Dissipation som en ressource til Quantum Reservoir Computing

Dissipation som en ressource til Quantum Reservoir Computing

Antonio Sannia, Rodrigo Martínez-Peña, Miguel C. Soriano, Gian Luca Giorgi og Roberta Zambrini

Institut for tværdisciplinær fysik og komplekse systemer (IFISC) UIB-CSIC, Campus Universitat Illes Balears, 07122, Palma de Mallorca, Spanien.

Finder du denne artikel interessant eller vil du diskutere? Scite eller efterlade en kommentar på SciRate.

Abstrakt

Dissipation induceret af interaktioner med et eksternt miljø hindrer typisk udførelsen af ​​kvanteberegninger, men kan i nogle tilfælde vise sig at være en nyttig ressource. Vi viser den potentielle forbedring induceret af dissipation inden for kvantereservoirberegning, der introducerer tunbare lokale tab i spinnetværksmodeller. Vores tilgang baseret på kontinuerlig dissipation er ikke kun i stand til at reproducere dynamikken i tidligere forslag til kvantereservoirberegning, baseret på diskontinuerlige slettekort, men også at forbedre deres ydeevne. Kontrol af dæmpningshastighederne er vist at booste populære maskinlærings-tidsmæssige opgaver som evnen til lineært og ikke-lineært at behandle inputhistorien og forudsige kaotiske serier. Endelig beviser vi formelt, at vores dissipative modeller under ikke-restriktive forhold udgør en universel klasse for reservoirberegning. Det betyder, at i betragtning af vores tilgang, er det muligt at tilnærme ethvert fading hukommelseskort med vilkårlig præcision.

Inden for kvanteberegningsområdet hævder den konventionelle opfattelse, at interaktioner med eksterne miljøer er skadelige for beregningsmæssig ydeevne. Vores forskning afslører imidlertid et paradigmeskifte, der viser den fordelagtige rolle, som dissipation spiller i kvantemaskinelæring. Specifikt inden for det spirende felt inden for kvantereservoirberegning viser vi fordelene ved at introducere manipuleret dissipation i spinnetværksmodeller. Gennem omfattende benchmarking-tests, der omfatter opgaver, der spænder over lineær og ikke-lineær hukommelse, samt prognosekapacitet, fandt vi en markant forbedring af beregningseffektiviteten. Desuden fastslår vi, gennem formel bevisførelse under ikke-begrænsende forhold, universaliteten af ​​vores dissipative modeller for reservoirberegning.

► BibTeX-data

► Referencer

[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] CL Degen, F. Reinhard og P. Cappellaro, "Quantum sensing" Rev. Mod. Phys. 89, 035002 (2017).
https://​/​doi.org/​10.1103/​RevModPhys.89.035002

[5] S. Pirandola, UL Andersen, L. Banchi, M. Berta, D. Bunandar, R. Colbeck, D. Englund, T. Gehring, C. Lupo, C. Ottaviani, JL Pereira, M. Razavi, J. Shamsul Shaari , M. Tomamichel, VC Usenko, G. Vallone, P. Villoresi og P. Wallden, "Advances in quantum cryptography" Adv. Opt. Foton. 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 Logaritms on a Quantum Computer" SIAM J. Comput. 26, 1484-1509 (1997).
https://​/​doi.org/​10.1137/​S0097539795293172

[8] Lov K Grover "En hurtig kvantemekanisk algoritme til databasesøgning" Proceedings af det otteogtyvende årlige ACM-symposium om Theory of computing 212-219 (1996).
https://​/​doi.org/​10.1145/​237814.237866

[9] David Deutsch og Richard Jozsa "Hurtig løsning af problemer ved kvanteberegning" Proceedings of the Royal Society of London. Serie 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 og 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 og Enrique Lizaso, "Quantum computing for finance: Overview and prospects" Anmeldelser i 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 og Stefan Woerner, "Option prissætning ved hjælp af kvantecomputere" 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 og 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 og Tim Menke, "Støjende mellemskala kvantealgoritmer" Anmeldelser af moderne fysik 94 , 015004 (2022).
https://​/​doi.org/​10.1103/​RevModPhys.94.015004

