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Abstract

In the age of quantum computers and quantum simulators appearing in the daily news, a proper understanding and controllability of quantum many-body systems forming the underlying principles becomes more and more important, albeit it is far from complete.

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References

  1. Feynman RP (1982) Simulating physics with computers. Int J Theor Phys 21(6):467–488. https://doi.org/10.1007/BF02650179

  2. Nielsen MA, Chuang IL (2010) Quantum Computation and Quantum Information: 10th, Anniversary edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511976667

  3. Ignacio Cirac J, Zoller P (2012) Goals and opportunities in quantum simulation. Nat Phys 8:264. https://doi.org/10.1038/nphys2275

  4. Jurcevic P, Lanyon BP, Hauke P, Hempel C, Zoller P, Blatt R, Roos CF (2014) Quasiparticle engineering and entanglement propagation in a quantum many-body system. Nature 511:202. https://doi.org/10.1038/nature13461

  5. Britton JW, Sawyer BC, Keith AC, Joseph Wang C-C, Freericks JK, Uys H, Biercuk MJ, Bollinger JJ (2012) Engineered two-dimensional using interactions in a trapped-ion quantum simulator with hundreds of spins. Nature 484:489. https://doi.org/10.1038/nature10981

  6. Zhang J, Pagano G, Hess PW, Kyprianidis A, Becker P, Kaplan H, Gorshkov AV, Gong Z-X, Monroe C (2017) Observation of a many-body dynamical phase transition with a 53-qubit quantum simulator. Nature 551:601. https://doi.org/10.1038/nature24654

  7. Blatt R, Roos CF (2012) Quantum simulations with trapped ions. Nat. Phys. 8:277. https://doi.org/10.1038/nphys2252

  8. Schauß P, Cheneau M, Endres M, Fukuhara T, Hild S, Omran A, Pohl T, Gross C, Kuhr S, Bloch I (2012) Observation of spatially ordered structures in a two-dimensional Rydberg gas. Nature 491:87. https://doi.org/10.1038/nature11596

  9. Bernien H, Schwartz S, Keesling A, Levine H, Omran A, Pichler H, Choi S, Zibrov AS, Endres M, Greiner M, Vuletić V, Lukin MD (2017) Probing many-body dynamics on a 51-atom quantum simulator. Nature 551:579. https://doi.org/10.1038/nature24622

  10. Barredo D, Lienhard V, de Léséleuc S, Lahaye T, Browaeys A (2018) Synthetic three-dimensional atomic structures assembled atom by atom. Nature 561:79–82. https://doi.org/10.1038/s41586-018-0450-2

  11. Günter G, Schempp H, Robert-de Saint-Vincent M, Gavryusev V, Helmrich S, Hofmann CS, Whitlock S, Weidemüller M (2013) Observing the dynamics of dipole-mediated energy transport by interaction-enhanced imaging. Science 342(6161):954–956. https://science.sciencemag.org/content/342/6161/954

  12. Hazzard KRA, Gadway B, Foss-Feig M, Yan B, Moses SA, Covey JP, Yao NY, Lukin MD, Ye J, Jin DS, Rey AM (2014) Many-body dynamics of dipolar molecules in an optical lattice. Phys Rev Lett 113:195302. https://link.aps.org/doi/10.1103/PhysRevLett.113.195302

  13. Braun S, Friesdorf M, Hodgman SS, Schreiber M, Ronzheimer JP, Riera A, del Rey M, Bloch I, Eisert J, Schneider U (2015) Emergence of coherence and the dynamics of quantum phase transitions. PNAS 112(12):3641–3646. http://www.pnas.org/content/112/12/3641.abstract

  14. Nicklas E, Karl M, Höfer M, Johnson A, Muessel W, Strobel H, Tomkovič J, Gasenzer T, Oberthaler MK (2015) Observation of scaling in the dynamics of a strongly quenched quantum gas. Phys Rev Lett 115:245301. https://link.aps.org/doi/10.1103/PhysRevLett.115.245301

  15. Trotzky S, Pollet L, Gerbier F, Schnorrberger U, Bloch I, Prokof’ev NV, Svistunov B, Troyer M (2010) Suppression of the critical temperature for superfluidity near the Mott transition. Nat Phys 6:998. https://doi.org/10.1038/nphys1799

