- Physical Review Journals
All JournalsPhysics Magazine

Physical Review B

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Quantum phase detection generalization from marginal quantum neural network models

Saverio Monaco1,2,*, Oriel Kiss1,3,*, Antonio Mandarino4,†, Sofia Vallecorsa1, and Michele Grossi1,‡

  • 1European Organization for Nuclear Research (CERN), Geneva 1211, Switzerland
  • 2Department of Physics, University of Padova, 35122 Padova PD, Italy
  • 3Department of Particle and Nuclear Physics, University of Geneva, Geneva 1211, Switzerland
  • 4International Centre for Theory of Quantum Technologies, University of Gdańsk, Jana Bażyńskiego 1A, 80-309 Gdańsk, Poland

  • *These authors contributed equally to this work.
  • †antonio.mandarino@ug.edu.pl
  • ‡michele.grossi@cern.ch
PDF

Phys. Rev. B 107, L081105 – Published 10 February, 2023

DOI: https://doi.org/10.1103/PhysRevB.107.L081105

Abstract

Quantum machine learning offers a promising advantage in extracting information about quantum states, e.g., phase diagram. However, access to training labels is a major bottleneck for any supervised approach, preventing getting insights about new physics. In this Letter, using quantum convolutional neural networks, we overcome this limit by determining the phase diagram of a model where analytical solutions are lacking, by training only on marginal points of the phase diagram, where integrable models are represented. More specifically, we consider the axial next-nearest-neighbor Ising Hamiltonian, which possesses a ferromagnetic, paramagnetic, and antiphase, showing that the whole phase diagram can be reproduced.

View figure in article

Physics Subject Headings (PhySH)

See Also

Finite-size criticality in fully connected spin models on superconducting quantum hardware

Michele Grossi, Oriel Kiss, Francesco De Luca, Carlo Zollo, Ian Gremese, and Antonio Mandarino
Phys. Rev. E 107, 024113 (2023)

Article Text

Supplemental Material

References (59)

