Institute for Cross-Disciplinary Physics and Complex Systems (IFISC) UIB-CSIC, Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spain.
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Abstract
Dissipation induced by interactions with an external environment typically hinders the performance of quantum computation, but in some cases can be turned out as a useful resource. We show the potential enhancement induced by dissipation in the field of quantum reservoir computing introducing tunable local losses in spin network models. Our approach based on continuous dissipation is able not only to reproduce the dynamics of previous proposals of quantum reservoir computing, based on discontinuous erasing maps but also to enhance their performance. Control of the damping rates is shown to boost popular machine learning temporal tasks as the capability to linearly and non-linearly process the input history and to forecast chaotic series. Finally, we formally prove that, under non-restrictive conditions, our dissipative models form a universal class for reservoir computing. It means that considering our approach, it is possible to approximate any fading memory map with arbitrary precision.
Featured image: Schematic of the dissipative spin network model proposed. The discrete input (bottom right) is injected uniformly into the network nodes through a time-dependent magnetic field (bottom left). The output layer is constructed by measuring a portion of the observables of the density matrix of the reservoir.
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[1] Engineering National Academies of Sciencesand Medicine “Quantum Computing: Progress and Prospects” The National Academies Press (2019).
https://doi.org/10.17226/25196
[2] Ivan H. Deutsch “Harnessing the Power of the Second Quantum Revolution” PRX Quantum 1, 020101 (2020).
https://doi.org/10.1103/PRXQuantum.1.020101
[3] Nicolas Gisinand Rob Thew “Quantum communication” Nature Photonics 1, 165–171 (2007).
https://doi.org/10.1038/nphoton.2007.22
[4] C. L. Degen, F. Reinhard, and P. Cappellaro, “Quantum sensing” Rev. Mod. Phys. 89, 035002 (2017).
https://doi.org/10.1103/RevModPhys.89.035002
[5] S. Pirandola, U. L. Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, J. L. Pereira, M. Razavi, J. Shamsul Shaari, M. Tomamichel, V. C. Usenko, G. Vallone, P. Villoresi, and P. Wallden, “Advances in quantum cryptography” Adv. Opt. Photon. 12, 1012–1236 (2020).
https://doi.org/10.1364/AOP.361502
http://opg.optica.org/aop/abstract.cfm?URI=aop-12-4-1012
[6] Aram W. Harrowand Ashley Montanaro “Quantum computational supremacy” Nature 549, 203–209 (2017).
https://doi.org/10.1038/nature23458
[7] Peter W. Shor “Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer” SIAM J. Comput. 26, 1484–1509 (1997).
https://doi.org/10.1137/S0097539795293172
[8] Lov K Grover “A fast quantum mechanical algorithm for database search” Proceedings of the twenty-eighth annual ACM symposium on Theory of computing 212–219 (1996).
https://doi.org/10.1145/237814.237866
[9] David Deutschand Richard Jozsa “Rapid solution of problems by quantum computation” Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 439, 553–558 (1992).
https://doi.org/10.1098/rspa.1992.0167
[10] Ethan Bernsteinand Umesh Vazirani “Quantum complexity theory” SIAM Journal on computing 26, 1411–1473 (1997).
https://doi.org/10.1137/S0097539796300921
[11] Yudong Cao, Jonathan Romero, Jonathan P Olson, Matthias Degroote, Peter D Johnson, Mária Kieferová, Ian D Kivlichan, Tim Menke, Borja Peropadre, and Nicolas PD Sawaya, “Quantum chemistry in the age of quantum computing” Chemical reviews 119, 10856–10915 (2019).
https://doi.org/10.1021/acs.chemrev.8b00803
[12] Roman Orus, Samuel Mugel, and Enrique Lizaso, “Quantum computing for finance: Overview and prospects” Reviews in Physics 4, 100028 (2019).
https://doi.org/10.1016/j.revip.2019.100028
https://www.sciencedirect.com/science/article/pii/S2405428318300571
[13] Nikitas Stamatopoulos, Daniel J Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner, “Option pricing using quantum computers” Quantum 4, 291 (2020).
https://doi.org/10.22331/q-2020-07-06-291
[14] Jacob Biamonte, Peter Wittek, Nicola Pancotti, Patrick Rebentrost, Nathan Wiebe, and Seth Lloyd, “Quantum machine learning” Nature 549, 195–202 (2017).
https://doi.org/10.1038/nature23474
[15] John Preskill “Quantum Computing in the NISQ era and beyond” Quantum 2, 79 (2018).
https://doi.org/10.22331/q-2018-08-06-79
[16] Kishor Bharti, Alba Cervera-Lierta, Thi Ha Kyaw, Tobias Haug, Sumner Alperin-Lea, Abhinav Anand, Matthias Degroote, Hermanni Heimonen, Jakob S Kottmann, and Tim Menke, “Noisy intermediate-scale quantum algorithms” Reviews of Modern Physics 94, 015004 (2022).
https://doi.org/10.1103/RevModPhys.94.015004
[17] Frank Verstraete, Michael M Wolf, and J Ignacio Cirac, “Quantum computation and quantum-state engineering driven by dissipation” Nature physics 5, 633–636 (2009).
https://doi.org/10.1038/nphys1342
[18] Fernando Pastawski, Lucas Clemente, and Juan Ignacio Cirac, “Quantum memories based on engineered dissipation” Physical Review A 83, 012304 (2011).
https://doi.org/10.1103/PhysRevA.83.012304
[19] Christiane P Koch “Controlling open quantum systems: tools, achievements, and limitations” Journal of Physics: Condensed Matter 28, 213001 (2016).
https://doi.org/10.1088/0953-8984/28/21/213001
[20] Sai Vinjanampathyand Janet Anders “Quantum thermodynamics” Contemporary Physics 57, 545–579 (2016).
https://doi.org/10.1080/00107514.2016.1201896
[21] Gonzalo Manzanoand Roberta Zambrini “Quantum thermodynamics under continuous monitoring: A general framework” AVS Quantum Science 4, 025302 (2022).
https://doi.org/10.1116/5.0079886
[22] Susana F Huelgaand Martin B Plenio “Vibrations, quanta and biology” Contemporary Physics 54, 181–207 (2013).
https://doi.org/10.1080/00405000.2013.829687
[23] Gonzalo Manzano, Fernando Galve, Gian Luca Giorgi, Emilio Hernández-García, and Roberta Zambrini, “Synchronization, quantum correlations and entanglement in oscillator networks” Scientific Reports 3, 1–6 (2013).
https://doi.org/10.1038/srep01439
[24] Albert Cabot, Fernando Galve, Víctor M Eguíluz, Konstantin Klemm, Sabrina Maniscalco, and Roberta Zambrini, “Unveiling noiseless clusters in complex quantum networks” npj Quantum Information 4, 1–9 (2018).
https://doi.org/10.1038/s41534-018-0108-9
[25] Pere Mujal, Rodrigo Martínez-Peña, Johannes Nokkala, Jorge García-Beni, Gian Luca Giorgi, Miguel C. Soriano, and Roberta Zambrini, “Opportunities in Quantum Reservoir Computing and Extreme Learning Machines” Advanced Quantum Technologies 4, 1–14 (2021).
https://doi.org/10.1002/qute.202100027
[26] Mantas Lukoševičius, Herbert Jaeger, and Benjamin Schrauwen, “Reservoir computing trends” KI-Künstliche Intelligenz 26, 365–371 (2012).
https://doi.org/10.1007/s13218-012-0204-5
[27] Wolfgang Maass, Thomas Natschläger, and Henry Markram, “Real-Time Computing Without Stable States: A New Framework for Neural Computation Based on Perturbations” Neural Computation 14, 2531–2560 (2002).
https://doi.org/10.1162/089976602760407955
[28] Herbert Jaeger “The “echo state” approach to analysing and training recurrent neural networks-with an erratum note” Bonn, Germany: German National Research Center for Information Technology GMD Technical Report 148, 13 (2001).
https://www.ai.rug.nl/minds/uploads/EchoStatesTechRep.pdf
[29] Gouhei Tanaka, Toshiyuki Yamane, Jean Benoit Héroux, Ryosho Nakane, Naoki Kanazawa, Seiji Takeda, Hidetoshi Numata, Daiju Nakano, and Akira Hirose, “Recent advances in physical reservoir computing: A review” Neural Networks 115, 100–123 (2019).
https://doi.org/10.1016/j.neunet.2019.03.005
https://www.sciencedirect.com/science/article/pii/S0893608019300784
[30] Kohei Nakajimaand Ingo Fischer “Reservoir Computing” Springer (2021).