  16. Mazurenko A, Chiu CS, Ji G, Parsons MF, Kanász-Nagy M, Schmidt R, Grusdt F, Demler E, Greif D, Greiner M (2017) A cold-atom Fermi-Hubbard antiferromagnet. Nature 545:462. https://doi.org/10.1038/nature22362

  17. Schreiber M, Hodgman SS, Bordia P, Lüschen HP, Fischer MH, Vosk R, Altman E, Schneider U, Bloch I (2015) Observation of many-body localization of interacting fermions in a quasirandom optical lattice. Science 349(6250):842–845. https://science.sciencemag.org/content/349/6250/842

  18. Bloch I, Dalibard J, Sylvain N (2012) Quantum simulations with ultracold quantum gases. Nat Phys 8:267. https://doi.org/10.1038/nphys2259

  19. Rigol M, Dunjko V, Olshanii M (2008) Thermalization and its mechanism for generic isolated quantum systems. Nature 452:854. https://doi.org/10.1038/nature06838

  20. Orús R (2014) A practical introduction to tensor networks: matrix product states and projected entangled pair states. Ann Phys 349:117–158. https://www.sciencedirect.com/science/article/pii/S0003491614001596

  21. White SR (1992) Density matrix formulation for quantum renormalization groups. Phys Rev Lett 69:2863–2866. https://link.aps.org/doi/10.1103/PhysRevLett.69.2863

  22. Vidal G (2004) Efficient simulation of one-dimensional quantum many-body systems. Phys Rev Lett 93:040502. https://link.aps.org/doi/10.1103/PhysRevLett.93.040502

  23. Schollwöck U (2011) The density-matrix renormalization group in the age of matrix product states. Ann Phys 326(1):96–192. http://www.sciencedirect.com/science/article/pii/S0003491610001752

  24. Bridgeman JC, Chubb CT (2017) Hand-waving and interpretive dance: an introductory course on tensor networks. J Phys A: Math Theor, 50(22):223001. https://doi.org/10.1088%2F1751-8121%2Faa6dc3

  25. White SR, Feiguin AE (2004) Real-time evolution using the density matrix renormalization group. Phys Rev Lett 93:076401. https://link.aps.org/doi/10.1103/PhysRevLett.93.076401

  26. Kollath C, Läuchli AM, Altman E (2007) Quench dynamics and nonequilibrium phase diagram of the Bose-Hubbard model. Phys Rev Lett 98:180601. https://link.aps.org/doi/10.1103/PhysRevLett.98.180601

  27. Sharma S, Suzuki S, Dutta A (2015) Quenches and dynamical phase transitions in a nonintegrable quantum Ising model. Phys Rev B 92:104306. https://link.aps.org/doi/10.1103/PhysRevB.92.104306

  28. Daley AJ, Kollath C, Schollwöck U, Vidal G (2004) Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces. J Stat Mech: Theory Exp 2004(04):P04005. http://stacks.iop.org/1742-5468/2004/i=04/a=P04005

  29. Haegeman J, Lubich C, Oseledets I, Vandereycken B, Verstraete F (2016) Unifying time evolution and optimization with matrix product states. Phys Rev B 94:165116. https://link.aps.org/doi/10.1103/PhysRevB.94.165116

  30. Polkovnikov A (2010) Phase space representation of quantum dynamics. Ann Phys 325(8):1790. https://doi.org/10.1016/j.aop.2010.02.006

  31. Blakie PB, Bradley AS, Davis MJ, Ballagh RJ, Gardiner CW (2008) Dynamics and statistical mechanics of ultra-cold bose gases using c-field techniques. Adv Phys 57(5):363–455. https://doi.org/10.1080/00018730802564254

  32. Karl M, Gasenzer T (2017) Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas. New J Phys 19(9):093014. https://doi.org/10.1088%2F1367-2630%2Faa7eeb

  33. Karl M, Nowak B, Gasenzer T (2013) Universal scaling at nonthermal fixed points of a two-component Bose gas. Phys Rev A 88:063615 Dec. https://link.aps.org/doi/10.1103/PhysRevA.88.063615

  34. Wootters WK (1987) A Wigner-function formulation of finite-state quantum mechanics. Ann Phys 176(1):1–21. http://www.sciencedirect.com/science/article/pii/000349168790176X

  35. Wootters WK (2003) Picturing qubits in phase space. arXiv:quant-ph/0306135

  36. Schachenmayer J, Pikovski A, Rey AM (2015) Dynamics of correlations in two-dimensional quantum spin models with long-range interactions: A phase-space Monte-Carlo study. New J Phys 17(6):065009. https://doi.org/10.1088/1367-2630/17/6/065009

