> Amin et al., 2018. Quantum Boltzmann Machine, Phys. Rev. X 8, 021050. (Introduced the QBM and training bounds .)</li>
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<li> Wu et al., 2020. Quantum restricted Boltzmann machine is universal for quantum computation, arXiv:2005.11970. (Defined the 2-local QRBM Hamiltonian and demonstrated its universality .)</li>
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<li> Huijgen et al., 2024. Training Quantum Boltzmann Machines with the beta-VQE, arXiv:2304.08631. (Presented the nested variational training algorithm .)</li>
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<li> Coopmans &amp; Benedetti, 2024. On the sample complexity of quantum Boltzmann machine learning, Commun. Phys. 7, 274. (Theoretical analysis of relative-entropy training and sample complexity .)</li>
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<li> Minervini et al., 2025. Evolved Quantum Boltzmann Machines, arXiv:2501.03367. (Proposed the eQBM ansatz mixing imaginary and real time evolution .)</li>
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<li> Nicosia et al., 2025. Expressive equivalence of classical and quantum RBMs, arXiv:2502.17562. (Introduced semi-quantum RBMs (sqRBMs) with commuting visible terms and non-commuting hidden terms; showed structural relationships with classical RBMs .)</li>
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<li> Stein et al., 2023. Unsupervised anomaly detection with Quantum Boltzmann Machines, IEEE QWeek (preprint arXiv:2306.04998). (Applied QBMs to fraud/anomaly detection; found QBMs could outperform classical RBMs on synthetic cybersecurity data .)</li>
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<li> Moro &amp; Prati, 2023. Anomaly detection speed-up by quantum restricted Boltzmann machines, Commun. Phys. 6, 269. (Demonstrated classical vs. quantum training loops on real datasets and observed large sampling speed-ups on a quantum annealer .)</li>
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<li> Sinno et al., 2025. Implementing Large Quantum Boltzmann Machines for Dataset Balancing, arXiv:2502.03086. (Embedded a 120&#215;120 QRBM on D-Wave Pegasus to generate millions of intrusion-detection samples, improving downstream classifier performance .)</li>
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‎doc/pub/week16/html/week16-reveal.html‎

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<p>Use an optimizer (e.g. gradient descent, Adam) with PennyLane&#8217;s gradient calculations to update parameters.</p>
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<section>
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<h2 id="references-on-qbms">References on QBMs </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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<ol>
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<p><li> Amin et al., 2018. Quantum Boltzmann Machine, Phys. Rev. X 8, 021050. (Introduced the QBM and training bounds .)</li>
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<p><li> Wu et al., 2020. Quantum restricted Boltzmann machine is universal for quantum computation, arXiv:2005.11970. (Defined the 2-local QRBM Hamiltonian and demonstrated its universality .)</li>
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<p><li> Huijgen et al., 2024. Training Quantum Boltzmann Machines with the beta-VQE, arXiv:2304.08631. (Presented the nested variational training algorithm .)</li>
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<p><li> Coopmans &amp; Benedetti, 2024. On the sample complexity of quantum Boltzmann machine learning, Commun. Phys. 7, 274. (Theoretical analysis of relative-entropy training and sample complexity .)</li>
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<p><li> Minervini et al., 2025. Evolved Quantum Boltzmann Machines, arXiv:2501.03367. (Proposed the eQBM ansatz mixing imaginary and real time evolution .)</li>
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<p><li> Nicosia et al., 2025. Expressive equivalence of classical and quantum RBMs, arXiv:2502.17562. (Introduced semi-quantum RBMs (sqRBMs) with commuting visible terms and non-commuting hidden terms; showed structural relationships with classical RBMs .)</li>
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<p><li> Stein et al., 2023. Unsupervised anomaly detection with Quantum Boltzmann Machines, IEEE QWeek (preprint arXiv:2306.04998). (Applied QBMs to fraud/anomaly detection; found QBMs could outperform classical RBMs on synthetic cybersecurity data .)</li>
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<p><li> Moro &amp; Prati, 2023. Anomaly detection speed-up by quantum restricted Boltzmann machines, Commun. Phys. 6, 269. (Demonstrated classical vs. quantum training loops on real datasets and observed large sampling speed-ups on a quantum annealer .)</li>
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<p><li> Sinno et al., 2025. Implementing Large Quantum Boltzmann Machines for Dataset Balancing, arXiv:2502.03086. (Embedded a 120&#215;120 QRBM on D-Wave Pegasus to generate millions of intrusion-detection samples, improving downstream classifier performance .)</li>
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‎doc/pub/week16/html/week16-solarized.html‎