https://doi.org/10.1007/978-981-13-1687-6
[31] John Moon, Wen Ma, Jong Hoon Shin, Fuxi Cai, Chao Du, Seung Hwan Lee, and Wei D Lu, “Temporal data classification and forecasting using a memristor-based reservoir computing system” Nature Electronics 2, 480–487 (2019).
https://doi.org/10.1038/s41928-019-0313-3
[32] Julie Grollier, Damien Querlioz, KY Camsari, Karin Everschor-Sitte, Shunsuke Fukami, and Mark D Stiles, “Neuromorphic spintronics” Nature electronics 3, 360–370 (2020).
https://doi.org/10.1038/s41928-019-0360-9
[33] Guy Van der Sande, Daniel Brunner, and Miguel C. Soriano, “Advances in photonic reservoir computing” Nanophotonics 6, 561–576 (2017).
[34] Keisuke Fujiiand Kohei Nakajima “Harnessing Disordered-Ensemble Quantum Dynamics for Machine Learning” Phys. Rev. Applied 8, 024030 (2017).
https://doi.org/10.1103/PhysRevApplied.8.024030
[35] Kohei Nakajima, Keisuke Fujii, Makoto Negoro, Kosuke Mitarai, and Masahiro Kitagawa, “Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing” Phys. Rev. Applied 11, 034021 (2019).
https://doi.org/10.1103/PhysRevApplied.11.034021
[36] Jiayin Chenand Hendra I. Nurdin “Learning nonlinear input–output maps with dissipative quantum systems” Quantum Information Processing 18 (2019).
https://doi.org/10.1007/s11128-019-2311-9
[37] Quoc Hoan Tranand Kohei Nakajima “Higher-order quantum reservoir computing” arXiv preprint arXiv:2006.08999 (2020).
https://doi.org/10.48550/ARXIV.2006.08999
https://arxiv.org/abs/2006.08999
[38] Rodrigo Martínez-Peña, Johannes Nokkala, Gian Luca Giorgi, Roberta Zambrini, and Miguel C Soriano, “Information processing capacity of spin-based quantum reservoir computing systems” Cognitive Computation 1–12 (2020).
https://doi.org/10.1007/s12559-020-09772-y
[39] Rodrigo Araiza Bravo, Khadijeh Najafi, Xun Gao, and Susanne F. Yelin, “Quantum Reservoir Computing Using Arrays of Rydberg Atoms” PRX Quantum 3, 030325 (2022).
https://doi.org/10.1103/PRXQuantum.3.030325
[40] W. D. Kalfus, G. J. Ribeill, G. E. Rowlands, H. K. Krovi, T. A. Ohki, and L. C. G. Govia, “Hilbert space as a computational resource in reservoir computing” Phys. Rev. Res. 4, 033007 (2022).
https://doi.org/10.1103/PhysRevResearch.4.033007
[41] Johannes Nokkala, Rodrigo Martínez-Peña, Gian Luca Giorgi, Valentina Parigi, Miguel C Soriano, and Roberta Zambrini, “Gaussian states of continuous-variable quantum systems provide universal and versatile reservoir computing” Communications Physics 4, 1–11 (2021).
https://doi.org/10.1038/s42005-021-00556-w
[42] L. C. G. Govia, G. J. Ribeill, G. E. Rowlands, H. K. Krovi, and T. A. Ohki, “Quantum reservoir computing with a single nonlinear oscillator” Phys. Rev. Research 3, 013077 (2021).
https://doi.org/10.1103/PhysRevResearch.3.013077
[43] Jiayin Chen, Hendra I Nurdin, and Naoki Yamamoto, “Temporal information processing on noisy quantum computers” Physical Review Applied 14, 024065 (2020).
https://doi.org/10.1103/PhysRevApplied.14.024065
[44] Yudai Suzuki, Qi Gao, Ken C Pradel, Kenji Yasuoka, and Naoki Yamamoto, “Natural quantum reservoir computing for temporal information processing” Scientific Reports 12, 1–15 (2022).
https://doi.org/10.1038/s41598-022-05061-w
[45] Tomoyuki Kubota, Yudai Suzuki, Shumpei Kobayashi, Quoc Hoan Tran, Naoki Yamamoto, and Kohei Nakajima, “Temporal information processing induced by quantum noise” Phys. Rev. Res. 5, 023057 (2023).
