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  • Review Article
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Engineered dissipation for quantum information science

Nature Reviews Physics volume 4, pages 660–671 (2022)Cite this article

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Abstract

Quantum information processing relies on the precise control of non-classical states in the presence of many uncontrolled environmental degrees of freedom. The interactions between the relevant degrees of freedom and the environment are often viewed as detrimental, as they dissipate energy and decohere quantum states. Nonetheless, when controlled, dissipation is an essential tool for manipulating quantum information: dissipation engineering enables quantum measurement, quantum-state preparation and quantum-state stabilization. The advances in quantum technologies, marked by improvements of characteristic coherence times and extensible architectures for quantum control, have coincided with the development of such dissipation engineering tools that interface quantum and classical degrees of freedom. This Review presents dissipation as a fundamental aspect of the measurement and control of quantum devices, and highlights the role of dissipation engineering in quantum error correction and quantum simulation.

Key points

  • Dissipation is essential for quantum information processing: resetting to the ground state, measurement and cooling all require dissipation.

  • Carefully engineered dissipation can protect quantum information, control dynamics and enforce constraints.

  • Dissipation finds applications in quantum error correction, quantum sensing and quantum simulation.

  • Much of dissipation engineering focuses on designing ‘dark’ or dissipation-free manifolds of states that are stabilized by the dissipative process.

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Fig. 1: Zeno effects and optical pumping in three-level systems.
Fig. 2: Pointer states in quantum measurement.
Fig. 3: Quantum sensing.
Fig. 4: Dissipation in quantum simulation.

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References

  1. Callen, H. B. & Welton, T. A. Irreversibility and generalized noise. Phys. Rev. 83, 34–40 (1951).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  2. Poyatos, J. F., Cirac, J. I. & Zoller, P. Quantum reservoir engineering with laser cooled trapped ions. Phys. Rev. Lett. 77, 4728–4731 (1996).

    Article  ADS  Google Scholar 

  3. Boutin, S., Andersen, C. K., Venkatraman, J., Ferris, A. J. & Blais, A. Resonator reset in circuit QED by optimal control for large open quantum systems. Phys. Rev. A 96, 042315 (2017).

    Article  ADS  Google Scholar 

  4. Magnard, P. et al. Fast and unconditional all-microwave reset of a superconducting qubit. Phys. Rev. Lett. 121, 060502 (2018).

    Article  ADS  Google Scholar 

  5. Valenzuela, S. O. et al. Microwave-induced cooling of a superconducting qubit. Science 314, 1589–1592 (2006).

    Article  ADS  Google Scholar 

  6. Geerlings, K. et al. Demonstrating a driven reset protocol for a superconducting qubit. Phys. Rev. Lett. 110, 120501 (2013).

    Article  ADS  Google Scholar 

  7. Holland, E. T. et al. Single-photon-resolved cross-Kerr interaction for autonomous stabilization of photon-number states. Phys. Rev. Lett. 115, 180501 (2015).

    Article  ADS  Google Scholar 

  8. Leghtas, Z. et al. Confining the state of light to a quantum manifold by engineered two-photon loss. Science 347, 853–857 (2015).

    Article  ADS  Google Scholar 

  9. Kimchi-Schwartz, M. E. et al. Stabilizing entanglement via symmetry-selective bath engineering in superconducting qubits. Phys. Rev. Lett. 116, 240503 (2016).

    Article  ADS  Google Scholar 

  10. Liu, Y. et al. Comparing and combining measurement-based and driven-dissipative entanglement stabilization. Phys. Rev. X 6, 011022 (2016).

    Google Scholar 

  11. Lu, Y. et al. Universal stabilization of a parametrically coupled qubit. Phys. Rev. Lett. 119, 150502 (2017).

    Article  ADS  Google Scholar 

  12. Andersen, C. K. et al. Entanglement stabilization using ancilla-based parity detection and real-time feedback in superconducting circuits. NPJ Quantum Inf. 5, 69 (2019).

    Article  ADS  Google Scholar 

  13. Bose, S., Knight, P. L., Plenio, M. B. & Vedral, V. Proposal for teleportation of an atomic state via cavity decay. Phys. Rev. Lett. 83, 5158–5161 (1999).

    Article  ADS  Google Scholar 

  14. Browne, D. E., Plenio, M. B. & Huelga, S. F. Robust creation of entanglement between ions in spatially separate cavities. Phys. Rev. Lett. 91, 067901 (2003).

    Article  ADS  Google Scholar 

  15. Sørensen, A. S. & Mølmer, K. Measurement induced entanglement and quantum computation with atoms in optical cavities. Phys. Rev. Lett. 91, 097905 (2003).

    Article  ADS  Google Scholar 

  16. Bretheau, L., Campagne-Ibarcq, P., Flurin, E., Mallet, F. & Huard, B. Quantum dynamics of an electromagnetic mode that cannot contain N photons. Science 348, 776–779 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  17. Hacohen-Gourgy, S., Ramasesh, V. V., De Grandi, C., Siddiqi, I. & Girvin, S. M. Cooling and autonomous feedback in a Bose–Hubbard chain with attractive interactions. Phys. Rev. Lett. 115, 240501 (2015).

    Article  ADS  Google Scholar 

  18. Ma, R. et al. A dissipatively stabilized Mott insulator of photons. Nature 566, 51–57 (2019).

    Article  ADS  Google Scholar 

  19. Yanay, Y., Braumüller, J., Gustavsson, S., Oliver, W. D. & Tahan, C. Two-dimensional hard-core Bose–Hubbard model with superconducting qubits. NPJ Quantum Inf. 6, 58 (2020).

    Article  ADS  Google Scholar 

  20. Andersen, C. K. et al. Repeated quantum error detection in a surface code. Nat. Phys. https://doi.org/10.1038/s41567-020-0920-y (2020).

  21. Kapit, E. The upside of noise: engineered dissipation as a resource in superconducting circuits. Quantum Sci. Technol. 2, 033002 (2017).

    Article  ADS  Google Scholar 

  22. Leghtas, Z. et al. Hardware-efficient autonomous quantum memory protection. Phys. Rev. Lett. 111, 120501 (2013).

    Article  ADS  Google Scholar 

  23. Touzard, S. et al. Coherent oscillations inside a quantum manifold stabilized by dissipation. Phys. Rev. X 8, 021005 (2018).

    Google Scholar 

  24. Chen, Z. et al. Exponential suppression of bit or phase errors with cyclic error correction. Nature 595, 383–387 (2021).

    Article  Google Scholar 

  25. Krinner, S. et al. Realizing repeated quantum error correction in a distance-three surface code. Nature 605, 669–674 (2022).

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  27. Altman, E. et al. Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021).

    Article  Google Scholar 

  28. Degasperis, A., Fonda, L. & Ghirardi, G. C. Does the lifetime of an unstable system depend on the measuring apparatus? Nuovo Cim. A 21, 471–484 (1974).

    Article  ADS  Google Scholar 

  29. Misra, B. & Sudarshan, E. C. G. The Zeno’s paradox in quantum theory. J. Math. Phys. 18, 756–763 (1977).

    Article  ADS  MathSciNet  Google Scholar 

  30. Itano, W. M., Heinzen, D. J., Bollinger, J. J. & Wineland, D. J. Quantum Zeno effect. Phys. Rev. A 41, 2295–2300 (1990).

    Article  ADS  Google Scholar 

  31. Lane, A. M. Decay at early times: larger or smaller than the golden rule? Phys. Lett. A 99, 359–360 (1983).

    Article  ADS  Google Scholar 

  32. Kofman, A. G. & Kurizki, G. Acceleration of quantum decay processes by frequent observations. Nature 405, 546–550 (2000).