  37. Schachenmayer J, Pikovski A, Rey AM (2015) Many-body quantum spin dynamics with Monte Carlo trajectories on a discrete phase space. Phys Rev X 5:011022. https://link.aps.org/doi/10.1103/PhysRevX.5.011022

  38. Pucci L, Roy A, Kastner M (2016) Simulation of quantum spin dynamics by phase space sampling of Bogoliubov-Born-Green-Kirkwood-Yvon trajectories. Phys Rev B 93(17):174302. https://link.aps.org/doi/10.1103/PhysRevB.93.174302

  39. Žunkovič B (2015) Continuous phase-space methods on discrete phase spaces. EPL 112:10003. https://doi.org/10.1209/0295-5075/112/10003

  40. Pucci L, Roy A, do Espirito Santo TS, Kaiser R, Kastner M, Bachelard R (2017) Quantum effects in the cooperative scattering of light by atomic clouds. Phys Rev A 95:053625. https://link.aps.org/doi/10.1103/PhysRevA.95.053625

  41. Zhu B, Rey AM, Schachenmayer J (2019) A generalized phase space approach for solving quantum spin dynamics. New J Phys 21(8):082001. https://doi.org/10.1088%2F1367-2630%2Fab354d

  42. Wurtz J, Polkovnikov A, Sels D (2018) Cluster truncated Wigner approximation in strongly interacting systems. Ann Phys 395:341–365. http://www.sciencedirect.com/science/article/pii/S0003491618301647

  43. Babadi M, Demler E, Knap M (2015) Far-from-equilibrium field theory of many-body quantum spin systems: Prethermalization and relaxation of spin spiral states in three dimensions. Phys Rev X 5:041005. https://link.aps.org/doi/10.1103/PhysRevX.5.041005

  44. Piñeiro Orioli A, Safavi-Naini A, Wall ML, Rey AM (2017) Nonequilibrium dynamics of spin-boson models from phase-space methods. Phys Rev A 96:033607. https://link.aps.org/doi/10.1103/PhysRevA.96.033607

  45. Piñeiro Orioli A, Signoles A, Wildhagen H, Günter G, Berges J, Whitlock S, Weidemüller M (2018) Relaxation of an isolated dipolar-interacting Rydberg quantum spin system. Phys Rev Lett 120:063601. https://link.aps.org/doi/10.1103/PhysRevLett.120.063601

  46. Covey JP, De Marco L, Acevedo ÓL, Rey AM, Ye J (2018) An approach to spin-resolved molecular gas microscopy. New J Phys 20(4):043031. https://doi.org/10.1088%2F1367-2630%2Faaba65

  47. Acevedo OL, Safavi-Naini A, Schachenmayer J, Wall ML, Nandkishore R, Rey AM (2017) Exploring many-body localization and thermalization using semiclassical methods. Phys Rev A 96:033604. https://link.aps.org/doi/10.1103/PhysRevA.96.033604

  48. Czischek S, Gärttner M, Oberthaler M, Kastner M, Gasenzer T (2018) Quenches near criticality of the quantum using chain-power and limitations of the discrete truncated Wigner approximation. Quantum Sci Technol 4(1):014006. http://stacks.iop.org/2058-9565/4/i=1/a=014006

  49. von der Linden W (1992) A quantum Monte Carlo approach to many-body physics. Phys Rep 220(2):53–162. http://www.sciencedirect.com/science/article/pii/037015739290029Y

  50. Masuo S (ed) (1986) Quantum monte carlo methods in equilibrium and nonequilibrium systems, vol 74. Solid-State sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83154-6

  51. Rubenstein B (2017) Introduction to the variational monte carlo method in quantum chemistry and physics, pp. 285–313. Springer, Singapore. https://doi.org/10.1007/978-981-10-2502-0_10

  52. Carleo G, Becca F, Schió M, Fabrizio M (2012) Localization and glassy dynamics of many-body quantum systems. Sci Rep 2:243. http://dx.doi.org/10.1038/srep00243

  53. Carleo G, Becca F, Sanchez-Palencia L, Sorella S, Fabrizio M (2014) Light-cone effect and supersonic correlations in one- and two-dimensional bosonic superfluids. Phys Rev A 89(3):031602. https://link.aps.org/doi/10.1103/PhysRevA.89.031602

