Efficient Characterization of Quantum Evolutions via a Recommender System

Priya Batra; Anukriti Singh; T. S. Mahesh

doi:10.22331/q-2021-12-06-598

Efficient Characterization of Quantum Evolutions via a Recommender System

Priya Batra, Anukriti Singh, and T. S. Mahesh

Department of Physics and NMR Research Center, Indian Institute of Science Education and Research, Pune 411008, India

Published:	2021-12-06, volume 5, page 598
Eprint:	arXiv:2005.10555v4
Doi:	https://doi.org/10.22331/q-2021-12-06-598
Citation:	Quantum 5, 598 (2021).

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.

Abstract

We demonstrate characterizing quantum evolutions via matrix factorization algorithm, a particular type of the recommender system (RS). A system undergoing a quantum evolution can be characterized in several ways. Here we choose (i) quantum correlations quantified by measures such as entropy, negativity, or discord, and (ii) state-fidelity. Using quantum registers with up to 10 qubits, we demonstrate that an RS can efficiently characterize both unitary and nonunitary evolutions. After carrying out a detailed performance analysis of the RS in two qubits, we show that it can be used to distinguish a clean database of quantum correlations from a noisy or a fake one. Moreover, we find that the RS brings about a significant computational advantage for building a large database of quantum discord, for which no simple closed-form expression exists. Also, RS can efficiently characterize systems undergoing nonunitary evolutions in terms of quantum discord reduction as well as state-fidelity. Finally, we utilize RS for the construction of discord phase space in a nonlinear quantum system.

Featured image: Can recommender system help completing a patchy quantum database?

Popular summary

Confused about choosing a product? Probably, the Recommender System (RS) might help. RS is a type of algorithm that is being used by online platforms to recommend products to consumers. They use the past history of an individual along with the similar choices of other consumers. Given a sparse database of the rating matrix, RS can fill out the remaining elements with pretty high accuracy. Here we use RS to complete a sparse quantum database of correlations, gate fidelities, etc. Interestingly, we found that RS can even predict quantum discord, a kind of quantum correlation that has no analytical expression. While one can think of many applications of such a prediction, here we demonstrate completing a sparse phase-space diagram of a nonlinear quantum system.

► BibTeX data

@article{Batra2021efficient,
  doi = {10.22331/q-2021-12-06-598},
  url = {https://doi.org/10.22331/q-2021-12-06-598},
  title = {Efficient {C}haracterization of {Q}uantum {E}volutions via a {R}ecommender {S}ystem},
  author = {Batra, Priya and Singh, Anukriti and Mahesh, T. S.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {5},
  pages = {598},
  month = dec,
  year = {2021}
}

► References

[1] G. Linden, B. Smith, and J. York. Amazon.com recommendations: item-to-item collaborative filtering. IEEE Internet Computing, 7 (1): 76–80, 2003. 10.1109/MIC.2003.1167344.
https://doi.org/10.1109/MIC.2003.1167344

[2] Simon Funk. Netflix update: Try this at home, 2006.

[3] J. Ben Schafer, Joseph A. Konstan, and John Riedl. E-Commerce Recommendation Applications, pages 115–153. Springer US, Boston, MA, 2001. ISBN 978-1-4615-1627-9. 10.1007/978-1-4615-1627-9_6. URL https://doi.org/10.1007/978-1-4615-1627-9_6.
https://doi.org/10.1007/978-1-4615-1627-9_6

[4] Henry Lieberman. Autonomous interface agents. In Proceedings of the ACM SIGCHI Conference on Human Factors in Computing Systems, CHI '97, page 67–74, New York, NY, USA, 1997. Association for Computing Machinery. ISBN 0897918029. 10.1145/258549.258592. URL https://doi.org/10.1145/258549.258592.
https://doi.org/10.1145/258549.258592

[5] Pattie Maes. Agents that reduce work and information overload. In RONALD M. BAECKER, JONATHAN GRUDIN, WILLIAM A.S. BUXTON, and SAUL GREENBERG, editors, Readings in Human–Computer Interaction, Interactive Technologies, pages 811–821. Morgan Kaufmann, 1995. ISBN 978-0-08-051574-8. https://doi.org/10.1016/B978-0-08-051574-8.50084-4. URL https://www.sciencedirect.com/science/article/pii/B9780080515748500844.
https://doi.org/10.1016/B978-0-08-051574-8.50084-4
https://www.sciencedirect.com/science/article/pii/B9780080515748500844

[6] Robin Burke. Knowledge-based recommender systems. Encyclopedia of library and information systems, 69 (Supplement 32): 175–186, 2000.