    Article  ADS  Google Scholar 

  33. Harrington, P. M., Monroe, J. T. & Murch, K. W. Quantum Zeno effects from measurement controlled qubit-bath interactions. Phys. Rev. Lett. 118, 240401 (2017).

    Article  ADS  Google Scholar 

  34. Beige, A., Braun, D., Tregenna, B. & Knight, P. L. Quantum computing using dissipation to remain in a decoherence-free subspace. Phys. Rev. Lett. 85, 1762–1765 (2000).

    Article  ADS  Google Scholar 

  35. Facchi, P. & Pascazio, S. Quantum Zeno dynamics: mathematical and physical aspects. J. Phys. A 41, 493001 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  36. Facchi, P. & Pascazio, S. Quantum Zeno subspaces. Phys. Rev. Lett. 89, 080401 (2002).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  37. Lidar, D. A., Chuang, I. L. & Whaley, K. B. Decoherence-free subspaces for quantum computation. Phys. Rev. Lett. 81, 2594–2597 (1998).

    Article  ADS  Google Scholar 

  38. Hacohen-Gourgy, S., García-Pintos, L. P., Martin, L. S., Dressel, J. & Siddiqi, I. Incoherent qubit control using the quantum Zeno effect. Phys. Rev. Lett. 120, 020505 (2018).

    Article  ADS  Google Scholar 

  39. Sørensen, J. J. W. H., Dalgaard, M., Kiilerich, A. H., Mølmer, K. & Sherson, J. F. Quantum control with measurements and quantum Zeno dynamics. Phys. Rev. A 98, 062317 (2018).

    Article  ADS  Google Scholar 

  40. Mark, M. J. et al. Interplay between coherent and dissipative dynamics of bosonic doublons in an optical lattice. Phys. Rev. Res. 2, 043050 (2020).

    Article  MathSciNet  Google Scholar 

  41. Raimond, J. M. et al. Phase space tweezers for tailoring cavity fields by quantum Zeno dynamics. Phys. Rev. Lett. 105, 213601 (2010).

    Article  ADS  Google Scholar 

  42. Raimond, J. M. et al. Quantum Zeno dynamics of a field in a cavity. Phys. Rev. A 86, 032120 (2012).

    Article  ADS  Google Scholar 

  43. Kumar, P., Snizhko, K., Gefen, Y. & Rosenow, B. Optimized steering: quantum state engineering and exceptional points. Phys. Rev. A 105, L010203 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  44. Snizhko, K., Kumar, P. & Romito, A. Quantum Zeno effect appears in stages. Phys. Rev. Res. 2, 033512 (2020).

    Article  Google Scholar 

  45. Zhu, B. et al. Suppressing the loss of ultracold molecules via the continuous quantum Zeno effect. Phys. Rev. Lett. 112, 070404 (2014).

    Article  ADS  Google Scholar 

  46. Chen, T. et al. Quantum Zeno effects across a parity-time symmetry breaking transition in atomic momentum space. NPJ Quantum Inf. https://doi.org/10.1038/s41534-021-00417-y (2021).

  47. Ozawa, T. et al. Topological photonics. Rev. Mod. Phys. 91, 015006 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  48. Aliferis, P. & Preskill, J. Fault-tolerant quantum computation against biased noise. Phys. Rev. A 78, 052331 (2008).

    Article  ADS  Google Scholar 

  49. Shruti, P. et al. Bias-preserving gates with stabilized cat qubits. Sci. Adv. 6, eaay5901 (2020).

    Article  Google Scholar 

  50. Blumenthal, E. et al. Demonstration of universal control between non-interacting qubits using the Quantum Zeno effect. npj Quantum Inf. 8, 88 (2022).

    Article  ADS  Google Scholar 

  51. Shankar, S. et al. Autonomously stabilized entanglement between two superconducting quantum bits. Nature 504, 419 (2013).

    Article  ADS  Google Scholar 

  52. Murch, K. W. et al. Cavity-assisted quantum bath engineering. Phys. Rev. Lett. 109, 183602 (2012).

    Article  ADS  Google Scholar 

  53. Puri, S., Boutin, S. & Blais, A. Engineering the quantum states of light in a Kerr-nonlinear resonator by two-photon driving. NPJ Quantum Inf. 3, 18 (2017).

    Article  ADS  Google Scholar 

  54. Mamaev, M., Govia, L. C. G. & Clerk, A. A. Dissipative stabilization of entangled cat states using a driven Bose–Hubbard dimer. Quantum 2, 58 (2018).

    Article  Google Scholar 

  55. Krauter, H. et al. Entanglement generated by dissipation and steady state entanglement of two macroscopic objects. Phys. Rev. Lett. 107, 080503 (2011).

    Article  ADS  Google Scholar 

  56. Souquet, J.-R. & Clerk, A. A. Fock-state stabilization and emission in superconducting circuits using dc-biased Josephson junctions. Phys. Rev. A 93, 060301 (2016).

    Article  ADS  Google Scholar 

  57. Lin, Y. et al. Dissipative production of a maximally entangled steady state of two quantum bits. Nature 504, 415–418 (2013).

    Article  ADS  Google Scholar 

  58. Kienzler, D. et al. Quantum harmonic oscillator state synthesis by reservoir engineering. Science 347, 53–56 (2015).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  59. Plenio, M. B., Huelga, S. F., Beige, A. & Knight, P. L. Cavity-loss-induced generation of entangled atoms. Phys. Rev. A 59, 2468–2475 (1999).

    Article  ADS  Google Scholar 

  60. Kraus, B. et al. Preparation of entangled states by quantum Markov processes. Phys. Rev. A 78, 042307 (2008).

    Article  ADS  Google Scholar 

  61. Kastoryano, M. J., Reiter, F. & Sørensen, A. S. Dissipative preparation of entanglement in optical cavities. Phys. Rev. Lett. 106, 090502 (2011).

    Article  ADS  Google Scholar 

  62. Morigi, G. et al. Dissipative quantum control of a spin chain. Phys. Rev. Lett. 115, 200502 (2015).

    Article  ADS  Google Scholar 

  63. Ma, X., Viennot, J. J., Kotler, S., Teufel, J. D. & Lehnert, K. W. Non-classical energy squeezing of a macroscopic mechanical oscillator. Nat. Phys. 17, 322–326 (2021).

    Article  Google Scholar 

  64. Cole, D. C. et al. Resource-efficient dissipative entanglement of two trapped-ion qubits. Phys. Rev. Lett. 128, 080502 (2022).

    Article  ADS  Google Scholar 

  65. Aron, C., Kulkarni, M. & Türeci, H. E. Steady-state entanglement of spatially separated qubits via quantum bath engineering. Phys. Rev. A 90, 062305 (2014).

    Article  ADS  Google Scholar 

  66. Rao, D. D. B. & Mølmer, K. Deterministic entanglement of Rydberg ensembles by engineered dissipation. Phys. Rev. A 90, 062319 (2014).

    Article  ADS  Google Scholar 

  67. Martin, L., Sayrafi, M. & Whaley, K. B. What is the optimal way to prepare a Bell state using measurement and feedback? Quantum Sci. Technol. 2, 044006 (2017).

    Article  ADS  Google Scholar 

  68. Rao, D. D. B., Yang, S. & Wrachtrup, J. Dissipative entanglement of solid-state spins in diamond. Phys. Rev. A 95, 022310 (2017).

    Article  ADS  Google Scholar 

  69. Schuetz, M. J. A., Kessler, E. M., Vandersypen, L. M. K., Cirac, J. I. & Giedke, G. Nuclear spin dynamics in double quantum dots: multistability, dynamical polarization, criticality, and entanglement. Phys. Rev. B 89, 195310 (2014).