https://doi.org/10.1103/PhysRevResearch.5.023057
[46] Michele Spagnolo, Joshua Morris, Simone Piacentini, Michael Antesberger, Francesco Massa, Andrea Crespi, Francesco Ceccarelli, Roberto Osellame, and Philip Walther, “Experimental photonic quantum memristor” Nature Photonics 16, 318–323 (2022).
https://doi.org/10.1038/s41566-022-00973-5
[47] Gerasimos Angelatos, Saeed A. Khan, and Hakan E. Türeci, “Reservoir Computing Approach to Quantum State Measurement” Phys. Rev. X 11, 041062 (2021).
https://doi.org/10.1103/PhysRevX.11.041062
[48] Sanjib Ghosh, Tanjung Krisnanda, Tomasz Paterek, and Timothy CH Liew, “Realising and compressing quantum circuits with quantum reservoir computing” Communications Physics 4, 1–7 (2021).
https://doi.org/10.1038/s42005-021-00606-3
[49] Sanjib Ghosh, Andrzej Opala, Michał Matuszewski, Tomasz Paterek, and Timothy CH Liew, “Quantum reservoir processing” npj Quantum Information 5, 35 (2019).
https://doi.org/10.1038/s41534-019-0149-8
[50] Sanjib Ghosh, Andrzej Opala, Michal Matuszewski, Tomasz Paterek, and Timothy C. H. Liew, “Reconstructing Quantum States With Quantum Reservoir Networks” IEEE Transactions on Neural Networks and Learning Systems 32, 3148–3155 (2021).
https://doi.org/10.1109/tnnls.2020.3009716
[51] Sanjib Ghosh, Tomasz Paterek, and Timothy C. H. Liew, “Quantum Neuromorphic Platform for Quantum State Preparation” Phys. Rev. Lett. 123, 260404 (2019).
https://doi.org/10.1103/PhysRevLett.123.260404
[52] Tanjung Krisnanda, Tomasz Paterek, Mauro Paternostro, and Timothy C. H. Liew, “Quantum neuromorphic approach to efficient sensing of gravity-induced entanglement” Physical Review D 107 (2023).
https://doi.org/10.1103/physrevd.107.086014
[53] Johannes Nokkala “Online quantum time series processing with random oscillator networks” Scientific Reports 13 (2023).
https://doi.org/10.1038/s41598-023-34811-7
[54] Joni Dambre, David Verstraeten, Benjamin Schrauwen, and Serge Massar, “Information processing capacity of dynamical systems” Scientific reports 2, 1–7 (2012).
https://doi.org/10.1038/srep00514
[55] Pere Mujal, Rodrigo Martínez-Peña, Gian Luca Giorgi, Miguel C. Soriano, and Roberta Zambrini, “Time-series quantum reservoir computing with weak and projective measurements” npj Quantum Information 9, 16 (2023).
https://doi.org/10.1038/s41534-023-00682-z
[56] Jorge García-Beni, Gian Luca Giorgi, Miguel C. Soriano, and Roberta Zambrini, “Scalable Photonic Platform for Real-Time Quantum Reservoir Computing” Physical Review Applied 20 (2023).
https://doi.org/10.1103/physrevapplied.20.014051
[57] Fangjun Hu, Gerasimos Angelatos, Saeed A. Khan, Marti Vives, Esin Türeci, Leon Bello, Graham E. Rowlands, Guilhem J. Ribeill, and Hakan E. Türeci, “Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks” Physical Review X 13 (2023).
https://doi.org/10.1103/physrevx.13.041020
[58] Izzet B Yildiz, Herbert Jaeger, and Stefan J Kiebel, “Re-visiting the echo state property” Neural networks 35, 1–9 (2012).
https://doi.org/10.1016/j.neunet.2012.07.005
https://www.sciencedirect.com/science/article/pii/S0893608012001852
[59] Bruno Del Papa, Viola Priesemann, and Jochen Triesch, “Fading memory, plasticity, and criticality in recurrent networks” Springer (2019).
https://doi.org/10.1007/978-3-030-20965-0_6
[60] Sanjukta Krishnagopal, Michelle Girvan, Edward Ott, and Brian R. Hunt, “Separation of chaotic signals by reservoir computing” Chaos: An Interdisciplinary Journal of Nonlinear Science 30, 023123 (2020).
https://doi.org/10.1063/1.5132766
[61] Pere Mujal, Johannes Nokkala, Rodrigo Martínez-Peña, Gian Luca Giorgi, Miguel C Soriano, and Roberta Zambrini, “Analytical evidence of nonlinearity in qubits and continuous-variable quantum reservoir computing” Journal of Physics: Complexity 2, 045008 (2021).
https://doi.org/10.1088/2632-072x/ac340e
[62] M. D. SAJID ANIS et al. “Qiskit: An Open-source Framework for Quantum Computing” (2021).
https://doi.org/10.5281/zenodo.2573505
[63] Marco Cattaneo, Matteo A.C. Rossi, Guillermo García-Pérez, Roberta Zambrini, and Sabrina Maniscalco, “Quantum Simulation of Dissipative Collective Effects on Noisy Quantum Computers” PRX Quantum 4 (2023).
https://doi.org/10.1103/prxquantum.4.010324
[64] Heinz-Peter Breuerand Francesco Petruccione “The theory of open quantum systems” Oxford University Press on Demand (2002).
https://doi.org/10.1093/acprof:oso/9780199213900.001.0001
[65] Goran Lindblad “On the generators of quantum dynamical semigroups” Communications in Mathematical Physics 48, 119–130 (1976).
https://doi.org/10.1007/BF01608499
[66] Vittorio Gorini, Andrzej Kossakowski, and Ennackal Chandy George Sudarshan, “Completely positive dynamical semigroups of N-level systems” Journal of Mathematical Physics 17, 821–825 (1976).
https://doi.org/10.1063/1.522979
[67] Marco Cattaneo, Gian Luca Giorgi, Sabrina Maniscalco, and Roberta Zambrini, “Local versus global master equation with common and separate baths: superiority of the global approach in partial secular approximation” New Journal of Physics 21, 113045 (2019).
https://doi.org/10.1088/1367-2630/ab54ac
[68] Lyudmila Grigoryevaand Juan-Pablo Ortega “Echo state networks are universal” Neural Networks 108, 495–508 (2018).
https://doi.org/10.1016/j.neunet.2018.08.025
https://www.sciencedirect.com/science/article/pii/S089360801830251X
[69] Georg Fetteand Julian Eggert “Short term memory and pattern matching with simple echo state networks” International Conference on Artificial Neural Networks 13–18 (2005).
https://doi.org/10.1007/11550822_3
[70] Sepp Hochreiterand Jürgen Schmidhuber “Long short-term memory” Neural computation 9, 1735–1780 (1997).
https://doi.org/10.1007/978-3-642-24797-2_4
[71] Gavan Linternand Peter N Kugler “Self-organization in connectionist models: Associative memory, dissipative structures, and thermodynamic law” Human Movement Science 10, 447–483 (1991).
https://doi.org/10.1016/0167-9457(91)90015-P
https://www.sciencedirect.com/science/article/pii/016794579190015P
[72] Rodrigo Martínez-Peña, Gian Luca Giorgi, Johannes Nokkala, Miguel C Soriano, and Roberta Zambrini, “Dynamical phase transitions in quantum reservoir computing” Physical Review Letters 127, 100502 (2021).
https://doi.org/10.1103/PhysRevLett.127.100502
[73] Michael C Mackeyand Leon Glass “Oscillation and chaos in physiological control systems” Science 197, 287–289 (1977).
https://doi.org/10.1126/science.267326
[74] J Doyne Farmerand John J Sidorowich “Predicting chaotic time series” Physical Review Letters 59, 845 (1987).
https://doi.org/10.1103/PhysRevLett.59.845
[75] Herbert Jaegerand Harald Haas “Harnessing nonlinearity: Predicting chaotic systems and saving energy in wireless communication” Science 304, 78–80 (2004).
https://doi.org/10.1126/science.1091277
[76] S Ortín, Miguel C Soriano, L Pesquera, Daniel Brunner, D San-Martín, Ingo Fischer, CR Mirasso, and JM Gutiérrez, “A unified framework for reservoir computing and extreme learning machines based on a single time-delayed neuron” Scientific reports 5, 1–11 (2015).
https://doi.org/10.1038/srep14945
[77] Jaideep Pathak, Zhixin Lu, Brian R Hunt, Michelle Girvan, and Edward Ott, “Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data” Chaos 27, 121102 (2017).
https://doi.org/10.1063/1.5010300
[78] Kristian Baumann, Christine Guerlin, Ferdinand Brennecke, and Tilman Esslinger, “Dicke quantum phase transition with a superfluid gas in an optical cavity” Nature 464, 1301–1306 (2010).
https://doi.org/10.1038/nature09009
[79] Zhang Zhiqiang, Chern Hui Lee, Ravi Kumar, K. J. Arnold, Stuart J. Masson, A. S. Parkins, and M. D. Barrett, “Nonequilibrium phase transition in a spin-1 Dicke model” Optica 4, 424 (2017).
https://doi.org/10.1364/optica.4.000424
[80] Juan A. Muniz, Diego Barberena, Robert J. Lewis-Swan, Dylan J. Young, Julia R. K. Cline, Ana Maria Rey, and James K. Thompson, “Exploring dynamical phase transitions with cold atoms in an optical cavity” Nature 580, 602–607 (2020).
https://doi.org/10.1038/s41586-020-2224-x
[81] Mattias Fitzpatrick, Neereja M. Sundaresan, Andy C. Y. Li, Jens Koch, and Andrew A. Houck, “Observation of a Dissipative Phase Transition in a One-Dimensional Circuit QED Lattice” Physical Review X 7 (2017).
https://doi.org/10.1103/physrevx.7.011016
[82] Sam Genway, Weibin Li, Cenap Ates, Benjamin P. Lanyon, and Igor Lesanovsky, “Generalized Dicke Nonequilibrium Dynamics in Trapped Ions” Physical Review Letters 112 (2014).
https://doi.org/10.1103/physrevlett.112.023603
[83] Julio T. Barreiro, Markus Müller, Philipp Schindler, Daniel Nigg, Thomas Monz, Michael Chwalla, Markus Hennrich, Christian F. Roos, Peter Zoller, and Rainer Blatt, “An open-system quantum simulator with trapped ions” Nature 470, 486–491 (2011).
https://doi.org/10.1038/nature09801
[84] R. Blattand C. F. Roos “Quantum simulations with trapped ions” Nature Physics 8, 277–284 (2012).
https://doi.org/10.1038/nphys2252
[85] Javad Kazemiand Hendrik Weimer “Driven-Dissipative Rydberg Blockade in Optical Lattices” Physical Review Letters 130 (2023).
https://doi.org/10.1103/physrevlett.130.163601
[86] Vincent R. Overbeck, Mohammad F. Maghrebi, Alexey V. Gorshkov, and Hendrik Weimer, “Multicritical behavior in dissipative Ising models” Physical Review A 95 (2017).
https://doi.org/10.1103/physreva.95.042133
[87] Jiasen Jin, Alberto Biella, Oscar Viyuela, Cristiano Ciuti, Rosario Fazio, and Davide Rossini, “Phase diagram of the dissipative quantum Ising model on a square lattice” Physical Review B 98 (2018).
https://doi.org/10.1103/physrevb.98.241108
[88] Cenap Ates, Beatriz Olmos, Juan P. Garrahan, and Igor Lesanovsky, “Dynamical phases and intermittency of the dissipative quantum Ising model” Physical Review A 85 (2012).
https://doi.org/10.1103/physreva.85.043620
[89] A. Bermudez, T. Schaetz, and M. B. Plenio, “Dissipation-Assisted Quantum Information Processing with Trapped Ions” Physical Review Letters 110 (2013).
https://doi.org/10.1103/physrevlett.110.110502
[90] Haggai Landa, Marco Schiró, and Grégoire Misguich, “Multistability of Driven-Dissipative Quantum Spins” Physical Review Letters 124 (2020).
https://doi.org/10.1103/physrevlett.124.043601
[91] Sam Genway, Weibin Li, Cenap Ates, Benjamin P. Lanyon, and Igor Lesanovsky, “Generalized Dicke Nonequilibrium Dynamics in Trapped Ions” Physical Review Letters 112 (2014).
https://doi.org/10.1103/physrevlett.112.023603
[92] Heike Schwager, J. Ignacio Cirac, and Géza Giedke, “Dissipative spin chains: Implementation with cold atoms and steady-state properties” Physical Review A 87 (2013).
https://doi.org/10.1103/physreva.87.022110
[93] Tony E. Leeand Ching-Kit Chan “Heralded Magnetism in Non-Hermitian Atomic Systems” Physical Review X 4 (2014).
