Quantum Machine Learning with SQUID

Alessandro Roggero1,2, Jakub Filipek3, Shih-Chieh Hsu4, and Nathan Wiebe5,6,4

1Institute for Nuclear Theory, University of Washington, Seattle, WA 98195, USA
2InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, USA
3Paul G. Allen School of Computer Science & Engineering, University of Washington, Seattle, WA 98195, USA
4Department of Physics, University of Washington, Seattle 98195, USA
5University of Toronto, Department of Computer Science, Toronto, ON M5G 1V7, Canada
6Pacific Northwest National Laboratory, Richland, WA 99352, USA

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In this work we present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. The classical infrastructure is based on PyTorch and we provide a standardized design to implement a variety of quantum models with the capability of back-propagation for efficient training. We present the structure of our framework and provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset. In particular, we highlight the implications for scalability for gradient-based optimization of quantum models on the choice of output for variational quantum models.

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► References

[1] Vedran Dunjko and Peter Wittek. A non-review of Quantum Machine Learning: trends and explorations. Quantum Views, 4: 32, March 2020. 10.22331/​qv-2020-03-17-32. URL https:/​/​doi.org/​10.22331/​qv-2020-03-17-32.

[2] Nathan Wiebe. Key questions for the quantum machine learner to ask themselves. New Journal of Physics, 22 (9): 091001, sep 2020. 10.1088/​1367-2630/​abac39. URL https:/​/​doi.org/​10.1088/​1367-2630/​abac39.

[3] Wen Guan, Gabriel Perdue, Arthur Pesah, Maria Schuld, Koji Terashi, Sofia Vallecorsa, and Jean-Roch Vlimant. Quantum machine learning in high energy physics. Machine Learning: Science and Technology, 2 (1): 011003, Mar 2021. ISSN 2632-2153. 10.1088/​2632-2153/​abc17d. URL http:/​/​dx.doi.org/​10.1088/​2632-2153/​abc17d.

[4] M. Cerezo, Andrew Arrasmith, Ryan Babbush, Simon C. Benjamin, Suguru Endo, Keisuke Fujii, Jarrod R. McClean, Kosuke Mitarai, Xiao Yuan, Lukasz Cincio, and Patrick J. Coles. Variational quantum algorithms. Nature Reviews Physics, 3 (9): 625–644, aug 2021. 10.1038/​s42254-021-00348-9. URL https:/​/​doi.org/​10.1038/​s42254-021-00348-9.

[5] Patrick Rebentrost, Masoud Mohseni, and Seth Lloyd. Quantum support vector machine for big data classification. Phys. Rev. Lett., 113: 130503, Sep 2014. 10.1103/​PhysRevLett.113.130503. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.113.130503.

[6] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd. Quantum machine learning. Nature, 549: 195–202, 2017. 10.1038/​nature23474. URL https:/​/​doi.org/​10.1038/​nature23474.

[7] Hsin-Yuan Huang, Michael Broughton, Masoud Mohseni, Ryan Babbush, Sergio Boixo, Hartmut Neven, and Jarrod R. McClean. Power of data in quantum machine learning. Nature Communications, 12 (1), may 2021a. 10.1038/​s41467-021-22539-9. URL https:/​/​doi.org/​10.1038/​s41467-021-22539-9.

[8] Hsin-Yuan Huang, Richard Kueng, and John Preskill. Information-theoretic bounds on quantum advantage in machine learning. Phys. Rev. Lett., 126: 190505, May 2021b. 10.1103/​PhysRevLett.126.190505. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.126.190505.

[9] Yunchao Liu, Srinivasan Arunachalam, and Kristan Temme. A rigorous and robust quantum speed-up in supervised machine learning. Nature Physics, 17 (9): 1013–1017, jul 2021. 10.1038/​s41567-021-01287-z. URL https:/​/​doi.org/​10.1038/​s41567-021-01287-z.

[10] Maria Schuld and Nathan Killoran. Quantum machine learning in feature hilbert spaces. Phys. Rev. Lett., 122: 040504, Feb 2019. 10.1103/​PhysRevLett.122.040504. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.122.040504.

[11] Jarrod R. McClean, Sergio Boixo, Vadim N. Smelyanskiy, Ryan Babbush, and Hartmut Neven. Barren plateaus in quantum neural network training landscapes. Nature Communications, 9 (1), nov 2018. 10.1038/​s41467-018-07090-4. URL https:/​/​doi.org/​10.1038/​s41467-018-07090-4.

