{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T03:50:21Z","timestamp":1777002621752,"version":"3.51.4"},"reference-count":115,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T00:00:00Z","timestamp":1756425600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"Building upon recent progress in Lindblad engineering for quantum Gibbs state preparation algorithms, we propose a simplified protocol that is shown to be efficient under the eigenstate thermalization hypothesis (ETH). The ETH reduces circuit overheads of the Lindblad simulation algorithm and ensures a fast convergence toward the target Gibbs state. Moreover, we show that the realized Lindblad dynamics exhibits an inherent resilience against stochastic noise, opening up the path to a first demonstration on quantum computers. We complement our claims with numerical studies of the algorithm&apos;s convergence in various regimes of the mixed-field Ising model. In line with our predictions, we observe a mixing time scaling polynomially with system size when the ETH is satisfied. In addition, we assess the impact of algorithmic and hardware-induced errors on the algorithm&apos;s performance by carrying out quantum circuit simulations of our Lindblad simulation protocol with a local depolarizing noise model. This work bridges the gap between recent theoretical advances in dissipative Gibbs state preparation algorithms and their eventual quantum hardware implementation.<\/jats:p>","DOI":"10.22331\/q-2025-08-29-1843","type":"journal-article","created":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T08:57:41Z","timestamp":1756457861000},"page":"1843","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Lindblad engineering for quantum Gibbs state preparation under the eigenstate thermalization hypothesis"],"prefix":"10.22331","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7631-6528","authenticated-orcid":false,"given":"Eric","family":"Brunner","sequence":"first","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6501-5420","authenticated-orcid":false,"given":"Luuk","family":"Coopmans","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3373-0128","authenticated-orcid":false,"given":"Gabriel","family":"Matos","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"},{"name":"Quantinuum, 17 Beaumont St., Oxford OX1 2NA, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1605-9141","authenticated-orcid":false,"given":"Matthias","family":"Rosenkranz","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3363-5929","authenticated-orcid":false,"given":"Frederic","family":"Sauvage","sequence":"additional","affiliation":[{"name":"Quantinuum, Partnership House, Carlisle Place, London SW1P 1BX, United Kingdom"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1802-5260","authenticated-orcid":false,"given":"Yuta","family":"Kikuchi","sequence":"additional","affiliation":[{"name":"Quantinuum K.K., Otemachi Financial City Grand Cube 3F, 1-9-2 Otemachi, Chiyoda-ku, Tokyo, Japan"},{"name":"Interdisciplinary Theoretical and Mathematical Sciences Program (iTHEMS), RIKEN, Wako, Saitama 351-0198, Japan"}]}],"member":"9598","published-online":{"date-parts":[[2025,8,29]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, Andr\u00e1s Gily\u00e9n, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, and Fernando G. S. L. Brand\u00e3o. ``Quantum Algorithms: A Survey of Applications and End-to-end Complexities''. Cambridge University Press. Cambridge, UK (2025). arXiv:2310.03011.","DOI":"10.1017\/9781009639651"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Amira Abbas, Andris Ambainis, Brandon Augustino, Andreas B\u00e4rtschi, Harry Buhrman, Carleton Coffrin, Giorgio Cortiana, Vedran Dunjko, Daniel J. Egger, Bruce G. Elmegreen, Nicola Franco, Filippo Fratini, Bryce Fuller, Julien Gacon, Constantin Gonciulea, Sander Gribling, Swati Gupta, Stuart Hadfield, Raoul Heese, Gerhard Kircher, Thomas Kleinert, Thorsten Koch, Georgios Korpas, Steve Lenk, Jakub Marecek, Vanio Markov, Guglielmo Mazzola, Stefano Mensa, Naeimeh Mohseni, Giacomo Nannicini, Corey O'Meara, Elena Pe\u00f1a Tapia, Sebastian Pokutta, Manuel Proissl, Patrick Rebentrost, Emre Sahin, Benjamin C. B. Symons, Sabine Tornow, V\u00edctor Valls, Stefan Woerner, Mira L. Wolf-Bauwens, Jon Yard, Sheir Yarkoni, Dirk Zechiel, Sergiy Zhuk, and Christa Zoufal. ``Challenges and opportunities in quantum optimization''. Nat. Rev. Phys. 6, 718\u2013735 (2024).","DOI":"10.1038\/s42254-024-00770-9"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Barbara M. Terhal and David P. DiVincenzo. ``Problem of equilibration and the computation of correlation functions on a quantum computer''. Phys. Rev. A 61, 022301 (2000).","DOI":"10.1103\/PhysRevA.61.022301"},{"key":"3","doi-asserted-by":"publisher","unstructured":"David Poulin and Pawel Wocjan. ``Sampling from the Thermal Quantum Gibbs State and Evaluating Partition Functions with a Quantum Computer''. Phys. Rev. Lett. 103, 220502 (2009).","DOI":"10.1103\/PhysRevLett.103.220502"},{"key":"4","doi-asserted-by":"publisher","unstructured":"K. Temme, T. J. Osborne, K. G. Vollbrecht, D. Poulin, and F. Verstraete. ``Quantum Metropolis Sampling''. Nature 471, 87 (2011).","DOI":"10.1038\/nature09770"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Ersen Bilgin and Sergio Boixo. ``Preparing thermal states of quantum systems by dimension reduction''. Phys. Rev. Lett. 105, 170405 (2010).","DOI":"10.1103\/PhysRevLett.105.170405"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Man-Hong Yung and Al\u00e1n Aspuru-Guzik. ``A quantum\u2013quantum Metropolis algorithm''. Proc. Natl. Acad. Sci. U.S.A. 109, 754\u2013759 (2012).","DOI":"10.1073\/pnas.1111758109"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Michael J. Kastoryano and Fernando G. S. L. Brand\u00e3o. ``Quantum Gibbs Samplers: The Commuting Case''. Commun. Math. Phys. 344, 915\u2013957 (2016).","DOI":"10.1007\/s00220-016-2641-8"},{"key":"8","doi-asserted-by":"publisher","unstructured":"Fernando G. S. L. Brand\u00e3o and Michael J. Kastoryano. ``Finite Correlation Length Implies Efficient Preparation of Quantum Thermal States''. Commun. Math. Phys. 365, 1\u201316 (2019).","DOI":"10.1007\/s00220-018-3150-8"},{"key":"9","doi-asserted-by":"publisher","unstructured":"Anirban Narayan Chowdhury and Rolando D. Somma. ``Quantum algorithms for Gibbs sampling and hitting-time estimation''. Quant. Inf. Comput. 17, 0041\u20130064 (2017).","DOI":"10.26421\/QIC17.1-2-3"},{"key":"10","doi-asserted-by":"publisher","unstructured":"Mario Motta, Chong Sun, Adrian Teck Keng Tan, Matthew J. O' Rourke, Erika Ye, Austin J. Minnich, Fernando G. S. L. Brand\u00e3o, and Garnet Kin-Lic Chan. ``Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution''. Nat. Phys. 16, 205\u2013210 (2019).","DOI":"10.1038\/s41567-019-0704-4"},{"key":"11","doi-asserted-by":"publisher","unstructured":"Andr\u00e1s Gily\u00e9n, Yuan Su, Guang Hao Low, and Nathan Wiebe. ``Quantum singular value transformation and beyond: exponential improvements for quantum matrix arithmetics''. In Proceedings of the 51st Annual ACM SIGACT Symposium on Theory of Computing. Pages 193\u2013204. New York, NY, USA (2019). Association for Computing Machinery.","DOI":"10.1145\/3313276.3316366"},{"key":"12","doi-asserted-by":"publisher","unstructured":"Sirui Lu, Mari Carmen Ba\u00f1uls, and J. Ignacio Cirac. ``Algorithms for Quantum Simulation at Finite Energies''. PRX Quantum 2, 020321 (2021).","DOI":"10.1103\/PRXQuantum.2.020321"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Luuk Coopmans, Yuta Kikuchi, and Marcello Benedetti. ``Predicting Gibbs-State Expectation Values with Pure Thermal Shadows''. PRX Quantum 4, 010305 (2023).","DOI":"10.1103\/PRXQuantum.4.010305"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Zoe Holmes, Gopikrishnan Muraleedharan, Rolando D. Somma, Yigit Subasi, and Burak \u015eahino\u011flu. ``Quantum algorithms from fluctuation theorems: Thermal-state preparation''. Quantum 6, 825 (2022).","DOI":"10.22331\/q-2022-10-06-825"},{"key":"15","unstructured":"Daniel Zhang, Jan Lukas Bosse, and Toby Cubitt. ``Dissipative Quantum Gibbs Sampling'' (2023). arXiv:2304.04526."