[7] David Goldberg, David Nichols, Brian M. Oki, and Douglas Terry. Using collaborative filtering to weave an information tapestry. Commun. ACM, 35 (12): 61–70, dec 1992. ISSN 0001-0782. 10.1145/138859.138867. URL https://doi.org/10.1145/138859.138867.
https://doi.org/10.1145/138859.138867

[8] J. Ben Schafer, Dan Frankowski, Jon Herlocker, and Shilad Sen. Collaborative Filtering Recommender Systems, pages 291–324. Springer Berlin Heidelberg, Berlin, Heidelberg, 2007. ISBN 978-3-540-72079-9. 10.1007/978-3-540-72079-9_9. URL https://doi.org/10.1007/978-3-540-72079-9_9.
https://doi.org/10.1007/978-3-540-72079-9_9

[9] Yehuda Koren, Robert Bell, and Chris Volinsky. Matrix factorization techniques for recommender systems. Computer, 42 (8): 30–37, 2009. 10.1109/MC.2009.263.
https://doi.org/10.1109/MC.2009.263

[10] Giacomo Torlai, Guglielmo Mazzola, Juan Carrasquilla, Matthias Troyer, Roger Melko, and Giuseppe Carleo. Neural-network quantum state tomography. Nature Physics, 14 (5): 447–450, 2018. 10.1038/s41567-018-0048-5. URL https://doi.org/10.1038/s41567-018-0048-5.
https://doi.org/10.1038/s41567-018-0048-5

[11] Mária Kieferová and Nathan Wiebe. Tomography and generative training with quantum boltzmann machines. Phys. Rev. A, 96: 062327, Dec 2017. 10.1103/PhysRevA.96.062327. URL https://link.aps.org/doi/10.1103/PhysRevA.96.062327.
https://doi.org/10.1103/PhysRevA.96.062327

[12] Giacomo Torlai and Roger G. Melko. Neural decoder for topological codes. Phys. Rev. Lett., 119: 030501, Jul 2017. 10.1103/PhysRevLett.119.030501. URL https://link.aps.org/doi/10.1103/PhysRevLett.119.030501.
https://doi.org/10.1103/PhysRevLett.119.030501

[13] Moritz August and Xiaotong Ni. Using recurrent neural networks to optimize dynamical decoupling for quantum memory. Phys. Rev. A, 95: 012335, Jan 2017. 10.1103/PhysRevA.95.012335. URL https://link.aps.org/doi/10.1103/PhysRevA.95.012335.
https://doi.org/10.1103/PhysRevA.95.012335

[14] Juan Carrasquilla and Roger G Melko. Machine learning phases of matter. Nature Physics, 13 (5): 431–434, 2017. 10.1038/nphys4035. URL https://doi.org/10.1038/nphys4035.
https://doi.org/10.1038/nphys4035

[15] Askery Canabarro, Felipe Fernandes Fanchini, André Luiz Malvezzi, Rodrigo Pereira, and Rafael Chaves. Unveiling phase transitions with machine learning. Phys. Rev. B, 100: 045129, Jul 2019. 10.1103/PhysRevB.100.045129. URL https://link.aps.org/doi/10.1103/PhysRevB.100.045129.
https://doi.org/10.1103/PhysRevB.100.045129

[16] Giuseppe Carleo and Matthias Troyer. Solving the quantum many-body problem with artificial neural networks. Science, 355 (6325): 602–606, 2017. 10.1126/science.aag2302.
https://doi.org/10.1126/science.aag2302

[17] Xun Gao and Lu-Ming Duan. Efficient representation of quantum many-body states with deep neural networks. Nature communications, 8 (1): 1–6, 2017. 10.1038/s41467-017-00705-2. URL https://doi.org/10.1038/s41467-017-00705-2.
https://doi.org/10.1038/s41467-017-00705-2