  1. J. Biamonte, P. Wittek, N. Pancotti, P. Rebentrost, N. Wiebe, and S. Lloyd, Quantum machine learning, Nature (London) 549, 195 (2017).
  2. M. Benedetti, E. Lloyd, S. Sack, and M. Fiorentini, Parameterized quantum circuits as machine learning models, Quantum Sci. Technol. 4, 043001 (2019).
  3. O. Kiss, F. Tacchino, S. Vallecorsa, and I. Tavernelli, Quantum neural networks force field generation, Mach. Learn.: Sci. Technol. 3, 035004 (2022).
  4. V. S. Ngairangbam, M. Spannowsky, and M. Takeuchi, Anomaly detection in high-energy physics using a quantum autoencoder, Phys. Rev. D 105, 095004 (2022).
  5. C. Zhou, J. Chan, W. Guan, S. Sun, A. Z. Wang, S. L. Wu, M. Livny, F. Carminati, A. Di Meglio, A. C. Y. Li, J. Lykken, P. Spentzouris, S. Y.-C. Chen, S. Yoo, and T.-C. Wei, Application of quantum machine learning to high energy physics analysis at LHC using IBM quantum computer simulators and IBM quantum computer hardware, PoS 390, 930 (2021).
  6. S. L. Wu, J. Chan, W. Guan, S. Sun, A. Wang, C. Zhou, M. Livny, F. Carminati, A. D. Meglio, A. C. Y. Li, J. Lykken, P. Spentzouris, S. Y.-C. Chen, S. Yoo, and T.-C. Wei, Application of quantum machine learning using the quantum variational classifier method to high energy physics analysis at the LHC on IBM quantum computer simulator and hardware with 10 qubits, J. Phys. G: Nucl. Part. Phys. 48, 125003 (2021).
  7. Y. Li, R.-G. Zhou, R. Xu, J. Luo, and W. Hu, A quantum deep convolutional neural network for image recognition, Quantum Sci. Technol. 5, 044003 (2020).
  8. K. Mitarai, M. Negoro, M. Kitagawa, and K. Fujii, Quantum circuit learning, Phys. Rev. A 98, 032309 (2018).
  9. D. M. Brian Coyle, V. Danos, and E. Kashefi, The Born supremacy: Quantum advantage and training of an Ising Born machine, npj Quantum Inf. 6, 60 (2020).
  10. C. Zoufal, A. Lucchi, and S. Woerner, Quantum generative adversarial networks for learning and loading random distributions, npj Quantum Inf. 5, 103 (2019).
  11. M. S. Rudolph, N. B. Toussaint, A. Katabarwa, S. Johri, B. Peropadre, and A. Perdomo-Ortiz, Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer, Phys. Rev. X 12, 031010 (2022).
  12. O. Kiss, M. Grossi, E. Kajomovitz, and S. Vallecorsa, Conditional Born machine for Monte Carlo event generation, Phys. Rev. A 106, 022612 (2022).
  13. A. Delgado and K. E. Hamilton, Unsupervised quantum circuit learning in high energy physics, Phys. Rev. D 106, 096006 (2022).
  14. A. Abbas, D. Sutter, C. Zoufal, A. Lucchi, A. Figalli, and S. Woerner, The power of quantum neural networks, Nat. Comput. Sci. 1, 403 (2021).
  15. H.-Y. Huang, M. Broughton, M. Mohseni, R. Babbush, S. Boixo, H. Neven, and J. R. McClean, Power of data in quantum machine learning, Nat. Commun. 12, 2631 (2021).
  16. J. R. Glick, T. P. Gujarati, A. D. Corcoles, Y. Kim, A. Kandala, J. M. Gambetta, and K. Temme, Covariant quantum kernels for data with group structure, arXiv:2105.03406.
  17. M. Schuld and N. Killoran, Is quantum advantage the right goal for quantum machine learning?” PRX Quantum 3, 030101 (2022).
  18. H.-Y. Huang, M. Broughton, J. Cotler, S. Chen, J. Li, M. Mohseni, H. Neven, R. Babbush, R. Kueng, J. Preskill, and J. R. McClean, Quantum advantage in learning from experiments, Science 376, 1182 (2022).
  19. C. D. Marciniak, T. Feldker, I. Pogorelov, R. Kaubruegger, D. V. Vasilyev, R. van Bijnen, P. Schindler, P. Zoller, R. Blatt, and T. Monz, Optimal metrology with programmable quantum sensors, Nature (London) 603, 604 (2022).
  20. I. Cong, S. Choi, and M. D. Lukin, Quantum convolutional neural networks, Nat. Phys. 15, 1273 (2019).
  21. A. V. Uvarov, A. S. Kardashin, and J. D. Biamonte, Machine learning phase transitions with a quantum processor, Phys. Rev. A 102, 012415 (2020).