    Article  ADS  Google Scholar 

  70. Shao, X. Q., Wu, J. H. & Yi, X. X. Dissipation-based entanglement via quantum Zeno dynamics and Rydberg antiblockade. Phys. Rev. A 95, 062339 (2017).

    Article  ADS  Google Scholar 

  71. Didier, N., Guillaud, J., Shankar, S. & Mirrahimi, M. Remote entanglement stabilization and concentration by quantum reservoir engineering. Phys. Rev. A 98, 012329 (2018).

    Article  ADS  Google Scholar 

  72. Reiter, F., Reeb, D. & Sørensen, A. S. Scalable dissipative preparation of many-body entanglement. Phys. Rev. Lett. 117, 040501 (2016).

    Article  ADS  Google Scholar 

  73. Ma, S.-l., Li, X.-k., Liu, X.-y., Xie, J.-k. & Li, F.-l. Stabilizing Bell states of two separated superconducting qubits via quantum reservoir engineering. Phys. Rev. A 99, 042336 (2019).

    Article  ADS  Google Scholar 

  74. Sharma, V. & Mueller, E. J. Driven-dissipative control of cold atoms in tilted optical lattices. Phys. Rev. A 103, 043322 (2021).

    Article  ADS  Google Scholar 

  75. Colladay, K. R. & Mueller, E. J. Driven dissipative preparation of few-body Laughlin states of Rydberg polaritons in twisted cavities. Preprint at https://arxiv.org/abs/2107.06346 (2021).

  76. Ticozzi, F. & Viola, L. Quantum Markovian subsystems: invariance, attractivity, and control. IEEE Trans. Automat. Contr. 53, 2048–2063 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  77. Braginskii, V., Manukin, A. & Tikhonov, M. Y. Investigation of dissipative ponderomotive effects of electromagnetic radiation. J. Exp. Theor. Phys. 31, 829 (1970).

    ADS  Google Scholar 

  78. Cohadon, P. F., Heidmann, A. & Pinard, M. Cooling of a mirror by radiation pressure. Phys. Rev. Lett. 83, 3174–3177 (1999).

    Article  ADS  Google Scholar 

  79. Chan, J. et al. Laser cooling of a nanomechanical oscillator into its quantum ground state. Nature 478, 89–92 (2011).

    Article  ADS  Google Scholar 

  80. Rivière, R. et al. Optomechanical sideband cooling of a micromechanical oscillator close to the quantum ground state. Phys. Rev. A 83, 063835 (2011).

    Article  ADS  Google Scholar 

  81. Yong-Chun, L., Yu-Wen, H., Wei, W. C. & Yun-Feng, X. Review of cavity optomechanical cooling. Chin. Phys. B 22, 114213 (2013).

    Article  ADS  Google Scholar 

  82. Wineland, D. J. & Itano, W. M. Laser cooling. Phys. Today 40, 34–40 (1987).

    Article  Google Scholar 

  83. Hänsch, T. & Schawlow, A. Cooling of gases by laser radiation. Opt. Commun. 13, 68–69 (1975).

    Article  ADS  Google Scholar 

  84. Schreck, F. & Druten, K. V. Laser cooling for quantum gases. Nat. Phys. 17, 1296–1304 (2021).

    Article  Google Scholar 

  85. Phillips, W. D. Nobel lecture: laser cooling and trapping of neutral atoms. Rev. Mod. Phys. 70, 721–741 (1998).

    Article  ADS  Google Scholar 

  86. Stenholm, S. The semiclassical theory of laser cooling. Rev. Mod. Phys. 58, 699–739 (1986).

    Article  ADS  Google Scholar 

  87. Diedrich, F., Bergquist, J. C., Itano, W. M. & Wineland, D. J. Laser cooling to the zero-point energy of motion. Phys. Rev. Lett. 62, 403–406 (1989).

    Article  ADS  Google Scholar 

  88. Wiseman, H. M. & Milburn, G. J. All-optical versus electro-optical quantum-limited feedback. Phys. Rev. A 49, 4110–4125 (1994).

    Article  ADS  Google Scholar 

  89. Lloyd, S. Coherent quantum feedback. Phys. Rev. A 62, 022108 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  90. Zurek, W. H. Pointer basis of quantum apparatus: into what mixture does the wave packet collapse? Phys. Rev. D 24, 1516–1525 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  91. Jacobs, K. & Steck, D. A. A straightforward introduction to continuous quantum measurement. Contemp. Phys. 47, 279–303 (2006).

    Article  ADS  Google Scholar 

  92. Clerk, A. A., Devoret, M. H., Girvin, S. M., Marquardt, F. & Schoelkopf, R. J. Introduction to quantum noise, measurement, and amplification. Rev. Mod. Phys. 82, 1155–1208 (2010).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  93. Braginsky, V. B. & Khalili, F. Y. Quantum nondemolition measurements: the route from toys to tools. Rev. Mod. Phys. 68, 1–11 (1996).

    Article  ADS  MathSciNet  Google Scholar 

  94. Wheeler, J. A. & Zurek, W. H. (eds) Quantum Theory and Measurement (Princeton Univ. Press, 2014); https://doi.org/10.1515/9781400854554

  95. Hatridge, M. et al. Quantum back-action of an individual variable-strength measurement. Science 339, 178–181 (2013).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  96. Weber, S. J. et al. Mapping the optimal route between two quantum states. Nature 511, 570–573 (2014).

    Article  ADS  Google Scholar 

  97. Campagne-Ibarcq, P. et al. Observing quantum state diffusion by heterodyne detection of fluorescence. Phys. Rev. X 6, 011002 (2016).

    Google Scholar 

  98. Hacohen-Gourgy, S. et al. Quantum dynamics of simultaneously measured non-commuting observables. Nature 538, 491–494 (2016).

    Article  ADS  Google Scholar 

  99. Flurin, E., Martin, L. S., Hacohen-Gourgy, S. & Siddiqi, I. Using a recurrent neural network to reconstruct quantum dynamics of a superconducting qubit from physical observations. Phys. Rev. X 10, 011006 (2020).

    Google Scholar 

  100. Lloyd, S. & Viola, L. Engineering quantum dynamics. Phys. Rev. A 65, 010101 (2001).

    Article  ADS  MathSciNet  Google Scholar 

  101. Herasymenko, Y., Gornyi, I. & Gefen, Y. Measurement-driven navigation in many-body Hilbert space: active-decision steering. Preprint at https://arxiv.org/abs/2111.09306 (2021).

  102. Wiseman, H. M. & Milburn, G. J. Quantum Measurement and Control (Cambridge Univ. Press, 2009).

  103. Martin, L. S., Livingston, W. P., Hacohen-Gourgy, S., Wiseman, H. M. & Siddiqi, I. Implementation of a canonical phase measurement with quantum feedback. Nat. Phys. 16, 1046–1049 (2020).

    Article  Google Scholar 

  104. Gertler, J. M. et al. Protecting a bosonic qubit with autonomous quantum error correction. Nature 590, 243–248 (2021).

    Article  ADS  Google Scholar 

  105. Ahn, C., Doherty, A. C. & Landahl, A. J. Continuous quantum error correction via quantum feedback control. Phys. Rev. A 65, 042301 (2002).

    Article  ADS  Google Scholar 

  106. Atalaya, J. et al. Continuous quantum error correction for evolution under time-dependent Hamiltonians. Phys. Rev. A 103, 042406 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  107. Kerckhoff, J., Nurdin, H. I., Pavlichin, D. S. & Mabuchi, H. Designing quantum memories with embedded control: photonic circuits for autonomous quantum error correction. Phys. Rev. Lett. 105, 040502 (2010).