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<p>Use an optimizer (e.g. gradient descent, Adam) with PennyLane&#8217;s gradient calculations to update parameters.</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="references-on-qbms">References on QBMs </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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<ol>
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<li> Amin et al., 2018. Quantum Boltzmann Machine, Phys. Rev. X 8, 021050. (Introduced the QBM and training bounds .)</li>
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<li> Wu et al., 2020. Quantum restricted Boltzmann machine is universal for quantum computation, arXiv:2005.11970. (Defined the 2-local QRBM Hamiltonian and demonstrated its universality .)</li>
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<li> Huijgen et al., 2024. Training Quantum Boltzmann Machines with the beta-VQE, arXiv:2304.08631. (Presented the nested variational training algorithm .)</li>
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<li> Coopmans &amp; Benedetti, 2024. On the sample complexity of quantum Boltzmann machine learning, Commun. Phys. 7, 274. (Theoretical analysis of relative-entropy training and sample complexity .)</li>
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<li> Minervini et al., 2025. Evolved Quantum Boltzmann Machines, arXiv:2501.03367. (Proposed the eQBM ansatz mixing imaginary and real time evolution .)</li>
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<li> Nicosia et al., 2025. Expressive equivalence of classical and quantum RBMs, arXiv:2502.17562. (Introduced semi-quantum RBMs (sqRBMs) with commuting visible terms and non-commuting hidden terms; showed structural relationships with classical RBMs .)</li>
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<li> Stein et al., 2023. Unsupervised anomaly detection with Quantum Boltzmann Machines, IEEE QWeek (preprint arXiv:2306.04998). (Applied QBMs to fraud/anomaly detection; found QBMs could outperform classical RBMs on synthetic cybersecurity data .)</li>
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<li> Moro &amp; Prati, 2023. Anomaly detection speed-up by quantum restricted Boltzmann machines, Commun. Phys. 6, 269. (Demonstrated classical vs. quantum training loops on real datasets and observed large sampling speed-ups on a quantum annealer .)</li>
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<li> Sinno et al., 2025. Implementing Large Quantum Boltzmann Machines for Dataset Balancing, arXiv:2502.03086. (Embedded a 120&#215;120 QRBM on D-Wave Pegasus to generate millions of intrusion-detection samples, improving downstream classifier performance .)</li>
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‎doc/pub/week16/html/week16.html‎

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<p>Use an optimizer (e.g. gradient descent, Adam) with PennyLane&#8217;s gradient calculations to update parameters.</p>
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<!-- !split --><br><br><br><br><br><br><br><br><br><br>
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<h2 id="references-on-qbms">References on QBMs </h2>
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<div class="alert alert-block alert-block alert-text-normal">
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<b></b>
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<p>
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<ol>
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<li> Amin et al., 2018. Quantum Boltzmann Machine, Phys. Rev. X 8, 021050. (Introduced the QBM and training bounds .)</li>
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<li> Wu et al., 2020. Quantum restricted Boltzmann machine is universal for quantum computation, arXiv:2005.11970. (Defined the 2-local QRBM Hamiltonian and demonstrated its universality .)</li>
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<li> Huijgen et al., 2024. Training Quantum Boltzmann Machines with the beta-VQE, arXiv:2304.08631. (Presented the nested variational training algorithm .)</li>
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<li> Coopmans &amp; Benedetti, 2024. On the sample complexity of quantum Boltzmann machine learning, Commun. Phys. 7, 274. (Theoretical analysis of relative-entropy training and sample complexity .)</li>
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<li> Minervini et al., 2025. Evolved Quantum Boltzmann Machines, arXiv:2501.03367. (Proposed the eQBM ansatz mixing imaginary and real time evolution .)</li>
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<li> Nicosia et al., 2025. Expressive equivalence of classical and quantum RBMs, arXiv:2502.17562. (Introduced semi-quantum RBMs (sqRBMs) with commuting visible terms and non-commuting hidden terms; showed structural relationships with classical RBMs .)</li>
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<li> Stein et al., 2023. Unsupervised anomaly detection with Quantum Boltzmann Machines, IEEE QWeek (preprint arXiv:2306.04998). (Applied QBMs to fraud/anomaly detection; found QBMs could outperform classical RBMs on synthetic cybersecurity data .)</li>
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<li> Moro &amp; Prati, 2023. Anomaly detection speed-up by quantum restricted Boltzmann machines, Commun. Phys. 6, 269. (Demonstrated classical vs. quantum training loops on real datasets and observed large sampling speed-ups on a quantum annealer .)</li>
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<li> Sinno et al., 2025. Implementing Large Quantum Boltzmann Machines for Dataset Balancing, arXiv:2502.03086. (Embedded a 120&#215;120 QRBM on D-Wave Pegasus to generate millions of intrusion-detection samples, improving downstream classifier performance .)</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/week16/ipynb/ipynb-week16-src.tar.gz‎

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