  22. M. Lazzarin, D. E. Galli, and E. Prati, Multi-class quantum classifiers with tensor network circuits for quantum phase recognition, Phys. Lett. A 434, 128056 (2022).
  23. J. Herrmann, S. M. Llima, A. Remm, P. Zapletal, N. A. McMahon, C. Scarato, F. Swiadek, C. K. Andersen, C. Hellings, S. Krinner, N. Lacroix, S. Lazar, M. Kerschbaum, D. C. Zanuz, G. J. Norris, M. J. Hartmann, A. Wallraff, and C. Eichler, Realizing quantum convolutional neural networks on a superconducting quantum processor to recognize quantum phases, Nat. Commun. 13, 4144 (2022).
  24. K. Kottmann, P. Huembeli, M. Lewenstein, and A. Acín, Unsupervised Phase Discovery with Deep Anomaly Detection, Phys. Rev. Lett. 125, 170603 (2020).
  25. K. Kottmann, F. Metz, J. Fraxanet, and N. Baldelli, Variational quantum anomaly detection: Unsupervised mapping of phase diagrams on a physical quantum computer, Phys. Rev. Res. 3, 043184 (2021).
  26. M. C. Caro, H.-Y. Huang, M. Cerezo, K. Sharma, A. Sornborger, L. Cincio, and P. J. Coles, Generalization in quantum machine learning from few training data, Nat. Commun. 13, 4919 (2022).
  27. L. Banchi, J. Pereira, and S. Pirandola, Generalization in quantum machine learning: A quantum information standpoint, PRX Quantum 2, 040321 (2021).
  28. M. C. Caro, H.-Y. Huang, N. Ezzell, J. Gibbs, A. T. Sornborger, L. Cincio, P. J. Coles, and Z. Holmes, Out-of-distribution generalization for learning quantum dynamics, arXiv:2204.10268.
  29. H. Ye, C. Xie, T. Cai, R. Li, Z. Li, and L. Wang, Towards a theoretical framework of out-of-distribution generalization, in Advances in Neural Information Processing Systems, edited by A. Beygelzimer, Y. Dauphin, P. Liang, and J. W. Vaughan (Neural Information Processing Systems Foundation, San Diego, 2021).
  30. W. Selke, The ANNNI model — theoretical analysis and experimental application, Phys. Rep. 170, 213 (1988).
  31. P. R. C. Guimarães, J. A. Plascak, F. C. Sá Barreto, and J. Florencio, Quantum phase transitions in the one-dimensional transverse Ising model with second-neighbor interactions, Phys. Rev. B 66, 064413 (2002).
  32. A. K. Chandra and S. Dasgupta, Floating phase in the one-dimensional transverse axial next-nearest-neighbor Ising model, Phys. Rev. E 75, 021105 (2007).
  33. M. Beccaria, M. Campostrini, and A. Feo, Density-matrix renormalization-group study of the disorder line in the quantum axial next-nearest-neighbor Ising model, Phys. Rev. B 73, 052402 (2006).
  34. M. Beccaria, M. Campostrini, and A. Feo, Evidence for a floating phase of the transverse ANNNI model at high frustration, Phys. Rev. B 76, 094410 (2007).
  35. A. Canabarro, F. F. Fanchini, A. L. Malvezzi, R. Pereira, and R. Chaves, Unveiling phase transitions with machine learning, Phys. Rev. B 100, 045129 (2019).
  36. I Peschel and V. Emery, Calculation of spin correlations in two-dimensional Ising systems from one-dimensional kinetic models, Z. Phys. B 43, 241 (1981).
  37. A. Peruzzo, J. McClean, P. Shadbolt, M.-H. Yung, X.-Q. Zhou, P. J. Love, A. Aspuru-Guzik, and J. L. O'Brien, A variational eigenvalue solver on a photonic quantum processor, Nat. Commun. 5, 4213 (2014).
  38. A. Kandala, A. Mezzacapo, K. Temme, M. Takita, M. Brink, J. M. Chow, and J. M. Gambetta, Hardware-efficient variational quantum eigensolver for small molecules and quantum magnets, Nature (London) 549, 242 (2017).
  39. P. K. Barkoutsos, J. F. Gonthier, I. Sokolov, N. Moll, G. Salis, A. Fuhrer, M. Ganzhorn, D. J. Egger, M. Troyer, A. Mezzacapo, S. Filipp, and I. Tavernelli, Quantum algorithms for electronic structure calculations: Particle-hole hamiltonian and optimized wave-function expansions, Phys. Rev. A 98, 022322 (2018).