    Article  ADS  Google Scholar 

  108. Kapit, E. Hardware-efficient and fully autonomous quantum error correction in superconducting circuits. Phys. Rev. Lett. 116, 150501 (2016).

    Article  ADS  Google Scholar 

  109. Reiter, F., Sørensen, A. S., Zoller, P. & Muschik, C. A. Dissipative quantum error correction and application to quantum sensing with trapped ions. Nat. Commun. 8, 1822 (2017).

    Article  ADS  Google Scholar 

  110. Albert, V. V. et al. Pair-cat codes: autonomous error-correction with low-order nonlinearity. Quantum Sci. Technol. 4, 035007 (2019).

    Article  ADS  Google Scholar 

  111. Sarovar, M. & Milburn, G. J. Continuous quantum error correction by cooling. Phys. Rev. A 72, 012306 (2005).

    Article  ADS  Google Scholar 

  112. de Neeve, B. & Nguyen, T.-L. & Behrle, T. & Home, J. P. Error correction of a logical grid state qubit by dissipative pumping. Nat. Phys 18, 296300 (2022).

    Article  Google Scholar 

  113. Kristensen, L. B., Kjaergaard, M., Andersen, C. K. & Zinner, N. T. Hybrid quantum error correction in qubit architectures. Preprint at https://arxiv.org/abs/1909.09112 (2019).

  114. Lihm, J.-M., Noh, K. & Fischer, U. R. Implementation-independent sufficient condition of the Knill–Laflamme type for the autonomous protection of logical qudits by strong engineered dissipation. Phys. Rev. A 98, 012317 (2018).

    Article  ADS  Google Scholar 

  115. Gyenis, A. et al. Moving beyond the transmon: noise-protected superconducting quantum circuits. PRX Quantum 2, 030101 (2021).

    Article  ADS  Google Scholar 

  116. Peres, A. Reversible logic and quantum computers. Phys. Rev. A 32, 3266–3276 (1985).

    Article  ADS  MathSciNet  Google Scholar 

  117. Bultink, C. C. et al. Protecting quantum entanglement from leakage and qubit errors via repetitive parity measurements. Sci. Adv. 6, eaay3050 (2020).

    Article  ADS  Google Scholar 

  118. Fowler, A. G., Mariantoni, M., Martinis, J. M. & Cleland, A. N. Surface codes: towards practical large-scale quantum computation. Phys. Rev. A 86, 032324 (2012).

    Article  ADS  Google Scholar 

  119. Córcoles, A. et al. Demonstration of a quantum error detection code using a square lattice of four superconducting qubits. Nat. Commun. https://doi.org/10.1038/ncomms7979 (2015).

  120. Versluis, R. et al. Scalable quantum circuit and control for a superconducting surface code. Phys. Rev. Appl. 8, 034021 (2017).

    Article  ADS  Google Scholar 

  121. Cai, W., Ma, Y., Wang, W., Zou, C.-L. & Sun, L. Bosonic quantum error correction codes in superconducting quantum circuits. Fundam. Res. 1, 50–67 (2021).

    Article  Google Scholar 

  122. Michael, M. H. et al. New class of quantum error-correcting codes for a bosonic mode. Phys. Rev. X 6, 031006 (2016).

    Google Scholar 

  123. Axline, C. J. et al. On-demand quantum state transfer and entanglement between remote microwave cavity memories. Nat. Phys. 14, 705–710 (2018).

    Article  Google Scholar 

  124. Mirrahimi, M. et al. Dynamically protected cat-qubits: a new paradigm for universal quantum computation. New J. Phys. 16, 045014 (2014).

    Article  ADS  MATH  Google Scholar 

  125. Guillaud, J. & Mirrahimi, M. Repetition cat qubits for fault-tolerant quantum computation. Phys. Rev. X 9, 041053 (2019).

    Google Scholar 

  126. Grimm, A. et al. Stabilization and operation of a Kerr-cat qubit. Nature 584, 205–209 (2020).

    Article  ADS  Google Scholar 

  127. Tóth, L. D., Bernier, N. R., Nunnenkamp, A., Feofanov, A. K. & Kippenberg, T. J. A dissipative quantum reservoir for microwave light using a mechanical oscillator. Nat. Phys. 13, 787–793 (2017).

    Article  Google Scholar 

  128. Ofek, N. et al. Extending the lifetime of a quantum bit with error correction in superconducting circuits. Nature 536, 441–445 (2016).

    Article  ADS  Google Scholar 

  129. Hu, L. et al. Quantum error correction and universal gate set operation on a binomial bosonic logical qubit. Nat. Phys. 15, 503–508 (2019).

    Article  Google Scholar 

  130. Gottesman, D., Kitaev, A. & Preskill, J. Encoding a qubit in an oscillator. Phys. Rev. A 64, 012310 (2001).

    Article  ADS  Google Scholar 

  131. Campagne-Ibarcq, P. et al. Quantum error correction of a qubit encoded in grid states of an oscillator. Nature 584, 368–372 (2020).

    Article  Google Scholar 

  132. Flühmann, C. et al. Encoding a qubit in a trapped-ion mechanical oscillator. Nature 566, 513–517 (2019).

    Article  ADS  Google Scholar 

  133. Livingston, W. P. et al. Experimental demonstration of continuous quantum error correction. Nat. Commun. 13, 2307 (2022).

    Article  ADS  Google Scholar 

  134. Minev, Z. K. et al. To catch and reverse a quantum jump mid-flight. Nature 570, 200–204 (2019).

    Article  ADS  Google Scholar 

  135. Degen, C. L., Reinhard, F. & Cappellaro, P. Quantum sensing. Rev. Mod. Phys. 89, 035002 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  136. Maze, J. R. et al. Nanoscale magnetic sensing with an individual electronic spin in diamond. Nature 455, 644–647 (2008).

    Article  ADS  Google Scholar 

  137. Balasubramanian, G. et al. Nanoscale imaging magnetometry with diamond spins under ambient conditions. Nature 455, 648–651 (2008).

    Article  ADS  Google Scholar 

  138. Kolkowitz, S. et al. Probing Johnson noise and ballistic transport in normal metals with a single-spin qubit. Science 347, 1129–1132 (2015).

    Article  ADS  Google Scholar 

  139. Zu, C. et al. Emergent hydrodynamics in a strongly interacting dipolar spin ensemble. Nature 597, 45–50 (2021).

    Article  ADS  Google Scholar 

  140. Serniak, K. et al. Direct dispersive monitoring of charge parity in offset-charge-sensitive transmons. Phys. Rev. Appl. 12, 014052 (2019).

    Article  ADS  Google Scholar 

  141. Braginsky, V. B., Vorontsov, Y. I. & Thorne, K. S. Quantum nondemolition measurements. Science 209, 547–557 (1980).

    Article  ADS  Google Scholar 

  142. Lupaşcu, A. et al. Quantum non-demolition measurement of a superconducting two-level system. Nat. Phys. 3, 119–123 (2007).

    Article  Google Scholar 

  143. Xie, Y. et al. Dissipative quantum sensing with a magnetometer based on nitrogen-vacancy centers in diamond. Phys. Rev. Appl. 14, 014013 (2020).

    Article  ADS  Google Scholar 

  144. Khanahmadi, M. & Mølmer, K. Time-dependent atomic magnetometry with a recurrent neural network. Phys. Rev. A 103, 032406 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  145. Nolan, S. P., Smerzi, A. & Pezzè, L. A machine learning approach to Bayesian parameter estimation. Preprint at https://arxiv.org/abs/2006.02369 (2021).

  146. Altman, E. et al. Quantum simulators: architectures and opportunities. PRX Quantum 2, 017003 (2021).

    Article  Google Scholar 

  147. Blatt, R. & Roos, C. F. Quantum simulations with trapped ions. Nat. Phys. 8, 277–284 (2012).

    Article  Google Scholar 

  148. Aspuru-Guzik, A. & Walther, P. Photonic quantum simulators. Nat. Phys. 8, 285–291 (2012).

    Article  Google Scholar 

  149. Gross, C. & Bloch, I. Quantum simulations with ultracold atoms in optical lattices. Science 357, 995–1001 (2017).

    Article  ADS  Google Scholar 

  150. Houck, A. A., Türeci, H. E. & Koch, J. On-chip quantum simulation with superconducting circuits. Nat. Phys. 8, 292–299 (2012).

    Article  Google Scholar 

  151. Schäfer, F., Fukuhara, T., Sugawa, S., Takasu, Y. & Takahashi, Y. Tools for quantum simulation with ultracold atoms in optical lattices. Nat. Rev. Phys. 2, 411–425 (2020).

    Article  Google Scholar 

  152. Noh, C. & Angelakis, D. G. Quantum simulations and many-body physics with light. Rep. Progr. Phys. 80, 016401 (2016).

    Article  ADS  Google Scholar 

  153. Georgescu, I. M., Ashhab, S. & Nori, F. Quantum simulation. Rev. Mod. Phys. 86, 153–185 (2014).

    Article  ADS  Google Scholar 

  154. Poplavskii, R. P. Thermodynamic models of information processes. Phys. Usp. 18, 222–241 (1975).

    Article  ADS  MathSciNet  Google Scholar 

  155. Manin, Y. I. Vychislimoe i nevychislimoe [Computable and uncomputable]. Sov. Radio Moscow 13–15 (1980).

  156. Feynman, R. P. Simulating physics with computers. Int. J. Theor. Phys. 21, 467–488 (1982).

    Article  MathSciNet  Google Scholar 

  157. Feynman, R. P. Quantum mechanical computers. Opt. News 11, 11–20 (1985).

    Article  Google Scholar 

  158. Weimer, H., Müller, M., Lesanovsky, I., Zoller, P. & Büchler, H. P. A Rydberg quantum simulator. Nat. Phys. 6, 382–388 (2010).

    Article  Google Scholar 

  159. Bernien, H. et al. Probing many-body dynamics on a 51-atom quantum simulator. Nature 551, 579–584 (2017).

    Article  ADS  Google Scholar 

  160. Barreiro, J. T. et al. An open-system quantum simulator with trapped ions. Nature 470, 486–491 (2011).

    Article  ADS  Google Scholar 

  161. Kollár, A. J., Fitzpatrick, M. & Houck, A. A. Hyperbolic lattices in circuit quantum electrodynamics. Nature 571, 45–50 (2019).

    Article  ADS  Google Scholar 

  162. Hoening, M., Abdussalam, W., Fleischhauer, M. & Pohl, T. Antiferromagnetic long-range order in dissipative Rydberg lattices. Phys. Rev. A 90, 021603 (2014).

    Article  ADS  Google Scholar 

  163. Sieberer, L. M., Buchhold, M. & Diehl, S. Keldysh field theory for driven open quantum systems. Rep. Progr. Phys. 79, 096001 (2016).

    Article  ADS  Google Scholar 

  164. Foss-Feig, M. et al. Emergent equilibrium in many-body optical bistability. Phys. Rev. A 95, 043826 (2017).

    Article  ADS  Google Scholar 

  165. Cao, Y. et al. Quantum chemistry in the age of quantum computing. Chem. Rev. 119, 10856–10915 (2019).

    Article  Google Scholar 

  166. Reiher, M., Wiebe, N., Svore, K. M., Wecker, D. & Troyer, M. Elucidating reaction mechanisms on quantum computers. Proc. Natl Acad. Sci. USA 114, 7555–7560 (2017).

    Article  ADS  Google Scholar 

  167. O’Malley, P. J. J. et al. Scalable quantum simulation of molecular energies. Phys. Rev. X 6, 031007 (2016).

    Google Scholar 

  168. Dorner, R., Goold, J. & Vedral, V. Towards quantum simulations of biological information flow. Interface Focus 2, 522–528 (2012).

  169. Ribeiro, H. & Marquardt, F. Kinetics of many-body reservoir engineering. Phys. Rev. Res. 2, 033231 (2020).

    Article  Google Scholar 

  170. Wang, H. Quantum algorithm for preparing the ground state of a system via resonance transition. Sci. Rep. https://doi.org/10.1038/s41598-017-16396-0 (2017).

  171. Sharma, V. & Mueller, E. J. Driven-dissipative control of cold atoms in tilted optical lattices. Phys. Rev. A 103, 043322 (2021).

    Article  ADS  Google Scholar 

  172. Zhou, L., Choi, S. & Lukin, M. D. Symmetry-protected dissipative preparation of matrix product states. Phys. Rev. A 104, 032418 (2021).

    Article  ADS  MathSciNet  Google Scholar 

  173. Kjaergaard, M. et al. Superconducting qubits: current state of play. Annu. Rev. Condens. Matter Phys. 11, 369–395 (2020).

    Article  ADS  Google Scholar 

  174. Roy, S., Chalker, J. T., Gornyi, I. V. & Gefen, Y. Measurement-induced steering of quantum systems. Phys. Rev. Res. 2, 033347 (2020).

    Article  Google Scholar 

  175. Ramos, T., Pichler, H., Daley, A. J. & Zoller, P. Quantum spin dimers from chiral dissipation in cold-atom chains. Phys. Rev. Lett. 113, 237203 (2014).

    Article  ADS  Google Scholar 

  176. Das, A. & Chakrabarti, B. K. Colloquium: Quantum annealing and analog quantum computation. Rev. Mod. Phys. 80, 1061–1081 (2008).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  177. Stormer, H. L., Tsui, D. C. & Gossard, A. C. The fractional quantum Hall effect. Rev. Mod. Phys. 71, S298–S305 (1999).

    Article  MathSciNet  Google Scholar 

  178. Moore, G. & Read, N. Nonabelions in the fractional quantum Hall effect. Nucl. Phys. B 360, 362–396 (1991).

    Article  MathSciNet  Google Scholar 

  179. Roncaglia, M., Rizzi, M. & Cirac, J. I. Pfaffian state generation by strong three-body dissipation. Phys. Rev. Lett. 104, 096803 (2010).

    Article  ADS  Google Scholar 

  180. Daley, A. J., Taylor, J. M., Diehl, S., Baranov, M. & Zoller, P. Atomic three-body loss as a dynamical three-body interaction. Phys. Rev. Lett. 102, 040402 (2009).

    Article  ADS  Google Scholar 

  181. Diehl, S., Baranov, M., Daley, A. J. & Zoller, P. Quantum field theory for the three-body constrained lattice Bose gas. I. Formal developments. Phys. Rev. B 82, 064509 (2010).

    Article  ADS  Google Scholar 

  182. Diehl, S., Baranov, M., Daley, A. J. & Zoller, P. Quantum field theory for the three-body constrained lattice Bose gas. II. Application to the many-body problem. Phys. Rev. B 82, 064510 (2010).

    Article  ADS  Google Scholar 

  183. Dogra, N. et al. Dissipation-induced structural instability and chiral dynamics in a quantum gas. Science 366, 1496–1499 (2019).

    Article  ADS  Google Scholar 

  184. Zundel, L. A. et al. Energy-dependent three-body loss in 1D Bose gases. Phys. Rev. Lett. 122, 013402 (2019).

    Article  ADS  Google Scholar 

  185. Bonnes, L. & Wessel, S. Pair superfluidity of three-body constrained bosons in two dimensions. Phys. Rev. Lett. 106, 185302 (2011).

    Article  ADS  Google Scholar 

  186. Syassen, N. et al. Strong dissipation inhibits losses and induces correlations in cold molecular gases. Science 320, 1329–1331 (2008).

    Article  ADS  Google Scholar 

  187. Fröml, H., Muckel, C., Kollath, C., Chiocchetta, A. & Diehl, S. Ultracold quantum wires with localized losses: many-body quantum Zeno effect. Phys. Rev. B 101, 144301 (2020).

    Article  ADS  Google Scholar 

  188. Tomita, T., Nakajima, S., Takasu, Y. & Takahashi, Y. Dissipative Bose–Hubbard system with intrinsic two-body loss. Phys. Rev. A 99, 031601 (2019).

    Article  ADS  Google Scholar 

  189. Dürr, S. et al. Lieb–Liniger model of a dissipation-induced Tonks–Girardeau gas. Phys. Rev. A 79, 023614 (2009).

    Article  ADS  Google Scholar 

  190. Ramos, T., Pichler, H., Daley, A. J. & Zoller, P. Quantum spin dimers from chiral dissipation in cold-atom chains. Phys. Rev. Lett. 113, 237203 (2014).

    Article  ADS  Google Scholar 

  191. Bañuls, M. C. et al. Simulating lattice gauge theories within quantum technologies. Eur. Phys. J. D 74, 165 (2020).

    Article  ADS  Google Scholar 

  192. Stannigel, K. et al. Constrained dynamics via the Zeno effect in quantum simulation: implementing non-Abelian lattice gauge theories with cold atoms. Phys. Rev. Lett. 112, 120406 (2014).

    Article  ADS  Google Scholar 

  193. Caballar, R. C. F., Diehl, S., Mäkelä, H., Oberthaler, M. & Watanabe, G. Dissipative preparation of phase- and number-squeezed states with ultracold atoms. Phys. Rev. A 89, 013620 (2014).

    Article  ADS  Google Scholar 

  194. Carusotto, I. et al. Photonic materials in circuit quantum electrodynamics. Nat. Phys. 16, 268–279 (2020).

    Article  Google Scholar 

  195. Schmitt, J. et al. Observation of grand-canonical number statistics in a photon Bose–Einstein condensate. Phys. Rev. Lett. 112, 030401 (2014).

    Article  ADS  Google Scholar 

  196. Hafezi, M., Adhikari, P. & Taylor, J. M. Chemical potential for light by parametric coupling. Phys. Rev. B 92, 174305 (2015).

    Article  ADS  Google Scholar 

  197. Verstraete, F., Wolf, M. M. & Cirac, I. J. Quantum computation and quantum-state engineering driven by dissipation. Nat. Phys. 5, 633–636 (2009).

    Article  Google Scholar 

  198. Jaschke, D., Montangero, S. & Carr, L. D. One-dimensional many-body entangled open quantum systems with tensor network methods. Quantum Sci. Technol. 4, 013001 (2018).

    Article  ADS  Google Scholar 

  199. Yanay, Y. & Clerk, A. A. Reservoir engineering of bosonic lattices using chiral symmetry and localized dissipation. Phys. Rev. A 98, 043615 (2018).

    Article  ADS  Google Scholar 

  200. Diehl, S. et al. Quantum states and phases in driven open quantum systems with cold atoms. Nat. Phys. 4, 878–883 (2008).

    Article  Google Scholar 

  201. Diehl, S., Rico, E., Baranov, M. A. & Zoller, P. Topology by dissipation in atomic quantum wires. Nat. Phys. 7, 971–977 (2011).

    Article  Google Scholar 

  202. Cian, Z.-P. et al. Photon pair condensation by engineered dissipation. Phys. Rev. Lett. 123, 063602 (2019).

    Article  ADS  Google Scholar 

  203. Bardyn, C.-E. et al. Topology by dissipation. New J. Phys. 15, 085001 (2013).

    Article  ADS  MATH  Google Scholar 

  204. Shavit, G. & Goldstein, M. Topology by dissipation: transport properties. Phys. Rev. B 101, 125412 (2020).

    Article  ADS  Google Scholar 

  205. Goldstein, M. Dissipation-induced topological insulators: a no-go theorem and a recipe. SciPost Phys. 7, 67 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  206. Iemini, F., Rossini, D., Fazio, R., Diehl, S. & Mazza, L. Dissipative topological superconductors in number-conserving systems. Phys. Rev. B 93, 115113 (2016).

    Article  ADS  Google Scholar 

  207. Dangel, F., Wagner, M., Cartarius, H., Main, J. & Wunner, G. Topological invariants in dissipative extensions of the Su–Schrieffer–Heeger model. Phys. Rev. A 98, 013628 (2018).

    Article  ADS  Google Scholar 

  208. Barbarino, S., Yu, J., Zoller, P. & Budich, J. C. Preparing atomic topological quantum matter by adiabatic nonunitary dynamics. Phys. Rev. Lett. 124, 010401 (2020).

    Article  ADS  Google Scholar 

  209. Kitaev, A. & Laumann, C. Topological phases and quantum computation. In Exact Methods in Low-dimensional Statistical Physics and Quantum Computing. Lecture Notes of the Les Houches Summer School Vol. 89 (eds Jacobsen, J. et al.) 101–125 (Oxford Univ. Press, 2010).

  210. Pincus, M. A Monte Carlo method for the approximate solution of certain types of constrained optimization problems. Oper. Res. 18, 1225–1228 (1970).

    Article  MathSciNet  MATH  Google Scholar 

  211. Bishop, C. Pattern Recognition and Machine Learning (Springer, 2006).

  212. Chen, D., Meldgin, C. & DeMarco, B. Bath-induced band decay of a Hubbard lattice gas. Phys. Rev. A 90, 013602 (2014).

    Article  ADS  Google Scholar 

  213. Lena, R. G. & Daley, A. J. Dissipative dynamics and cooling rates of trapped impurity atoms immersed in a reservoir gas. Phys. Rev. A 101, 033612 (2020).

    Article  ADS  MathSciNet  Google Scholar 

  214. McKay, D. C., Meldgin, C., Chen, D. & DeMarco, B. Slow thermalization between a lattice and free Bose gas. Phys. Rev. Lett. 111, 063002 (2013).

    Article  ADS  Google Scholar 

  215. Shabani, A. & Neven, H. Artificial quantum thermal bath: engineering temperature for a many-body quantum system. Phys. Rev. A 94, 052301 (2016).

    Article  ADS  Google Scholar 

  216. Metcalf, M., Moussa, J. E., de Jong, W. A. & Sarovar, M. Engineered thermalization and cooling of quantum many-body systems. Phys. Rev. Res. 2, 023214 (2020).

    Article  Google Scholar 

  217. Su, H.-Y. & Li, Y. Quantum algorithm for the simulation of open-system dynamics and thermalization. Phys. Rev. A 101, 012328 (2020).

    Article  ADS  Google Scholar 

  218. Schönleber, D. W., Bentley, C. D. B. & Eisfeld, A. Engineering thermal reservoirs for ultracold dipole–dipole-interacting Rydberg atoms. New J. Phys. 20, 013011 (2018).

    Article  ADS  Google Scholar 

  219. Dive, B., Mintert, F. & Burgarth, D. Quantum simulations of dissipative dynamics: time dependence instead of size. Phys. Rev. A 92, 032111 (2015).

    Article  ADS  Google Scholar 

  220. Griessner, A., Daley, A. J., Clark, S. R., Jaksch, D. & Zoller, P. Dissipative dynamics of atomic Hubbard models coupled to a phonon bath: dark state cooling of atoms within a Bloch band of an optical lattice. New J. Phys. 9, 44–44 (2007).

    Article  ADS  Google Scholar 

  221. Yanay, Y. & Clerk, A. A. Reservoir engineering with localized dissipation: dynamics and prethermalization. Phys. Rev. Res. 2, 023177 (2020).

    Article  Google Scholar 

  222. Liu, Y.-C., Hu, Y.-W., Wong, C. W. & Xiao, Y.-F. Review of cavity optomechanical cooling. Chin. Phys. B 22, 114213 (2013).

    Article  ADS  Google Scholar 

  223. Letokhov, V. S., Ol’shanii, M. A. & Ovchinnikov, Y. B. Laser cooling of atoms: a review. Quantum Semiclass. Opt. 7, 5–40 (1995).

    Article  ADS  Google Scholar 

  224. Marquardt, F., Clerk, A. & Girvin, S. Quantum theory of optomechanical cooling. J. Mod. Opt. 55, 3329–3338 (2008).

    Article  ADS  MATH  Google Scholar 

  225. McKay, D. C. & DeMarco, B. Cooling in strongly correlated optical lattices: prospects and challenges. Rep. Progr. Phys. 74, 054401 (2011).

    Article  ADS  Google Scholar 

  226. Guo, J., Norte, R. & Gröblacher, S. Feedback cooling of a room temperature mechanical oscillator close to its motional ground state. Phys. Rev. Lett. 123, 223602 (2019).

    Article  ADS  Google Scholar 

  227. Shen, C. et al. Quantum channel construction with circuit quantum electrodynamics. Phys. Rev. B 95, 134501 (2017).

    Article  ADS  Google Scholar 

  228. Di Candia, R., Pedernales, J. S., del Campo, A., Solano, E. & Casanova, J. Quantum simulation of dissipative processes without reservoir engineering. Sci. Rep. 5, 9981 (2015).

    Article  Google Scholar 

  229. Chenu, A., Beau, M., Cao, J. & del Campo, A. Quantum simulation of generic many-body open system dynamics using classical noise. Phys. Rev. Lett. 118, 140403 (2017).

    Article  ADS  Google Scholar 

  230. Sweke, R., Sinayskiy, I., Bernard, D. & Petruccione, F. Universal simulation of Markovian open quantum systems. Phys. Rev. A 91, 062308 (2015).

    Article  ADS  Google Scholar 

  231. Zanardi, P., Marshall, J. & Campos Venuti, L. Dissipative universal Lindbladian simulation. Phys. Rev. A 93, 022312 (2016).

    Article  ADS  Google Scholar 

  232. Carmele, A., Knorr, A. & Milde, F. Stabilization of photon collapse and revival dynamics by a non-Markovian phonon bath. New J. Phys. 15, 105024 (2013).

    Article  ADS  Google Scholar 

  233. Lebreuilly, J. et al. Stabilizing strongly correlated photon fluids with non-Markovian reservoirs. Phys. Rev. A 96, 033828 (2017).

    Article  ADS  Google Scholar 

  234. Cai, Z., Schollwöck, U. & Pollet, L. Identifying a bath-induced Bose liquid in interacting spin-boson models. Phys. Rev. Lett. 113, 260403 (2014).

    Article  ADS  Google Scholar 

  235. Maghrebi, M. F. & Gorshkov, A. V. Nonequilibrium many-body steady states via Keldysh formalism. Phys. Rev. B 93, 014307 (2016).

    Article  ADS  Google Scholar 

  236. Hurst, H. M., Guo, S. & Spielman, I. B. Feedback induced magnetic phases in binary Bose–Einstein condensates. Phys. Rev. Research 2, 043325 (2020).

    Article  ADS  Google Scholar 

  237. Tomita, T., Nakajima, S., Danshita, I., Takasu, Y. & Takahashi, Y. Observation of the Mott insulator to superfluid crossover of a driven-dissipative Bose–Hubbard system. Sci. Adv. https://advances.sciencemag.org/content/3/12/e1701513 (2017).

  238. Rylands, C., Guo, Y., Lev, B. L., Keeling, J. & Galitski, V. Photon-mediated Peierls transition of a 1D gas in a multimode optical cavity. Phys. Rev. Lett. 125, 010404 (2020).

    Article  ADS  Google Scholar 

  239. Sieberer, L. M., Huber, S. D., Altman, E. & Diehl, S. Dynamical critical phenomena in driven-dissipative systems. Phys. Rev. Lett. 110, 195301 (2013).

    Article  ADS  Google Scholar 

  240. Essink, S., Wolff, S., Schütz, G. M., Kollath, C. & Popkov, V. Transition between dissipatively stabilized helical states. Phys. Rev. Res. 2, 022007 (2020).

    Article  Google Scholar 

  241. Scarlatella, O., Fazio, R. & Schiró, M. Emergent finite frequency criticality of driven-dissipative correlated lattice bosons. Phys. Rev. B 99, 064511 (2019).

    Article  ADS  Google Scholar 

  242. Mathey, S. & Diehl, S. Absence of criticality in the phase transitions of open Floquet systems. Phys. Rev. Lett. 122, 110602 (2019).

    Article  ADS  Google Scholar 

  243. Brennecke, F. et al. Real-time observation of fluctuations at the driven-dissipative Dicke phase transition. Proc. Natl Acad. Sci. USA 110, 11763–11767 (2013).

    Article  ADS  Google Scholar 

  244. Foss-Feig, M. et al. Emergent equilibrium in many-body optical bistability. Phys. Rev. A 95, 043826 (2017).

    Article  ADS  Google Scholar 

  245. Fitzpatrick, M., Sundaresan, N. M., Li, A. C. Y., Koch, J. & Houck, A. A. Observation of a dissipative phase transition in a one-dimensional circuit QED lattice. Phys. Rev. X 7, 011016 (2017).

    Google Scholar 

  246. Else, D. V., Monroe, C., Nayak, C. & Yao, N. Y. Discrete time crystals. Annu. Rev. Condens. Matter Phys. 11, 467–499 (2020).

    Article  ADS  Google Scholar 

  247. Sacha, K. & Zakrzewski, J. Time crystals: a review. Rep. Progr. Phys. 81, 016401 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  248. Riera-Campeny, A., Moreno-Cardoner, M. & Sanpera, A. Time crystallinity in open quantum systems. Quantum 4, 270 (2020).

    Article  Google Scholar 

  249. BuČa, B., Tindall, J. & Jaksch, D. Non-stationary coherent quantum many-body dynamics through dissipation. Nat. Commun. 10, 1730 (2019).

    Article  ADS  Google Scholar 

  250. Marais, A. et al. The future of quantum biology. J. R. Soc. Interface 15, 20180640 (2018).

    Article  Google Scholar 

  251. Fujii, K. & Nakajima, K. Harnessing disordered-ensemble quantum dynamics for machine learning. Phys. Rev. Appl. 8, 024030 (2017).

    Article  ADS  Google Scholar 

  252. Angelatos, G., Khan, S. A. & Türeci, H. E. Reservoir computing approach to quantum state measurement. Phys. Rev. X 11, 041062 (2021).

    Google Scholar 

  253. Carroll, T. L. Optimizing memory in reservoir computers. Chaos 32, 023123 (2022).

    Article  ADS  MathSciNet  Google Scholar 

  254. Koch, J. et al. Charge-insensitive qubit design derived from the Cooper pair box. Phys. Rev. A 76, 042319 (2007).

    Article  ADS  Google Scholar 

  255. Manucharyan, V. E., Koch, J., Glazman, L. I. & Devoret, M. H. Fluxonium: single Cooper-pair circuit free of charge offsets. Science 326, 113–116 (2009).

    Article  ADS  Google Scholar 

  256. Gyenis, A. et al. Moving beyond the transmon: noise-protected superconducting quantum circuits. PRX Quantum 2, 030101 (2021).