https://doi.org/10.1103/physrevx.4.041001
[94] J. Ignacio Ciracand Peter Zoller “New Frontiers in Quantum Information With Atoms and Ions” Physics Today 57, 38–44 (2004).
https://doi.org/10.1063/1.1712500
[95] Tony E. Lee, Sarang Gopalakrishnan, and Mikhail D. Lukin, “Unconventional Magnetism via Optical Pumping of Interacting Spin Systems” Physical Review Letters 110 (2013).
https://doi.org/10.1103/physrevlett.110.257204
[96] Danijela Markovićand Julie Grollier “Quantum neuromorphic computing” Applied Physics Letters 117, 150501 (2020).
https://doi.org/10.1063/5.0020014
[97] Marco Cattaneo, Gabriele De Chiara, Sabrina Maniscalco, Roberta Zambrini, and Gian Luca Giorgi, “Collision Models Can Efficiently Simulate Any Multipartite Markovian Quantum Dynamics” Physical Review Letters 126 (2021).
https://doi.org/10.1103/physrevlett.126.130403
[98] Inés de Vegaand Daniel Alonso “Dynamics of non-Markovian open quantum systems” Rev. Mod. Phys. 89, 015001 (2017).
https://doi.org/10.1103/RevModPhys.89.015001
[99] G Manjunath “Embedding information onto a dynamical system” Nonlinearity 35, 1131 (2022).
https://doi.org/10.1088/1361-6544/ac4817
[100] Jiayin Chen “Nonlinear Convergent Dynamics for Temporal Information Processing on Novel Quantum and Classical Devices” thesis (2022).
https://doi.org/10.26190/unsworks/24115
[101] Davide Nigro “On the uniqueness of the steady-state solution of the Lindblad–Gorini–Kossakowski–Sudarshan equation” Journal of Statistical Mechanics: Theory and Experiment 2019, 043202 (2019).
https://doi.org/10.1088/1742-5468/ab0c1c
[102] Lyudmila Grigoryevaand Juan-Pablo Ortega “Universal Discrete-Time Reservoir Computers with Stochastic Inputs and Linear Readouts Using Non-Homogeneous State-Affine Systems” J. Mach. Learn. Res. 19, 892–931 (2018).
https://dl.acm.org/doi/abs/10.5555/3291125.3291149
[103] Fabrizio Minganti, Alberto Biella, Nicola Bartolo, and Cristiano Ciuti, “Spectral theory of Liouvillians for dissipative phase transitions” Phys. Rev. A 98, 042118 (2018).
https://doi.org/10.1103/PhysRevA.98.042118
[104] E. Anderson, Z. Bai, C. Bischof, L. S. Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney, and D. Sorensen, “LAPACK Users’ Guide” Society for Industrial Applied Mathematics (1999).
https://doi.org/10.1137/1.9780898719604
Cited by
[1] Antonio Sannia, Francesco Tacchino, Ivano Tavernelli, Gian Luca Giorgi, and Roberta Zambrini, “Engineered dissipation to mitigate barren plateaus”, arXiv:2310.15037, (2023).
[2] P. Renault, J. Nokkala, G. Roeland, N. Y. Joly, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps, and V. Parigi, “Experimental Optical Simulator of Reconfigurable and Complex Quantum Environment”, PRX Quantum 4 4, 040310 (2023).
[3] Jorge García-Beni, Gian Luca Giorgi, Miguel C. Soriano, and Roberta Zambrini, “Squeezing as a resource for time series processing in quantum reservoir computing”, Optics Express 32 4, 6733 (2024).
[4] Johannes Nokkala, Gian Luca Giorgi, and Roberta Zambrini, “Retrieving past quantum features with deep hybrid classical-quantum reservoir computing”, arXiv:2401.16961, (2024).
[5] Shumpei Kobayashi, Quoc Hoan Tran, and Kohei Nakajima, “Hierarchy of the echo state property in quantum reservoir computing”, arXiv:2403.02686, (2024).
The above citations are from SAO/NASA ADS (last updated successfully 2024-03-20 16:06:38). The list may be incomplete as not all publishers provide suitable and complete citation data.
Could not fetch Crossref cited-by data during last attempt 2024-03-20 16:06:37: Could not fetch cited-by data for 10.22331/q-2024-03-20-1291 from Crossref. This is normal if the DOI was registered recently.
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.
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- Source: https://quantum-journal.org/papers/q-2024-03-20-1291/