  40. J. Romero, R. Babbush, J. R. McClean, C. Hempel, P. J. Love, and A. Aspuru-Guzik, Strategies for quantum computing molecular energies using the unitary coupled cluster ansatz, Quantum Sci. Technol. 4, 014008 (2019).
  41. E. F. Dumitrescu, A. J. McCaskey, G. Hagen, G. R. Jansen, T. D. Morris, T. Papenbrock, R. C. Pooser, D. J. Dean, and P. Lougovski, Cloud Quantum Computing of an Atomic Nucleus, Phys. Rev. Lett. 120, 210501 (2018).
  42. I. Stetcu, A. Baroni, and J. Carlson, Variational approaches to constructing the many-body nuclear ground state for quantum computing, Phys. Rev. C 105, 064308 (2022).
  43. O. Kiss, M. Grossi, P. Lougovski, F. Sanchez, S. Vallecorsa, and T. Papenbrock, Quantum computing of the Li6 nucleus via ordered unitary coupled clusters, Phys. Rev. C 106, 034325 (2022).
  44. A. Uvarov, J. D. Biamonte, and D. Yudin, Variational quantum eigensolver for frustrated quantum systems, Phys. Rev. B 102, 075104 (2020).
  45. M. Grossi, O. Kiss, F. De Luca, C. Zollo, I. Gremese, and A. Mandarino, Finite-size criticality in fully connected spin models on superconducting quantum hardware, Phys. Rev. E 107, 024113 (2023).
  46. S. Sim, P. D. Johnson, and A. Aspuru-Guzik, Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms, Adv. Quantum Technol. 2, 1900070 (2019).
  47. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018).
  48. M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information: 10th Anniversary Edition (Cambridge University Press, Cambridge, UK, 2010).
  49. D. P. Kingma and J. Ba, ADAM: A method for stochastic optimization, in 3rd International Conference on Learning Representations, ICLR 2015, San Diego, CA, USA, May 7–9, 2015, Conference Track Proceedings, edited by Y. Bengio and Y. LeCun (ICLR, 2015).
  50. S. M. Harwood, D. Trenev, S. T. Stober, P. Barkoutsos, T. P. Gujarati, S. Mostame, and D. Greenberg, Improving the variational quantum eigensolver using variational adiabatic quantum computing, ACM Trans. Quantum Comput. 3, 1 (2022).
  51. O. Higgott, D. Wang, and S. Brierley, Variational quantum computation of excited states, Quantum 3, 156 (2019).
  52. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevB.107.L081105 for details about the construction and accuracy of the variational quantum data set, the individual probabilities outputted by the supervised quantum convolutional neural network, and a complete description of the anomaly detection procedure.
  53. Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, and L. D. Jackel, Backpropagation applied to handwritten zip code recognition, Neural Comput. 1, 541 (1989).
  54. H.-Y. Huang, R. Kueng, G. Torlai, V. V. Albert, and J. Preskill, Provably efficient machine learning for quantum many-body problems, Science 377, eabk3333 (2022).
  55. A. Pesah, M. Cerezo, S. Wang, T. Volkoff, A. T. Sornborger, and P. J. Coles, Absence of Barren Plateaus in Quantum Convolutional Neural Networks, Phys. Rev. X 11, 041011 (2021).
  56. M. Bina, A. Mandarino, S. Olivares, and M. G. A. Paris, Drawbacks of the use of fidelity to assess quantum resources, Phys. Rev. A 89, 012305 (2014).
  57. A. Mandarino, M. Bina, S. Olivares, and M. G. Paris, About the use of fidelity in continuous variable systems, Int. J. Quantum Inf. 12, 1461015 (2014).
  58. A. Mandarino, M. Bina, C. Porto, S. Cialdi, S. Olivares, and M. G. A. Paris, Assessing the significance of fidelity as a figure of merit in quantum state reconstruction of discrete and continuous-variable systems, Phys. Rev. A 93, 062118 (2016).
  59. https://cern-qpd-annni.readthedocs.io/en/latest/.

Outline

Information

Phys. Rev. B 107, L081105– Published 10 February, 2023
  • Received 18 August 2022
  • Revised 9 December 2022
  • Accepted 17 January 2023
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation