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We define quantum chaos and integrability in open quantum many-body systems as a dynamical property of single stochastic realizations, referred to as quantum trajectories.
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If the Hilbert space is finite and the Liouvillian superoperator is time-independent, the existence of at least one steady state is guaranteed Rivas and Huelga 2012 . If the system is not invariant under any strong Liouvillian symmetry, the steady state is also unique Albert and Jiang 2014 . In this work, we consider open quantum systems admitting a unique steady state
2014
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P. Schlagheck, D. Ullmo, J. D. Urbina, K. Richter, and S. Tomsovic, Enhancement of many-body quantum interference in chaotic bosonic systems: The role of symmetry and dynamics, Physical Review Letters 123
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A. Schuckert and M. Knap, Many-body chaos near a thermal phase transition, SciPost Phys. 7
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R. Lescanne, M. Villiers, T. Peronnin, A. Sarlette, M. Delbecq, B. Huard, T. Kontos, M. Mirrahimi, and Z. Leghtas, Exponential suppression of bit-flips in a qubit encoded in an oscillator, Nature Physics 16
2020
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K. Jacobs, Quantum Measurement Theory and its Applications (Cambridge University Press, 2014)
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A. J. Daley, Quantum trajectories and open many-body quantum systems, Advances in Physics 63
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M. Rautenberg and M. Gärttner, Classical and quantum chaos in a three-mode bosonic system, Physical Review A 101
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2020
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A. L. Grimsmo and S. Puri, Quantum Error Correction with the Gottesman-Kitaev-Preskill Code, PRX Quantum 2
2021
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M. Ippoliti, M. J. Gullans, S. Gopalakrishnan, D. A. Huse, and V. Khemani, Entanglement Phase Transitions in Measurement-Only Dynamics, Physical Review X 11
2021
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J. Li, T. Prosen, and A. Chan, Spectral Statistics of Non-Hermitian Matrices and Dissipative Quantum Chaos, Physical Review Letters 127
2021
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H. Weimer, A. Kshetrimayum, and R. Orús, Simulation methods for open quantum many-body systems, Reviews of Modern Physics 93
2021
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E. Altman, K. R. Brown, G. Carleo, L. D. Carr, E. Demler, C. Chin, B. DeMarco, S. E. Economou, M. A. Eriksson, K.-M. C. Fu, M. Greiner, K. R. Hazzard, R. G. Hulet, A. J. Kollár, B. L. Lev, M. D. Lukin, R. Ma, X. Mi, S. Misra, C. Monroe, K. Murch, Z. Nazario, K.-K. Ni, A. C. Potter, P. Roushan, M. Saffman, M. Schleier-Smith, I. Siddiqi, R. Simmonds, M. Singh, I. Spielman, K. Temme, D. S. Weiss, J. Vučković, V. Vuletić, J. Ye, and M. Zwierlein, Quantum Simulators: Architectures and Opportunities, PRX Quantum 2
2021
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A. Blais, A. L. Grimsmo, S. Girvin, and A. Wallraff, Circuit quantum electrodynamics, Reviews of Modern Physics 93
2021
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F. P. García De Arquer, D. V. Talapin, V. I. Klimov, Y. Arakawa, M. Bayer, and E. H. Sargent, Semiconductor quantum dots: Technological progress and future challenges, Science 373
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2021
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H. Goto and T. Kanao, Chaos in coupled Kerr-nonlinear parametric oscillators, Physical Review Research 3
2021
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A rigorous derivation of the semiclassical limit of the Lindblad master equation indicates that the correct classical limit, i.e. ℏ → 0 \hbar\to 0 should include second-order correlations between fields Dubois et al. 2021 . Here we will identify the classical limit as the the mean-field approximation, which assumes that second-order correlators factor into field products
2021
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T. Bilitewski, S. Bhattacharjee, and R. Moessner, Classical many-body chaos with and without quasiparticles, Physical Review B 103
2021
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2021
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P. Zanardi and N. Anand, Information scrambling and chaos in open quantum systems, Physical Review A 103
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2021
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C. Chamberland, K. Noh, P. Arrangoiz-Arriola, E. T. Campbell, C. T. Hann, J. Iverson, H. Putterman, T. C. Bohdanowicz, S. T. Flammia, A. Keller, G. Refael, J. Preskill, L. Jiang, A. H. Safavi-Naeini, O. Painter, and F. G. Brandão, Building a fault-tolerant quantum computer using concatenated cat codes, PRX Quantum 3
2022
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T. Hillmann, F. Quijandría, A. L. Grimsmo, and G. Ferrini, Performance of Teleportation-Based Error-Correction Circuits for Bosonic Codes with Noisy Measurements, PRX Quantum 3
2022
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2022
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D. Dahan, G. Arwas, and E. Grosfeld, Classical and quantum chaos in chirally-driven, dissipative Bose-Hubbard systems, npj Quantum Information 8
2022
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A. M. García-García, L. Sá, and J. J. Verbaarschot, Symmetry Classification and Universality in Non-Hermitian Many-Body Quantum Chaos by the Sachdev-Ye-Kitaev Model, Physical Review X 12
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2022
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The choice of a cavity cutoff N c = 13 N_{c}=13 ensures the convergence of the spectral statistics as proposed in Sá et al. 2020a and Prasad et al. 2022 . We however note that with the proposed cutoff for some of the points in the phase diagram (in particular with F / U ≥ 3.5 F/U\geq 3.5 ), expectation values have not yet reached convergence. This however does not change the spectral distinction between chaos and integrability
2022
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D. Plankensteiner, C. Hotter, and H. Ritsch, QuantumCumulants.jl: A Julia framework for generalized mean-field equations in open quantum systems, Quantum 6
2022
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C. Berke, E. Varvelis, S. Trebst, A. Altland, and D. P. DiVincenzo, Transmon platform for quantum computing challenged by chaotic fluctuations, Nature Communications 13
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2022
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R. Di Candia, F. Minganti, K. V. Petrovnin, G. S. Paraoanu, and S. Felicetti, Critical parametric quantum sensing, npj Quantum Information 9
2023
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L. Gravina, F. Minganti, and V. Savona, Critical schrödinger cat qubit, PRX Quantum 4
2023
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L. Sá, P. Ribeiro, and T. Prosen, Symmetry Classification of Many-Body Lindbladians: Tenfold Way and Beyond, Physical Review X 13
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Since quantum trajectories in the unique steady state of an open quantum system are ergodic Beaulieu et al. 2023 , one can also let a single quantum trajectory evolve towards the steady state and then sample the sets ( λ j , c j ) m (\lambda_{j},c_{j})_{m} in time
2023
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W. Verstraelen, D. Huybrechts, T. Roscilde, and M. Wouters, Quantum and classical correlations in open quantum spin lattices via truncated-cumulant trajectories, PRX Quantum 4
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