[12] Kerstin Beer, Dmytro Bondarenko, Terry Farrelly, Tobias J. Osborne, Robert Salzmann, Daniel Scheiermann, and Ramona Wolf. Training deep quantum neural networks. Nature Communications, 11 (1), feb 2020. 10.1038/​s41467-020-14454-2. URL https:/​/​doi.org/​10.1038/​s41467-020-14454-2.

[13] Carlos Ortiz Marrero, Mária Kieferová, and Nathan Wiebe. Entanglement-induced barren plateaus. PRX Quantum, 2: 040316, Oct 2021. 10.1103/​PRXQuantum.2.040316. URL https:/​/​link.aps.org/​doi/​10.1103/​PRXQuantum.2.040316.

[14] Arthur Pesah, M. Cerezo, Samson Wang, Tyler Volkoff, Andrew T. Sornborger, and Patrick J. Coles. Absence of barren plateaus in quantum convolutional neural networks. Phys. Rev. X, 11: 041011, Oct 2021. 10.1103/​PhysRevX.11.041011. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevX.11.041011.

[15] Leonardo Banchi, Jason Pereira, and Stefano Pirandola. Generalization in quantum machine learning: A quantum information standpoint. PRX Quantum, 2: 040321, Nov 2021. 10.1103/​PRXQuantum.2.040321. URL https:/​/​link.aps.org/​doi/​10.1103/​PRXQuantum.2.040321.

[16] Yuxuan Du, Zhuozhuo Tu, Xiao Yuan, and Dacheng Tao. Efficient measure for the expressivity of variational quantum algorithms. Phys. Rev. Lett., 128: 080506, Feb 2022. 10.1103/​PhysRevLett.128.080506. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.128.080506.

[17] Vojtěch Havlíček, Antonio D. Córcoles, Kristan Temme, Aram W. Harrow, Abhinav Kandala, Jerry M. Chow, and Jay M. Gambetta. Supervised learning with quantum-enhanced feature spaces. Nature, 567 (7747): 209–212, Mar 2019. ISSN 1476-4687. 10.1038/​s41586-019-0980-2. URL http:/​/​dx.doi.org/​10.1038/​s41586-019-0980-2.

[18] Evan Peters, João Caldeira, Alan Ho, Stefan Leichenauer, Masoud Mohseni, Hartmut Neven, Panagiotis Spentzouris, Doug Strain, and Gabriel N. Perdue. Machine learning of high dimensional data on a noisy quantum processor. npj Quantum Information, (7): 161, 2021. 10.1038/​s41534-021-00498-9. URL https:/​/​doi.org/​10.1038/​s41534-021-00498-9.

[19] Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dandelion Mané, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viégas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng. TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https:/​/​www.tensorflow.org/​. Software available from tensorflow.org.

[20] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, et al. Pytorch: An imperative style, high-performance deep learning library. In H. Wallach, H. Larochelle, A. Beygelzimer, F. d' Alché-Buc, E. Fox, and R. Garnett, editors, Advances in Neural Information Processing Systems 32, pages 8026–8037. Curran Associates, Inc., 2019. URL http:/​/​papers.nips.cc/​paper/​9015-pytorch-an-imperative-style-high-performance-deep-learning-library.pdf.

[21] J. Filipek, A. Roggero, S. Hsu, and N. Wiebe. SQUID. https:/​/​bitbucket.org/​squid-qml/​, 2021.

[22] Robert S. Smith, Michael J. Curtis, and William J. Zeng. A practical quantum instruction set architecture. arXiv, (1608.03355), 2016. 10.48550/​ARXIV.1608.03355.

[23] Héctor Abraham et al. Qiskit: An open-source framework for quantum computing. 2019. 10.5281/​zenodo.2562110.

[24] Quantum AI team and collaborators. Cirq. October 2020. 10.5281/​zenodo.4062499. URL https:/​/​doi.org/​10.5281/​zenodo.4062499.

[25] Charles R. Harris, K. Jarrod Millman, St'efan J. van der Walt, Ralf Gommers, Pauli Virtanen, David Cournapeau, et al. Array programming with NumPy. Nature, 585 (7825): 357–362, September 2020. 10.1038/​s41586-020-2649-2. URL https:/​/​doi.org/​10.1038/​s41586-020-2649-2.

[26] Gilles Brassard, Peter Høyer, Michele Mosca, and Alain Tapp. Quantum amplitude amplification and estimation. Quantum Computation and Information, page 53–74, 2002. ISSN 0271-4132. 10.1090/​conm/​305/​05215. URL http:/​/​dx.doi.org/​10.1090/​conm/​305/​05215.