  54. Hinton GE (2012) A practical guide to training restricted boltzmann machines, pp 599–619. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35289-8_32

  55. Le Roux N, Bengio Y (2008) Representational power of restricted Boltzmann machines and deep belief networks. Neural Comput 20(6):1631–1649. https://doi.org/10.1162/neco.2008.04-07-510

  56. Torlai G, Melko RG (2016) Learning thermodynamics with Boltzmann machines. Phys Rev B 94:165134. https://link.aps.org/doi/10.1103/PhysRevB.94.165134

  57. Carleo G, Troyer M (2017) Solving the quantum many-body problem with artificial neural networks. Science 355(6325):602–606. http://science.sciencemag.org/content/355/6325/602

  58. Czischek S, Gärttner M, Gasenzer T (2018) Quenches near using quantum criticality as a challenge for artificial neural networks. Phys Rev B 98:024311. https://doi.org/10.1103/PhysRevB.98.024311

  59. Kungl AF, Schmitt S, Klähn J, Müller P, Baumbach A, Dold D, Kugele A, Müller E, Koke C, Kleider M, Mauch C, Breitwieser O, Leng L, Gürtler N, Güttler M, Husmann D, Husmann K, Hartel A, Karasenko V, Grübl A, Schemmel J, Meier K, Petrovici MA (2019) Accelerated physical emulation of bayesian inference in spiking neural networks. Front Neurosci 13:1201. https://www.frontiersin.org/article/10.3389/fnins.2019.01201

  60. Lu S, Gao X, Duan L-M (2019) Efficient representation of topologically ordered states with restricted Boltzmann machines. Phys Rev B 99:155136. https://link.aps.org/doi/10.1103/PhysRevB.99.155136

  61. Gao X, Duan L-M (2017) Efficient representation of quantum many-body states with deep neural networks. Nat Commun 8(1):662. https://doi.org/10.1038/s41467-017-00705-2

  62. Deng D-L, Li X, Das Sarma S (2017) Quantum entanglement in neural network states. Phys Rev X 7:021021. https://link.aps.org/doi/10.1103/PhysRevX.7.021021

  63. Nomura Y, Darmawan AS, Yamaji Y, Imada M (2017) Restricted Boltzmann machine learning for solving strongly correlated quantum systems. Phys Rev B 96:205152. https://link.aps.org/doi/10.1103/PhysRevB.96.205152

  64. Carrasquilla J, Torlai G, Melko RG, Aolita L (2019) Reconstructing quantum states with generative models. Nat Mach Intell 1(3):155–161. https://doi.org/10.1038/s42256-019-0028-1

  65. Hartmann MJ, Carleo G (2019) Neural-network approach to dissipative quantum many-body dynamics. Phys Rev Lett 122:250502. https://link.aps.org/doi/10.1103/PhysRevLett.122.250502

  66. Nagy A, Savona V (2019) Variational quantum Monte Carlo method with a neural-network ansatz for open quantum systems. Phys Rev Lett 122:250501. https://link.aps.org/doi/10.1103/PhysRevLett.122.250501

  67. Vicentini F, Biella A, Regnault N, Ciuti C (2019) Variational neural-network ansatz for steady states in open quantum systems. Phys Rev Lett 122:250503. https://link.aps.org/doi/10.1103/PhysRevLett.122.250503

  68. Yoshioka N, Hamazaki R (2019) Constructing neural stationary states for open quantum many-body systems. Phys Rev B 99:214306. https://link.aps.org/doi/10.1103/PhysRevB.99.214306

  69. Torlai G, Mazzola G, Carrasquilla J, Troyer M, Melko R, Carleo G (2018) Neural-network quantum state tomography. Nat Phys 14:447–450. https://doi.org/10.1038/s41567-018-0048-5

  70. Torlai G, Melko RG (2018) Latent space purification via neural density operators. Phys Rev Lett 120:240503. https://link.aps.org/doi/10.1103/PhysRevLett.120.240503

  71. Torlai G, Timar B, van Nieuwenburg EPL, Levine H, Omran A, Keesling A, Bernien H, Greiner M, Vuletić V, Lukin MD, Melko RG, Endres M (2019) Integrating neural networks with a quantum simulator for state reconstruction. Phys Rev Lett 123:230504. https://link.aps.org/doi/10.1103/PhysRevLett.123.230504

  72. Westerhout T, Astrakhantsev N, Tikhonov KS, Katsnelson M, Bagrov AA (2020) Generalization properties of neural network approximations to frustrated magnet ground states. Nat Commun 11(1):1593. https://doi.org/10.1038/s41467-020-15402-w

  73. Saito H (2017) Solving the Bose-Hubbard model with machine learning. J Phys Soc Jpn 86(9):093001. https://doi.org/10.7566/JPSJ.86.093001

  74. Cai Z, Liu J (2018) Approximating quantum many-body wave functions using artificial neural networks. Phys Rev B 97:035116. https://link.aps.org/doi/10.1103/PhysRevB.97.035116

  75. Deng D-L, Li X, Das Sarma S (2017) Machine learning topological states. Phys Rev B 96:195145. https://link.aps.org/doi/10.1103/PhysRevB.96.195145

  76. Kaubruegger R, Pastori L, Budich JC (2018) Chiral topological phases from artificial neural networks. Phys Rev B 97:195136. https://link.aps.org/doi/10.1103/PhysRevB.97.195136

  77. Freitas N, Morigi G, Dunjko V (2018) Neural network operations and Susuki-Trotter evolution of neural network states. Int J Quantum Inf 16(08):1840008. https://doi.org/10.1142/S0219749918400087

  78. Carleo G, Nomura Y, Imada M (2018) Constructing exact representations of quantum many-body systems with deep neural networks. Nat Commun 9(1):5322. https://doi.org/10.1038/s41467-018-07520-3

  79. Teng P (2018) Machine-learning quantum mechanics: solving quantum mechanics problems using radial basis function networks. Phys Rev E 98:033305. https://link.aps.org/doi/10.1103/PhysRevE.98.033305

  80. Huang Y, Moore JE (2017) Neural network representation of tensor network and chiral states. arXiv:1701.06246 [cond-mat.dis-nn]

  81. Glasser I, Pancotti N, August M, Rodriguez ID Ignacio Cirac J (2018) Neural-network quantum states, string-bond states, and chiral topological states. Phys Rev X 8:011006, Jan 2018. https://link.aps.org/doi/10.1103/PhysRevX.8.011006

  82. Clark SR (2018) Unifying neural-network quantum states and correlator product states via tensor networks. J Phys A: Math Theor 51(13):135301. http://stacks.iop.org/1751-8121/51/i=13/a=135301

  83. Chen J, Cheng S, Xie H, Wang L, Xiang T (2018) Equivalence of restricted Boltzmann machines and tensor network states. Phys Rev B 97:085104. https://link.aps.org/doi/10.1103/PhysRevB.97.085104

  84. Troyer M, Wiese U-J (2005) Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations. Phys Rev Lett 94:170201. https://link.aps.org/doi/10.1103/PhysRevLett.94.170201

  85. Anagnostopoulos KN, Nishimura J (2002) New approach to the complex-action problem and its application to a nonperturbative study of superstring theory. Phys Rev D 66:106008. https://link.aps.org/doi/10.1103/PhysRevD.66.106008

  86. Nakamura T, Hatano N, Nishimori H (1992) Reweighting method for quantum Monte Carlo simulations with the negative-sign problem. J Phys Soc Jpn 61(10):3494–3502. https://doi.org/10.1143/JPSJ.61.3494

  87. Loh EY, Gubernatis JE, Scalettar RT, White SR, Scalapino DJ, Sugar RL (1990) Sign problem in the numerical simulation of many-electron systems. Phys Rev B 41:9301–9307. https://link.aps.org/doi/10.1103/PhysRevB.41.9301

  88. Broecker P, Carrasquilla J, Melko RG, Trebst S (2017) Machine learning quantum phases of matter beyond the fermion sign problem. Sci Rep 7:8823. https://doi.org/10.1038/s41598-017-09098-0

  89. Torlai G, Carrasquilla J, Fishman MT, Melko RG, Fisher MPA (2019) Wavefunction positivization via automatic differentiation. arXiv:1906.04654 [quant-ph]

  90. Hangleiter D, Roth I, Nagaj D, Eisert J (2019) Easing the Monte Carlo sign problem. arXiv:1906.02309 [quant-ph]

  91. Czischek S, Pawlowski JM, Gasenzer T, Gärttner M (2019) Sampling scheme for neuromorphic simulation of entangled quantum systems. Phys Rev B 100:195120. https://link.aps.org/doi/10.1103/PhysRevB.100.195120