[18] Xiao-Ming Lu, Jian Ma, Zhengjun Xi, and Xiaoguang Wang. Optimal measurements to access classical correlations of two-qubit states. Phys. Rev. A, 83: 012327, Jan 2011. 10.1103/PhysRevA.83.012327. URL https://link.aps.org/doi/10.1103/PhysRevA.83.012327.
https://doi.org/10.1103/PhysRevA.83.012327

[19] Yue-Chi Ma and Man-Hong Yung. Transforming bell’s inequalities into state classifiers with machine learning. npj Quantum Information, 4 (1): 1–10, 2018. 10.1038/s41534-018-0081-3. URL https://doi.org/10.1038/s41534-018-0081-3.
https://doi.org/10.1038/s41534-018-0081-3

[20] Jun Gao, Lu-Feng Qiao, Zhi-Qiang Jiao, Yue-Chi Ma, Cheng-Qiu Hu, Ruo-Jing Ren, Ai-Lin Yang, Hao Tang, Man-Hong Yung, and Xian-Min Jin. Experimental machine learning of quantum states. Phys. Rev. Lett., 120: 240501, Jun 2018. 10.1103/PhysRevLett.120.240501. URL https://link.aps.org/doi/10.1103/PhysRevLett.120.240501.
https://doi.org/10.1103/PhysRevLett.120.240501

[21] Mu Yang, Chang-liang Ren, Yue-chi Ma, Ya Xiao, Xiang-Jun Ye, Lu-Lu Song, Jin-Shi Xu, Man-Hong Yung, Chuan-Feng Li, and Guang-Can Guo. Experimental simultaneous learning of multiple nonclassical correlations. Phys. Rev. Lett., 123: 190401, Nov 2019. 10.1103/PhysRevLett.123.190401. URL https://link.aps.org/doi/10.1103/PhysRevLett.123.190401.
https://doi.org/10.1103/PhysRevLett.123.190401

[22] Valeria Cimini, Marco Barbieri, Nicolas Treps, Mattia Walschaers, and Valentina Parigi. Neural networks for detecting multimode wigner negativity. Phys. Rev. Lett., 125: 160504, Oct 2020. 10.1103/PhysRevLett.125.160504. URL https://link.aps.org/doi/10.1103/PhysRevLett.125.160504.
https://doi.org/10.1103/PhysRevLett.125.160504

[23] Xiao-Yu Li, Qin-Sheng Zhu, Ming-Zheng Zhu, Yi-Ming Huang, Hao Wu, and Shao-Yi Wu. Machine learning study of the relationship between the geometric and entropy discord. EPL (Europhysics Letters), 127 (2): 20009, sep 2019. 10.1209/0295-5075/127/20009. URL https://doi.org/10.1209/0295-5075/127/20009.
https://doi.org/10.1209/0295-5075/127/20009

[24] Wikipedia contributors. Matrix factorization (recommender systems) — Wikipedia, the free encyclopedia, 2020.

[25] Andrew Ng, Stanford Machine Learning Course. URL https://www.coursera.org/learn/machine-learning.
https://www.coursera.org/learn/machine-learning

[26] V Al Osipov, H-J Sommers, and K Życzkowski. Random bures mixed states and the distribution of their purity. Journal of Physics A: Mathematical and Theoretical, 43 (5): 055302, jan 2010. 10.1088/1751-8113/43/5/055302. URL https://doi.org/10.1088/1751-8113/43/5/055302.
https://doi.org/10.1088/1751-8113/43/5/055302

[27] Jonas Maziero. Random sampling of quantum states: a survey of methods. Brazilian Journal of Physics, 45 (6): 575–583, 2015. 10.1007/s13538-015-0367-2. URL https://doi.org/10.1007/s13538-015-0367-2.
https://doi.org/10.1007/s13538-015-0367-2

[28] Martin B. Plenio and Shashank S. Virmani. An Introduction to Entanglement Theory, pages 173–209. Springer International Publishing, Cham, 2014. ISBN 978-3-319-04063-9. 10.1007/978-3-319-04063-9_8. URL https://doi.org/10.1007/978-3-319-04063-9_8.
https://doi.org/10.1007/978-3-319-04063-9_8

[29] Harold Ollivier and Wojciech H. Zurek. Quantum discord: A measure of the quantumness of correlations. Phys. Rev. Lett., 88: 017901, Dec 2001. 10.1103/PhysRevLett.88.017901. URL https://link.aps.org/doi/10.1103/PhysRevLett.88.017901.
https://doi.org/10.1103/PhysRevLett.88.017901