[17] Frank Verstraete, Michael M Wolf og J Ignacio Cirac, "Kvanteberegning og kvantetilstandsteknik drevet af dissipation" Naturfysik 5, 633-636 (2009).
https://doi.org/​10.1038/​nphys1342

[18] Fernando Pastawski, Lucas Clemente og Juan Ignacio Cirac, "Kvanteminder baseret på manipuleret dissipation" Physical Review A 83, 012304 (2011).
https://​/​doi.org/​10.1103/​PhysRevA.83.012304

[19] Christiane P Koch "Kontrollering af åbne kvantesystemer: værktøjer, præstationer og begrænsninger" Journal of Physics: Condensed Matter 28, 213001 (2016).
https:/​/​doi.org/​10.1088/​0953-8984/​28/​21/​213001

[20] Sai Vinjanampathy og Janet Anders "Quantum thermodynamics" Contemporary Physics 57, 545-579 (2016).
https://​/​doi.org/​10.1080/​00107514.2016.1201896

[21] Gonzalo Manzano og 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 "Vibrationer, kvante og biologi" 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 og 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 og Roberta Zambrini, "Afsløring af lydløse klynger i komplekse kvantenetværk" 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 og 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 og 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 og 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 "Ekkotilstanden"-tilgangen til at analysere og træne tilbagevendende neurale netværk - med en erratum-note" Bonn, Tyskland: Det tyske nationale forskningscenter for informationsteknologi 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 og Akira Hirose, "Nylige fremskridt inden for fysisk reservoirberegning: En gennemgang" 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 og 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 og 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 og Miguel C. Soriano, "Advances in photonic reservoir computing" Nanophotonics 6, 561-576 (2017).

[34] Keisuke Fujiiand Kohei Nakajima "Harnessing Disorder-Ensemble Quantum Dynamics for Machine Learning" Phys. Rev. ansøgt 8, 024030 (2017).
https://​/​doi.org/​10.1103/​PhysRevApplied.8.024030

[35] Kohei Nakajima, Keisuke Fujii, Makoto Negoro, Kosuke Mitarai og Masahiro Kitagawa, "Boosting Computational Power through Spatial Multiplexing in Quantum Reservoir Computing" Phys. Rev. Anvendt 11, 034021 (2019).
https://​/​doi.org/​10.1103/​PhysRevApplied.11.034021

[36] Jiayin Chenand Hendra I. Nurdin "Læring af ikke-lineære input-outputkort med dissipative kvantesystemer" 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 og Miguel C Soriano, "Informationsbehandlingskapacitet af spin-baserede kvantereservoir-beregningssystemer" Cognitive Computation 1-12 (2020).
https://​/​doi.org/​10.1007/​s12559-020-09772-y

[39] Rodrigo Araiza Bravo, Khadijeh Najafi, Xun Gao og 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] WD Kalfus, GJ Ribeill, GE Rowlands, HK Krovi, TA Ohki og LCG Govia, "Hilbert space as a computational ressource 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 og Roberta Zambrini, "Gaussiske tilstande af kontinuerte variable kvantesystemer giver universel og alsidig reservoirberegning" Communications Physics 4, 1-11 (2021).
https://​/​doi.org/​10.1038/​s42005-021-00556-w

[42] LCG Govia, GJ Ribeill, GE Rowlands, HK Krovi og TA Ohki, "Quantum reservoir computing with a single non-linear oscillator" Phys. Rev. Research 3, 013077 (2021).
https://​/​doi.org/​10.1103/​PhysRevResearch.3.013077

[43] Jiayin Chen, Hendra I Nurdin og Naoki Yamamoto, "Tidsmæssig informationsbehandling på støjende kvantecomputere" Physical Review Applied 14, 024065 (2020).
https://​/​doi.org/​10.1103/​PhysRevApplied.14.024065

[44] Yudai Suzuki, Qi Gao, Ken C Pradel, Kenji Yasuoka og Naoki Yamamoto, "Naturlig kvantereservoirberegning til tidsmæssig informationsbehandling" 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 og Kohei Nakajima, "Tidsmæssig informationsbehandling induceret af kvantestøj" Fysisk. 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 og 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 og 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 og Timothy CH Liew, "Realisering og komprimering af kvantekredsløb med kvantereservoirberegning" Communications Physics 4, 1-7 (2021).
https:/​/​doi.org/​10.1038/​s42005-021-00606-3

[49] Sanjib Ghosh, Andrzej Opala, Michał Matuszewski, Tomasz Paterek og 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 og Timothy CH Liew, "Reconstructing Quantum States With Quantum Reservoir Networks" IEEE Transactions on Neurale Networks and Learning Systems 32, 3148-3155 (2021).
https://​/​doi.org/​10.1109/​tnnls.2020.3009716

[51] Sanjib Ghosh, Tomasz Paterek og Timothy CH 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 og Timothy CH Liew, "Quantum neuromorphic tilgang til effektiv sansning af tyngdekraftsinduceret sammenfiltring" Fysisk gennemgang D 107 (2023).
https://​/​doi.org/​10.1103/​physrevd.107.086014

[53] Johannes Nokkala "Online kvantetidsseriebehandling med tilfældige oscillatornetværk" Scientific Reports 13 (2023).
https:/​/​doi.org/​10.1038/​s41598-023-34811-7

[54] Joni Dambre, David Verstraeten, Benjamin Schrauwen og Serge Massar, "Informationsbehandlingskapacitet for dynamiske systemer" Videnskabelige rapporter 2, 1-7 (2012).
https://​/​doi.org/​10.1038/​srep00514

[55] Pere Mujal, Rodrigo Martínez-Peña, Gian Luca Giorgi, Miguel C. Soriano og 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 og 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 og Hakan E. Türeci, “Tackling Sampling Noise in Physical Systems for Machine Learning Applications: Fundamental Limits and Eigentasks” Fysisk gennemgang X 13 (2023).
https://​/​doi.org/​10.1103/​physrevx.13.041020

[58] Izzet B Yildiz, Herbert Jaeger og Stefan J Kiebel, "Re-visiting the echo state property" Neurale netværk 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 og 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 og 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 og Roberta Zambrini, "Analytisk bevis for ikke-linearitet i qubits og kontinuert-variabel kvantereservoir-beregning" Journal of Physics: Complexity 2, (045008).
https:/​/​doi.org/​10.1088/​2632-072x/​ac340e

[62] MD SAJID ANIS et al. "Qiskit: An Open source Framework for Quantum Computing" (2021).
https://​/​doi.org/​10.5281/​zenodo.2573505

[63] Marco Cattaneo, Matteo AC Rossi, Guillermo García-Pérez, Roberta Zambrini og 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 Breuer og Francesco Petruccione "Teorien om åbne kvantesystemer" 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 og Ennackal Chandy George Sudarshan, "Fuldstændig positive dynamiske 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 og Roberta Zambrini, "Lokal versus global hovedligning med fælles og separate bade: overlegenhed af den globale tilgang i delvis sekulær tilnærmelse" New Journal of Physics 21, 113045 (2019).
https://​/​doi.org/​10.1088/​1367-2630/​ab54ac

[68] Lyudmila Grigoryev og Juan-Pablo Ortega "Ekkostatsnetværk er universelle" Neurale netværk 108, 495-508 (2018).
https://​/​doi.org/​10.1016/​j.neunet.2018.08.025
https://​/​www.sciencedirect.com/​science/​article/​pii/​S089360801830251X

[69] Georg Fette og 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 "Lang korttidshukommelse" Neural computation 9, 1735-1780 (1997).
https:/​/​doi.org/​10.1007/​978-3-642-24797-2_4

[71] Gavan Linternand Peter N Kugler "Selvorganisering i forbindelsesmodeller: Associativ hukommelse, dissipative strukturer og termodynamisk lov" 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 og Roberta Zambrini, "Dynamiske faseovergange i kvantereservoirberegning" Physical Review Letters 127, 100502 (2021).
https://​/​doi.org/​10.1103/​PhysRevLett.127.100502

[73] Michael C Mackey og Leon Glass "Oscillation og kaos i fysiologiske kontrolsystemer" Science 197, 287-289 (1977).
https://​doi.org/​10.1126/​science.267326

[74] J Doyne Farmer og 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 "Udnyttelse af ikke-linearitet: Forudsigelse af kaotiske systemer og energibesparelse i trådløs kommunikation" 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 og JM Gutiérrez, "En samlet ramme for reservoirberegning og ekstreme læringsmaskiner baseret på en enkelt tidsforsinket neuron" Videnskabelige rapporter 5, 1-11 (2015).
https://​/​doi.org/​10.1038/​srep14945

[77] Jaideep Pathak, Zhixin Lu, Brian R Hunt, Michelle Girvan og Edward Ott, "Brug af maskinlæring til at replikere kaotiske attraktorer og beregne Lyapunov-eksponenter ud fra data" Chaos 27, 121102 (2017).
https://​/​doi.org/​10.1063/​1.5010300

[78] Kristian Baumann, Christine Guerlin, Ferdinand Brennecke og Tilman Esslinger, "Dicke kvantefaseovergang med en superfluid gas i et optisk hulrum" Nature 464, 1301-1306 (2010).
https://​/​doi.org/​10.1038/​nature09009

[79] Zhang Zhiqiang, Chern Hui Lee, Ravi Kumar, KJ Arnold, Stuart J. Masson, AS Parkins og MD 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 RK Cline, Ana Maria Rey og James K. Thompson, "Udforsker dynamiske faseovergange med kolde atomer i et optisk hulrum" Nature 580, 602-607 (2020).
https://​/​doi.org/​10.1038/​s41586-020-2224-x

[81] Mattias Fitzpatrick, Neereja M. Sundaresan, Andy CY Li, Jens Koch og 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 og Igor Lesanovsky, "Generaliseret 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 og Rainer Blatt, "An open-system quantum simulator with fangede ioner" Nature 470, 486 –491 (2011).
https://​/​doi.org/​10.1038/​nature09801

[84] R. Blattand CF Roos "Kvantesimuleringer med fangede ioner" Nature Physics 8, 277-284 (2012).
https://doi.org/​10.1038/​nphys2252

[85] Javad Kazemi og 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 og Hendrik Weimer, "Multikritisk adfærd i dissipative Ising-modeller" Physical Review A 95 (2017).
https://​/​doi.org/​10.1103/​physreva.95.042133

[87] Jiasen Jin, Alberto Biella, Oscar Viyuela, Cristiano Ciuti, Rosario Fazio og Davide Rossini, "Fasediagram af den dissipative kvante Ising-model på et kvadratisk gitter" Physical Review B 98 (2018).
https://​/​doi.org/​10.1103/​physrevb.98.241108

[88] Cenap Ates, Beatriz Olmos, Juan P. Garrahan og Igor Lesanovsky, "Dynamiske faser og intermittens af den dissipative kvante Ising-model" Physical Review A 85 (2012).
https://​/​doi.org/​10.1103/​physreva.85.043620

[89] A. Bermudez, T. Schaetz og MB 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 og 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 og Igor Lesanovsky, "Generaliseret 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 og Géza Giedke, "Dissipative spin-kæder: Implementering med kolde atomer og steady-state-egenskaber" Fysisk gennemgang A 87 (2013).
https://​/​doi.org/​10.1103/​physreva.87.022110

[93] Tony E. Leeand Ching-Kit Chan "Bebudet magnetisme i ikke-ermitiske atomsystemer" Fysisk gennemgang 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 og Mikhail D. Lukin, "Ukonventionel magnetisme via optisk pumpning af interagerende spinsystemer" Physical Review Letters 110 (2013).
https://​/​doi.org/​10.1103/​physrevlett.110.257204

[96] Danijela Marković og 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 og Gian Luca Giorgi, "Kollisionsmodeller kan effektivt simulere enhver flerparts 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 "Indlejring af information i et dynamisk system" Nonlinearity 35, 1131 (2022).
https://​/​doi.org/​10.1088/​1361-6544/​ac4817

[100] Jiayin Chen "Ikke-lineær konvergent dynamik til tidsmæssig informationsbehandling på nye kvante- og klassiske enheder"-afhandling (2022).
https://​/​doi.org/​10.26190/​unsworks/​24115

[101] Davide Nigro "Om det unikke ved steady-state-løsningen af ​​Lindblad-Gorini-Kossakowski-Sudarshan-ligningen" Journal of Statistical Mechanics: Theory and Experiment 2019, 043202 (2019).
https:/​/​doi.org/​10.1088/​1742-5468/​ab0c1c

[102] Lyudmila Grigoryev og Juan-Pablo Ortega "Universelle diskrete-tidsbeholdercomputere med stokastiske input og lineære udlæsninger, der bruger ikke-homogene statsaffine systemer" J. Mach. Lære. Res. 19, 892-931 (2018).
https://​/​dl.acm.org/​doi/​abs/​10.5555/​3291125.3291149

[103] Fabrizio Minganti, Alberto Biella, Nicola Bartolo og Cristiano Ciuti, "Spektral teori om Liouvillians for dissipative faseovergange" Phys. Rev. A 98, 042118 (2018).
https://​/​doi.org/​10.1103/​PhysRevA.98.042118

[104] E. Anderson, Z. Bai, C. Bischof, LS Blackford, J. Demmel, J. Dongarra, J. Du Croz, A. Greenbaum, S. Hammarling, A. McKenney og D. Sorensen, “LAPACK Users' Guide ” Selskab for industriel anvendt matematik (1999).
https://​/​doi.org/​10.1137/​1.9780898719604

Citeret af

[1] Antonio Sannia, Francesco Tacchino, Ivano Tavernelli, Gian Luca Giorgi og Roberta Zambrini, "Konstrueret dissipation for at afbøde golde plateauer", arXiv: 2310.15037, (2023).

[2] P. Renault, J. Nokkala, G. Roeland, NY Joly, R. Zambrini, S. Maniscalco, J. Piilo, N. Treps og 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 og Roberta Zambrini, "Squeezing as a ressource for time series processing in quantum reservoir computing", Optics Express 32 4, 6733 (2024).

[4] Johannes Nokkala, Gian Luca Giorgi og Roberta Zambrini, "Hentning af tidligere kvantefunktioner med dyb hybrid klassisk-kvantereservoir-beregning", arXiv: 2401.16961, (2024).

[5] Shumpei Kobayashi, Quoc Hoan Tran og Kohei Nakajima, "Hierarki af ekkostatens ejendom i kvantereservoirberegning", arXiv: 2403.02686, (2024).

Ovenstående citater er fra SAO/NASA ADS (sidst opdateret 2024-03-21 04:08:40). Listen kan være ufuldstændig, da ikke alle udgivere leverer passende og fuldstændige citatdata.

On Crossrefs citeret af tjeneste ingen data om at citere værker blev fundet (sidste forsøg 2024-03-21 04:08:38).

Tidsstempel:

Mere fra Quantum Journal