  92. Sachdev S (2011) Quantum phase transitions, 2nd edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511973765

  93. Pfeuty P (1970) The one-dimensional using model with a transverse field. Ann Phys (NY) 57:79–90. https://doi.org/10.1016/0003-4916(70)90270-8

  94. Lieb E, Schultz T, Mattis D (1961) Two soluble models of an antiferromagnetic chain. Ann Phys 16(3):407–466. http://www.sciencedirect.com/science/article/pii/0003491661901154

  95. Calabrese P, Essler FHL, Fagotti M (2012) Quantum quench in the transverse field using chain: I. time evolution of order parameter correlators. J Stat Mech: Theory Exp 2012(07):P07016. https://doi.org/10.1088%2F1742-5468%2F2012%2F07%2Fp07016

  96. Calabrese P, Essler FHL, Fagotti M (2012) Quantum quenches in the transverse field using chain: II. stationary state properties. J Stat Mech: Theory Exp 2012(07):P07022. https://doi.org/10.1088%2F1742-5468%2F2012%2F07%2Fp07022

  97. Chiocchetta A, Gambassi A, Diehl S, Marino J (2017) Dynamical crossovers in prethermal critical states. Phys Rev Lett 118:135701. https://link.aps.org/doi/10.1103/PhysRevLett.118.135701

  98. Delfino G (2014) Quantum quenches with integrable pre-quench dynamics. J Phys A: Math Theor 47(40):402001. http://stacks.iop.org/1751-8121/47/i=40/a=402001

  99. Delfino G, Viti J (2017) On the theory of quantum quenches in near-critical systems. J Phys A: Math Theor 50(8):084004. http://stacks.iop.org/1751-8121/50/i=8/a=084004

  100. Karl M, Cakir H, Halimeh JC, Oberthaler MK, Kastner M, Gasenzer T (2017) Universal equilibrium scaling functions at short times after a quench. Phys Rev E 96:022110 Aug. https://link.aps.org/doi/10.1103/PhysRevE.96.022110

  101. Di Ventra M, Traversa FL (2018) Perspective: Memcomputing: Leveraging memory and physics to compute efficiently. J Appl Phys 123(18):180901. https://doi.org/10.1063/1.5026506

  102. Petrovici MA (2016) Form versus function: theory and models for neuronal substrates. Springer International Publishing, Berlin. https://doi.org/10.1007/978-3-319-39552-4

  103. Petrovici MA, Bill J, Bytschok I, Schemmel J, Meier K (2016) Stochastic inference with spiking neurons in the high-conductance state. Phys Rev E 94:042312 Oct. https://link.aps.org/doi/10.1103/PhysRevE.94.042312

  104. Schemmel J, Brüderle D, Grübl A, Hock M, Meier K, Millner S (2010) A wafer-scale neuromorphic hardware system for large-scale neural modeling, pp 1947–1950. https://ieeexplore.ieee.org/document/5536970/

  105. Buesing L, Bill J, Nessler B, Maass W (2011) Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons. PLoS Comput Biol 7(11):1–22. https://doi.org/10.1371/journal.pcbi.1002211

  106. Wunderlich T, Kungl AF, Müller E, Hartel A, Stradmann Y, Aamir SA, Grübl A, Heimbrecht A, Schreiber K, Stöckel D, Pehle C, Billaudelle S, Kiene G, Mauch C, Schemmel J, Meier K, Petrovici MA. Demonstrating advantages of neuromorphic computation: a pilot study. Front Neurosci 13:260. https://www.frontiersin.org/article/10.3389/fnins.2019.00260

  107. John Stewart Bell (1964) On the Einstein Podolsky Rosen paradox. Physics 1(3):195–200. https://cds.cern.ch/record/111654

  108. Bell JS (1966) On the problem of hidden variables in quantum mechanics. Rev Mod Phys 38:447–452. https://link.aps.org/doi/10.1103/RevModPhys.38.447

  109. Bell JS, Aspect A (2004) Speakable and unspeakable in quantum mechanics: collected papers on quantum philosophy, 2 edn. Cambridge University Press, Cambridge. https://doi.org/10.1017/CBO9780511815676

  110. Greenberger DM, Horne MA, Zeilinger A (1989) Going beyond bell’s theorem, pp 69–72. Springer Netherlands, Dordrecht. https://doi.org/10.1007/978-94-017-0849-4_10

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Czischek, S. (2020). Introduction. In: Neural-Network Simulation of Strongly Correlated Quantum Systems. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-52715-0_1

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