The reservoir learning power across quantum many-body localization transition

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.

Graphical abstract

Keywords

quantum reservoir computing / many-body localization / quantum ergodic / edge of quantum ergodicity / optimal learning power

References

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

[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)

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

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

[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)

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

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

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

[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)

[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)

[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)

[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)

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

[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)

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

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

[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)

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

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

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

[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)

[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)

[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)

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

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

[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)

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

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

[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)

[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)

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

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

[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)

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

[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)

[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)

[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)

[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)

[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)

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

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

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

[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)

[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)

[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)

[49] M. Serbyn, M. Knap, S. Gopalakrishnan, Z. Papić, 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)

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

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

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

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

[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)

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

[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)

[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)

RIGHTS & PERMISSIONS

Higher Education Press