Skip to main content
SpringerLink
Log in

The reservoir learning power across quantum many-body localization transition

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Harnessing the quantum computation power of the present noisy-intermediate-size-quantum devices has received tremendous interest in the last few years. Here we study the learning power of a one-dimensional long-range randomly-coupled quantum spin chain, within the framework of reservoir computing. In time sequence learning tasks, we find the system in the quantum many-body localized (MBL) phase holds long-term memory, which can be attributed to the emergent local integrals of motion. On the other hand, MBL phase does not provide sufficient nonlinearity in learning highly-nonlinear time sequences, which we show in a parity check task. This is reversed in the quantum ergodic phase, which provides sufficient nonlinearity but compromises memory capacity. In a complex learning task of Mackey—Glass prediction that requires both sufficient memory capacity and nonlinearity, we find optimal learning performance near the MBL-to-ergodic transition. This leads to a guiding principle of quantum reservoir engineering at the edge of quantum ergodicity reaching optimal learning power for generic complex reservoir learning tasks. Our theoretical finding can be tested with near-term NISQ quantum devices.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. F. Arute, K. Arya, R. Babbush, D. Bacon, J. C. Bardin, et al., Quantum supremacy using a programmable superconducting processor, Nature 574(7779), 505 (2019)

    Article  ADS  Google Scholar 

  2. H. S. Zhong, H. Wang, Y. H. Deng, M. C. Chen, L. C. Peng, Y. H. Luo, J. Qin, D. Wu, X. Ding, Y. Hu, P. Hu, X. Y. Yang, W. J. Zhang, H. Li, Y. Li, X. Jiang, L. Gan, G. Yang, L. You, Z. Wang, L. Li, N. L. Liu, C. Y. Lu, and J. W. Pan, Quantum computational advantage using photons, Science 370(6523), 1460 (2020)

    Article  ADS  Google Scholar 

  3. J. Preskill, Quantum computing in the NISQ era and beyond, Quantum 2, 79 (2018)

    Article  Google Scholar 

  4. I. H. Deutsch, Harnessing the power of the second quantum revolution, PRX Quantum 1(2), 020101 (2020)

    Article  Google Scholar 

  5. E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, et al., Quantum simulators: Architectures and opportunities, PRX Quantum 2(1), 017003 (2021)

    Article  Google Scholar 

  6. C. Gross and I. Bloch, Quantum simulations with ultracold atoms in optical lattices, Science 357(6355), 995 (2017)

    Article  ADS  Google Scholar 

  7. F. Flamini, N. Spagnolo, and F. Sciarrino, Photonic quantum information processing: A review, Rep. Prog. Phys. 82(1), 016001 (2019)

    Article  ADS  Google Scholar 

  8. J. Wang, F. Sciarrino, A. Laing, and M. G. Thompson, Integrated photonic quantum technologies, Nat. Photonics 14(5), 273 (2020)

    Article  ADS  Google Scholar 

  9. M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I. J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11(1), 369 (2020)

    Article  ADS  Google Scholar 

  10. F. A. Zwanenburg, A. S. Dzurak, A. Morello, M. Y. Simmons, L. C. L. Hollenberg, G. Klimeck, S. Rogge, S. N. Coppersmith, and M. A. Eriksson, Silicon quantum electronics, Rev. Mod. Phys. 85(3), 961 (2013)

    Article  ADS  Google Scholar 

  11. Y. Alexeev, D. Bacon, K. R. Brown, R. Calderbank, L. D. Carr, F. T. Chong, B. DeMarco, D. Englund, E. Farhi, B. Fefferman, A. V. Gorshkov, A. Houck, J. Kim, S. Kimmel, M. Lange, S. Lloyd, M. D. Lukin, D. Maslov, P. Maunz, C. Monroe, J. Preskill, M. Roetteler, M. J. Savage, and J. Thompson, Quantum computer systems for scientific discovery, PRX Quantum 2(1), 017001 (2021)

    Article  Google Scholar 

  12. R. Mengoni, D. Ottaviani, and P. Iorio, Breaking RSA security with a low noise D-wave 2000Q quantum annealer: Computational times, limitations and prospects, arXiv: 2005.02268 (2020).

  13. P. Hauke, H. G. Katzgraber, W. Lechner, H. Nishimori, and W. D. Oliver, Perspectives of quantum annealing: Methods and implementations, Rep. Prog. Phys. 83(5), 054401 (2020)

    Article  ADS  Google Scholar 

  14. K. Nakajima, Physical reservoir computing — an introductory perspective, Jpn. J. Appl. Phys. 59(6), 060501 (2020)

    Article  ADS  Google Scholar 

  15. N. H. Packard, Adaptation Toward the Edge of Chaos, in: Dynamic Patterns in Complex Systems, World Scientific, 1988, pp 293–301

  16. C. G. Langton, Computation at the edge of chaos: Phase transitions and emergent computation, Physica D 42(1–3), 12 (1990)

    Article  ADS  Google Scholar 

  17. N. Bertschinger and T. Natschläger, Real-time computation at the edge of chaos in recurrent neural networks, Neural Comput. 16(7), 1413 (2004)

    Article  MATH  Google Scholar 

  18. R. Legenstein and W. Maass, Edge of chaos and prediction of computational performance for neural circuit models, Neural Netw. 20(3), 323 (2007)

    Article  MATH  Google Scholar 

  19. M. Rafayelyan, J. Dong, Y. Tan, F. Krzakala, and S. Gigan, Large-scale optical reservoir computing for spatiotemporal chaotic systems prediction, Phys. Rev. X 10(4), 041037 (2020)

    Google Scholar 

  20. K. Fujii and K. Nakajima, Harnessing disordered-ensemble quantum dynamics for machine learning, Phys. Rev. Appl. 8(2), 024030 (2017)

    Article  ADS  Google Scholar 

  21. S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, Quantum reservoir processing, npj Quantum Inf. 5, 35 (2019)

    Article  ADS  Google Scholar 

  22. J. Chen, H. I. Nurdin, and N. Yamamoto, Temporal information processing on noisy quantum computers, Phys. Rev. Appl. 14(2), 024065 (2020)

    Article  ADS  Google Scholar 

  23. S. Ghosh, A. Opala, M. Matuszewski, T. Paterek, and T. C. H. Liew, Reconstructing quantum states with quantum reservoir networks, IEEE Trans. Neural Netw. Learn. Syst. 32(7), 1 (2020)

    Google Scholar 

  24. J. Nokkala, R. Martínez-Peña, G. L. Giorgi, V. Parigi, M. C. Soriano, and R. Zambrini, Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing, Commun. Phys. 4(1), 53 (2021)

    Article  Google Scholar 

  25. K. Fujii and K. Nakajima, Quantum reservoir computing: A reservoir approach toward quantum machine learning on near-term quantum devices, arXiv: 2011.04890 (2020)

  26. M. Serbyn, Z. Papić, and D. A. Abanin, Local conservation laws and the structure of the many-body localized states, Phys. Rev. Lett. 111(12), 127201 (2013)

    Article  ADS  Google Scholar 

  27. D. A. Huse, R. Nandkishore, and V. Oganesyan, Phenomenology of fully many-body-localized systems, Phys. Rev. B 90(17), 174202 (2014)

    Article  ADS  Google Scholar 

  28. V. Ros, M. Müller, and A. Scardicchio, Integrals of motion in the many-body localized phase, Nucl. Phys. B 891, 420 (2015)

    Article  ADS  MATH  Google Scholar 

  29. A. Chandran, I. H. Kim, G. Vidal, and D. A. Abanin, Constructing local integrals of motion in the many-body localized phase, Phys. Rev. B 91(8), 085425 (2015)

    Article  ADS  Google Scholar 

  30. D. A. Abanin, E. Altman, I. Bloch, and M. Serbyn, Many-body localization, thermalization, and entanglement, Rev. Mod. Phys. 91(2), 021001 (2019)

    Article  ADS  Google Scholar 

  31. M. C. Mackey and L. Glass, Oscillation and chaos in physiological control systems, Science 197(4300), 287 (1977)

    Article  ADS  MATH  Google Scholar 

  32. R. Martínez-Peña, G. L. Giorgi, J. Nokkala, M. C. Soriano, and R. Zambrini, Dynamical phase transitions in quantum reservoir computing, Phys. Rev. Lett. 127(10), 100502 (2021)

    Article  ADS  Google Scholar 

  33. A. O. Maksymov and A. L. Burin, Many-body localization in spin chains with long-range transverse interactions: Scaling of critical disorder with system size, Phys. Rev. B 101(2), 024201 (2020)

    Article  ADS  Google Scholar 

  34. L. M. K. Vandersypen and I. L. Chuang, NMR techniques for quantum control and computation, Rev. Mod. Phys. 76(4), 1037 (2005)

    Article  ADS  Google Scholar 

  35. L. M. Duan and C. Monroe, Quantum networks with trapped ions, Rev. Mod. Phys. 82(2), 1209 (2010)

    Article  ADS  Google Scholar 

  36. J. M. Pino, J. M. Dreiling, C. Figgatt, J. P. Gaebler, S. A. Moses, M. S. Allman, C. H. Baldwin, M. Foss-Feig, D. Hayes, K. Mayer, C. Ryan-Anderson, and B. Neyenhuis, Demonstration of the trapped-ion quantum CCD computer architecture, Nature 592(7853), 209 (2021)

    Article  ADS  Google Scholar 

  37. A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16(2), 132 (2020)

    Article  Google Scholar 

  38. D. W. Leung, I. L. Chuang, F. Yamaguchi, and Y. Yamamoto, Efficient implementation of coupled logic gates for quantum computation, Phys. Rev. A 61(4), 042310 (2000)

    Article  ADS  Google Scholar 

  39. J. Li, R. Fan, H. Wang, B. Ye, B. Zeng, H. Zhai, X. Peng, and J. Du, Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator, Phys. Rev. X 7(3), 031011 (2017)

    Google Scholar 

  40. J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys. 12(10), 907 (2016)

    Article  Google Scholar 

  41. J. Zhang, P. W. Hess, A. Kyprianidis, P. Becker, A. Lee, J. Smith, G. Pagano, I. D. Potirniche, A. C. Potter, A. Vishwanath, N. Y. Yao, and C. Monroe, Observation of a discrete time crystal, Nature 543(7644), 217 (2017)

    Article  ADS  Google Scholar 

  42. X. Wu, X. Liang, Y. Tian, F. Yang, C. Chen, Y. C. Liu, M. K. Tey, and L. You, A concise review of Rydberg atom based quantum computation and quantum simulation, Chin. Phys. B 30(2), 020305 (2020)

    Article  Google Scholar 

  43. M. Morgado and S. Whitlock, Quantum simulation and computing with Rydberg-interacting qubits, AVS Quantum Science 3(2), 023501 (2021)

    Article  ADS  Google Scholar 

  44. X. Qiu, P. Zoller, and X. Li, Programmable quantum annealing architectures with Ising quantum wires, PRX Quantum 1(2), 020311 (2020)

    Article  Google Scholar 

  45. D. A. Roberts, D. Stanford, and A. Streicher, Operator growth in the SYK model, J. High Energy Phys. 2018(6), 122 (2018)

    Article  MATH  Google Scholar 

  46. X. Li, G. Zhu, M. Han, and X. Wang, Quantum information scrambling through a high-complexity operator mapping, Phys. Rev. A 100(3), 032309 (2019)

    Article  ADS  Google Scholar 

  47. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109(1), 017202 (2012)

    Article  ADS  Google Scholar 

  48. M. Serbyn, Z. Papić, and D. A. Abanin, Universal slow growth of entanglement in interacting strongly disordered systems, Phys. Rev. Lett. 110(26), 260601 (2013)

    Article  ADS  Google Scholar 

  49. M. Serbyn, M. Knap, S. Gopalakrishnan, Z. Papic, N. Y. Yao, C. R. Laumann, D. A. Abanin, M. D. Lukin, and E. A. Demler, Interferometric probes of many-body localization, Phys. Rev. Lett. 113(14), 147204 (2014)

    Article  ADS  Google Scholar 

  50. A. Larkin and Y. N. Ovchinnikov, Quasiclassical method in the theory of superconductivity, Sov. Phys. JETP 28, 1200 (1969)

    ADS  Google Scholar 

  51. S. H. Shenker and D. Stanford, Black holes and the butterfly effect, J. High Energy Phys. 2014(3), 67 (2014)

    Article  MATH  Google Scholar 

  52. J. Maldacena, S. H. Shenker, and D. Stanford, A bound on chaos, J. High Energy Phys. 2016(8), 106 (2016)

    Article  MATH  Google Scholar 

  53. H. Jaeger and H. Haas, Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication, Science 304(5667), 78 (2004)

    Article  ADS  Google Scholar 

  54. K. Srinivasan, I. Raja Mohamed, K. Murali, M. Lakshmanan, and S. Sinha, Design of time delayed chaotic circuit with threshold controller, Int. J. Bifurcat. Chaos 21(3), 725 (2011)

    Article  MATH  Google Scholar 

  55. J. Dambre, D. Verstraeten, B. Schrauwen, and S. Massar, Information processing capacity of dynamical systems, Sci. Rep. 2(1), 514 (2012)

    Article  ADS  Google Scholar 

  56. R. Martínez-Peña, J. Nokkala, G. L. Giorgi, R. Zambrini, and M. C. Soriano, Information processing capacity of spin-based quantum reservoir computing systems, Cognit. Comput. (2020)

  57. J. Nokkala, R. Martínez-Peña, G. L. Giorgi, V. Parigi, M. C. Soriano, and R. Zambrini, Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing, Commun. Phys. 4(1), 53 (2021)

    Article  Google Scholar 

  58. J. H. Bardarson, F. Pollmann, and J. E. Moore, Unbounded growth of entanglement in models of many-body localization, Phys. Rev. Lett. 109(1), 017202 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. State Key Laboratory of Surface Physics, Institute of Nanoelectronics and Quantum Computing, and Department of Physics, Fudan University, Shanghai, 200433, China

    Wei Xia, Jie Zou, Xingze Qiu & Xiaopeng Li

  2. Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, 518055, China

    Xingze Qiu

  3. Shanghai Qi Zhi Institute, AI Tower, Xuhui District, Shanghai, 200232, China

    Xiaopeng Li

Authors
  1. Wei Xia
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jie Zou
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Xingze Qiu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiaopeng Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xingze Qiu or Xiaopeng Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Xia, W., Zou, J., Qiu, X. et al. The reservoir learning power across quantum many-body localization transition. Front. Phys. 17, 33506 (2022). https://doi.org/10.1007/s11467-022-1158-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-022-1158-1

Keywords

Search

Navigation