[30] Hemant Katiyar, Soumya Singha Roy, T. S. Mahesh, and Apoorva Patel. Evolution of quantum discord and its stability in two-qubit nmr systems. Phys. Rev. A, 86: 012309, Jul 2012. 10.1103/PhysRevA.86.012309. URL https://link.aps.org/doi/10.1103/PhysRevA.86.012309.
https://doi.org/10.1103/PhysRevA.86.012309

[31] Yichen Huang. Computing quantum discord is NP-complete. New Journal of Physics, 16 (3): 033027, mar 2014. 10.1088/1367-2630/16/3/033027. URL https://doi.org/10.1088/1367-2630/16/3/033027.
https://doi.org/10.1088/1367-2630/16/3/033027

[32] Michael A Nielsen and Isaac Chuang. Quantum computation and quantum information, 2002.

[33] B. Georgeot and D. L. Shepelyansky. Emergence of quantum chaos in the quantum computer core and how to manage it. Phys. Rev. E, 62: 6366–6375, Nov 2000. 10.1103/PhysRevE.62.6366. URL https://link.aps.org/doi/10.1103/PhysRevE.62.6366.
https://doi.org/10.1103/PhysRevE.62.6366

[34] Philipp Hauke, Fernando M Cucchietti, Luca Tagliacozzo, Ivan Deutsch, and Maciej Lewenstein. Can one trust quantum simulators? Reports on Progress in Physics, 75 (8): 082401, jul 2012. 10.1088/0034-4885/75/8/082401. URL https://doi.org/10.1088/0034-4885/75/8/082401.
https://doi.org/10.1088/0034-4885/75/8/082401

[35] Fritz Haake, M Kuś, and Rainer Scharf. Classical and quantum chaos for a kicked top. Zeitschrift für Physik B Condensed Matter, 65 (3): 381–395, 1987. 10.1007/BF01303727. URL https://doi.org/10.1007/BF01303727.
https://doi.org/10.1007/BF01303727

[36] Vaibhav Madhok, Vibhu Gupta, Denis-Alexandre Trottier, and Shohini Ghose. Signatures of chaos in the dynamics of quantum discord. Phys. Rev. E, 91: 032906, Mar 2015. 10.1103/PhysRevE.91.032906. URL https://link.aps.org/doi/10.1103/PhysRevE.91.032906.
https://doi.org/10.1103/PhysRevE.91.032906

[37] V. R. Krithika, V. S. Anjusha, Udaysinh T. Bhosale, and T. S. Mahesh. Nmr studies of quantum chaos in a two-qubit kicked top. Phys. Rev. E, 99: 032219, Mar 2019. 10.1103/PhysRevE.99.032219. URL https://link.aps.org/doi/10.1103/PhysRevE.99.032219.
https://doi.org/10.1103/PhysRevE.99.032219

[38] J. F. Poyatos, J. I. Cirac, and P. Zoller. Complete characterization of a quantum process: The two-bit quantum gate. Phys. Rev. Lett., 78: 390–393, Jan 1997. 10.1103/PhysRevLett.78.390. URL https://link.aps.org/doi/10.1103/PhysRevLett.78.390.
https://doi.org/10.1103/PhysRevLett.78.390

Cited by

[1] Giovanni Pilato and Filippo Vella, "A Survey on Quantum Computing for Recommendation Systems", Information 14 1, 20 (2022).

[2] Kavita Dorai and Arvind, "NMR Quantum Information Processing: Indian Contributions and Perspectives", Journal of the Indian Institute of Science 103 2, 569 (2023).

[3] Priya Batra, M. Harshanth Ram, and T.S. Mahesh, "Recommender system expedited quantum control optimization", Physics Open 14, 100127 (2023).

The above citations are from Crossref's cited-by service (last updated successfully 2023-11-28 22:39:37) and SAO/NASA ADS (last updated successfully 2023-11-28 22:39:38). The list may be incomplete as not all publishers provide suitable and complete citation data.

This Paper is published in Quantum under the Creative Commons Attribution 4.0 International (CC BY 4.0) license. Copyright remains with the original copyright holders such as the authors or their institutions.