    Article  ADS  Google Scholar 

  257. Deffner, S. & Campbell, S. Quantum Thermodynamics, 2053–2571 (Morgan & Claypool, 2019); https://doi.org/10.1088/2053-2571/ab21c6

  258. Vinjanampathy, S. & Anders, J. Quantum thermodynamics. Contemp. Phys. 57, 545–579 (2016).

    Article  ADS  Google Scholar 

  259. Polkovnikov, A., Sengupta, K., Silva, A. & Vengalattore, M. Colloquium: nonequilibrium dynamics of closed interacting quantum systems. Rev. Mod. Phys. 83, 863–883 (2011).

    Article  ADS  Google Scholar 

  260. Maldacena, J., Shenker, S. H. & Stanford, D. A bound on chaos. J. High Energy Phys. 2016, 106 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  261. Nahum, A., Vijay, S. & Haah, J. Operator spreading in random unitary circuits. Phys. Rev. X 8, 021014 (2018).

    Google Scholar 

  262. Li, Y. & Fisher, M. P. A. Statistical mechanics of quantum error correcting codes. Phys. Rev. B 103, 104306 (2021).

    Article  ADS  Google Scholar 

  263. D’Alessio, L., Kafri, Y., Polkovnikov, A. & Rigol, M. From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Adv. Phys. 65, 239–362 (2016).

    Article  ADS  Google Scholar 

  264. Luitz, D. J. & Bar Lev, Y. Information propagation in isolated quantum systems. Phys. Rev. B 96, 020406 (2017).

    Article  ADS  Google Scholar 

  265. Chan, A., Nandkishore, R. M., Pretko, M. & Smith, G. Unitary-projective entanglement dynamics. Phys. Rev. B 99, 224307 (2019).

    Article  ADS  Google Scholar 

  266. Li, Y., Chen, X. & Fisher, M. P. A. Measurement-driven entanglement transition in hybrid quantum circuits. Phys. Rev. B 100, 134306 (2019).

    Article  ADS  Google Scholar 

  267. Skinner, B., Ruhman, J. & Nahum, A. Measurement-induced phase transitions in the dynamics of entanglement. Phys. Rev. X 9, 031009 (2019).

    Google Scholar 

  268. Ippoliti, M., Gullans, M. J., Gopalakrishnan, S., Huse, D. A. & Khemani, V. Entanglement phase transitions in measurement-only dynamics. Phys. Rev. X 11, 011030 (2021).

    Google Scholar 

  269. Marino, J. Universality class of Ising critical states with long-range losses. Preprint at https://arxiv.org/abs/2108.12422 (2021).

  270. Deutsch, J. M. Quantum statistical mechanics in a closed system. Phys. Rev. A 43, 2046–2049 (1991).

    Article  ADS  Google Scholar 

  271. Nandkishore, R. & Huse, D. A. Many-body localization and thermalization in quantum statistical mechanics. Annu. Rev. Condens. Matter Phys. 6, 15–38 (2015).

    Article  ADS  Google Scholar 

  272. Abanin, D. A., Altman, E., Bloch, I. & Serbyn, M. Colloquium: Many-body localization, thermalization, and entanglement. Rev. Mod. Phys. 91, 021001 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  273. Khemani, V., Vishwanath, A. & Huse, D. A. Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws. Phys. Rev. X 8, 031057 (2018).

    Google Scholar 

  274. Valdez, M. A., Jaschke, D., Vargas, D. L. & Carr, L. D. Quantifying complexity in quantum phase transitions via mutual information complex networks. Phys. Rev. Lett. 119, 225301 (2017).

    Article  ADS  Google Scholar 

  275. Walschaers, M., Treps, N., Sundar, B., Carr, L. D. & Parigi, V. Emergent complex quantum networks in continuous-variables non-Gaussian states. Preprint at https://arxiv.org/abs/2012.15608 (2021).

  276. Zwolak, M. & Vidal, G. Mixed-state dynamics in one-dimensional quantum lattice systems: a time-dependent superoperator renormalization algorithm. Phys. Rev. Lett. 93, 207205 (2004).

    Article  ADS  Google Scholar 

  277. Cui, J., Cirac, J. I. & Bañuls, M. C. Variational matrix product operators for the steady state of dissipative quantum systems. Phys. Rev. Lett. 114, 220601 (2015).

    Article  ADS  Google Scholar 

  278. Nagy, A. & Savona, V. Variational quantum Monte Carlo method with a neural-network ansatz for open quantum systems. Phys. Rev. Lett. 122, 250501 (2019).

    Article  ADS  MathSciNet  Google Scholar 

  279. Hartmann, M. J. & Carleo, G. Neural-network approach to dissipative quantum many-body dynamics. Phys. Rev. Lett. 122, 250502 (2019).

    Article  ADS  Google Scholar 

  280. Vicentini, F., Biella, A., Regnault, N. & Ciuti, C. Variational neural-network ansatz for steady states in open quantum systems. Phys. Rev. Lett. 122, 250503 (2019).

    Article  ADS  Google Scholar 

  281. Yoshioka, N. & Hamazaki, R. Constructing neural stationary states for open quantum many-body systems. Phys. Rev. B 99, 214306 (2019).

    Article  ADS  Google Scholar 

  282. Liu, Z., Duan, L.-M. & Deng, D.-L. Solving quantum master equations with deep quantum neural networks. Phys. Rev. Res. 4, 013097 (2022).

    Article  Google Scholar 

  283. de Vega, I. & Alonso, D. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  284. Vacchini, B. Frontiers of Open Quantum System Dynamics, 71–85 (Springer, 2019); https://doi.org/10.1007/978-3-030-06122-7_4

  285. Braunstein, S. L. & Caves, C. M. Statistical distance and the geometry of quantum states. Phys. Rev. Lett. 72, 3439–3443 (1994).

    Article  ADS  MathSciNet  MATH  Google Scholar 

  286. Wootters, W. K. Statistical distance and Hilbert space. Phys. Rev. D 23, 357–362 (1981).

    Article  ADS  MathSciNet  Google Scholar 

  287. Breuer, H.-P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford Univ. Press, 2007).

  288. Naghiloo, M., Abbasi, M., Joglekar, Y. N. & Murch, K. W. Quantum state tomography across the exceptional point in a single dissipative qubit. Nat. Phys. 15, 1232–1236 (2019).

    Article  Google Scholar 

  289. El-Ganainy, R. et al. Non-Hermitian physics and PT symmetry. Nat. Phys. 14, 11–19 (2018).

    Article  Google Scholar 

  290. Kraus, K., Böhm, A., Dollard, J. D. & Wootters, W. H. States, Effects, and Operations: Fundamental Notions of Quantum Theory (Springer, 1983).

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Acknowledgements

We thank M. Hays, P. McMahon, A. Di Paulo and Y. Yanay for critical comments. This research was supported by an appointment to the Intelligence Community Postdoctoral Research Fellowship Program at MIT, administered by Oak Ridge Institute for Science and Education through an interagency agreement between the US Department of Energy and the Office of the Director of National Intelligence. This material is based upon work supported by the National Science Foundation under grant no. PHY-2110250, no. PHY-1752844 (CAREER), and a New Frontier Grant awarded by the College of Arts and Sciences at Cornell.

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  1. Research Laboratory of Electronics, Massachusetts Institute of Technology, Cambridge, MA, USA

    Patrick M. Harrington

  2. Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, NY, USA

    Erich J. Mueller

  3. Department of Physics, Washington University, St. Louis, MO, USA

    Kater W. Murch

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Harrington, P.M., Mueller, E.J. & Murch, K.W. Engineered dissipation for quantum information science. Nat Rev Phys 4, 660–671 (2022). https://doi.org/10.1038/s42254-022-00494-8

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