[27] Yohichi Suzuki, Shumpei Uno, Rudy Raymond, Tomoki Tanaka, Tamiya Onodera, and Naoki Yamamoto. Amplitude estimation without phase estimation. Quantum Information Processing, 19 (2), Jan 2020. ISSN 1573-1332. 10.1007/​s11128-019-2565-2. URL http:/​/​dx.doi.org/​10.1007/​s11128-019-2565-2.

[28] Dmitry Grinko, Julien Gacon, Christa Zoufal, and Stefan Woerner. Iterative quantum amplitude estimation. npj Quantum Information, 7 (1), Mar 2021. ISSN 2056-6387. 10.1038/​s41534-021-00379-1. URL http:/​/​dx.doi.org/​10.1038/​s41534-021-00379-1.

[29] András Gilyén, Srinivasan Arunachalam, and Nathan Wiebe. Optimizing quantum optimization algorithms via faster quantum gradient computation. In Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms, pages 1425–1444. SIAM, 2019. 10.1137/​1.9781611975482.87.

[30] Maria Schuld, Alex Bocharov, Krysta M. Svore, and Nathan Wiebe. Circuit-centric quantum classifiers. Phys. Rev. A, 101: 032308, Mar 2020. 10.1103/​PhysRevA.101.032308. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.101.032308.

[31] G. Vidal and C. M. Dawson. Universal quantum circuit for two-qubit transformations with three controlled-not gates. Phys. Rev. A, 69: 010301, Jan 2004. 10.1103/​PhysRevA.69.010301. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.69.010301.

[32] Farrokh Vatan and Colin Williams. Optimal quantum circuits for general two-qubit gates. Phys. Rev. A, 69: 032315, Mar 2004. 10.1103/​PhysRevA.69.032315. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevA.69.032315.

[33] Y. Lecun, L. Bottou, Y. Bengio, and P. Haffner. Gradient-based learning applied to document recognition. Proceedings of the IEEE, 86 (11): 2278–2324, 1998. 10.1109/​5.726791.

[34] Ville Bergholm, Josh Izaac, Maria Schuld, Christian Gogolin, M. Sohaib Alam, Shahnawaz Ahmed, Juan Miguel Arrazola, Carsten Blank, Alain Delgado, Soran Jahangiri, Keri McKiernan, Johannes Jakob Meyer, Zeyue Niu, Antal Száva, and Nathan Killoran. Pennylane: Automatic differentiation of hybrid quantum-classical computations. arXiv, (1811.04968), 2018. 10.48550/​ARXIV.1811.04968. URL https:/​/​arxiv.org/​abs/​1811.04968.

[35] Huitao Shen, Pengfei Zhang, Yi-Zhuang You, and Hui Zhai. Information scrambling in quantum neural networks. Phys. Rev. Lett., 124: 200504, May 2020. 10.1103/​PhysRevLett.124.200504. URL https:/​/​link.aps.org/​doi/​10.1103/​PhysRevLett.124.200504.

[36] Ding Liu, Shi-Ju Ran, Peter Wittek, Cheng Peng, Raul Blázquez García, Gang Su, and Maciej Lewenstein. Machine learning by unitary tensor network of hierarchical tree structure. New Journal of Physics, 21 (7): 073059, jul 2019. 10.1088/​1367-2630/​ab31ef. URL https:/​/​doi.org/​10.1088/​1367-2630/​ab31ef.

[37] Chase Roberts, Ashley Milsted, Martin Ganahl, Adam Zalcman, Bruce Fontaine, Yijian Zou, Jack Hidary, Guifre Vidal, and Stefan Leichenauer. Tensornetwork: A library for physics and machine learning. arXiv, (1905.01330), 2019. 10.48550/​ARXIV.1905.01330.

[38] K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii. Quantum circuit learning. Physical Review A, 98 (3), Sep 2018. ISSN 2469-9934. 10.1103/​physreva.98.032309. URL http:/​/​dx.doi.org/​10.1103/​PhysRevA.98.032309.

[39] Maria Schuld, Ville Bergholm, Christian Gogolin, Josh Izaac, and Nathan Killoran. Evaluating analytic gradients on quantum hardware. Physical Review A, 99 (3), Mar 2019. ISSN 2469-9934. 10.1103/​physreva.99.032331. URL http:/​/​dx.doi.org/​10.1103/​PhysRevA.99.032331.

Cited by

[1] Natalie Klco, Alessandro Roggero, and Martin J. Savage, "Standard model physics and the digital quantum revolution: thoughts about the interface", Reports on Progress in Physics 85 6, 064301 (2022).

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