},{"key":"16","doi-asserted-by":"publisher","unstructured":"Alexander Schuckert, Annabelle Bohrdt, Eleanor Crane, and Michael Knap. ``Probing finite-temperature observables in quantum simulators of spin systems with short-time dynamics''. Phys. Rev. B 107, L140410 (2023).","DOI":"10.1103\/PhysRevB.107.L140410"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Khaldoon Ghanem, Alexander Schuckert, and Henrik Dreyer. ``Robust Extraction of Thermal Observables from State Sampling and Real-Time Dynamics on Quantum Computers''. Quantum 7, 1163 (2023).","DOI":"10.22331\/q-2023-11-03-1163"},{"key":"18","doi-asserted-by":"publisher","unstructured":"K\u00e9vin H\u00e9mery, Khaldoon Ghanem, Eleanor Crane, Sara L. Campbell, Joan M. Dreiling, Caroline Figgatt, Cameron Foltz, John P. Gaebler, Jacob Johansen, Michael Mills, Steven A. Moses, Juan M. Pino, Anthony Ransford, Mary Rowe, Peter Siegfried, Russell P. Stutz, Henrik Dreyer, Alexander Schuckert, and Ramil Nigmatullin. ``Measuring the Loschmidt Amplitude for Finite-Energy Properties of the Fermi-Hubbard Model on an Ion-Trap Quantum Computer''. PRX Quantum 5, 030323 (2024).","DOI":"10.1103\/PRXQuantum.5.030323"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller, and Edward Teller. ``Equation of State Calculations by Fast Computing Machines''. J. Chem. Phys. 21, 1087\u20131092 (1953).","DOI":"10.1063\/1.1699114"},{"key":"20","doi-asserted-by":"publisher","unstructured":"W. K. Hastings. ``Monte Carlo Sampling Methods Using Markov Chains and Their Applications''. Biometrika 57, 97\u2013109 (1970).","DOI":"10.2307\/2334940"},{"key":"21","unstructured":"Jonathan E. Moussa. ``Low-Depth Quantum Metropolis Algorithm'' (2019). arXiv:1903.01451."},{"key":"22","unstructured":"Jiaqing Jiang and Sandy Irani. ``Quantum Metropolis Sampling via Weak Measurement'' (2024). arXiv:2406.16023."},{"key":"23","doi-asserted-by":"publisher","unstructured":"Seth Lloyd. ``Universal quantum simulators''. Science 273, 1073\u20131078 (1996).","DOI":"10.1126\/science.273.5278.1073"},{"key":"24","doi-asserted-by":"publisher","unstructured":"Goran Lindblad. ``On the Generators of Quantum Dynamical Semigroups''. Commun. Math. Phys. 48, 119 (1976).","DOI":"10.1007\/BF01608499"},{"key":"25","doi-asserted-by":"publisher","unstructured":"M. Kliesch, T. Barthel, C. Gogolin, M. Kastoryano, and J. Eisert. ``Dissipative quantum church-turing theorem''. Phys. Rev. Lett. 107, 120501 (2011).","DOI":"10.1103\/PhysRevLett.107.120501"},{"key":"26","doi-asserted-by":"publisher","unstructured":"Andrew M. Childs and Tongyang Li. ``Efficient simulation of sparse Markovian quantum dynamics''. Quant. Inf. Comput. 17, 0901\u20130947 (2017).","DOI":"10.26421\/QIC17.11-12-1"},{"key":"27","unstructured":"Richard Cleve and Chunhao Wang. ``Efficient Quantum Algorithms for Simulating Lindblad Evolution'' (2019). arXiv:1612.09512."},{"key":"28","doi-asserted-by":"publisher","unstructured":"Pawel Wocjan and Kristan Temme. ``Szegedy Walk Unitaries for Quantum Maps''. Commun. Math. Phys. 402, 3201\u20133231 (2023).","DOI":"10.1007\/s00220-023-04797-4"},{"key":"29","unstructured":"Oles Shtanko and Ramis Movassagh. ``Preparing thermal states on noiseless and noisy programmable quantum processors'' (2021). arXiv:2112.14688."},{"key":"30","doi-asserted-by":"publisher","unstructured":"Patrick Rall, Chunhao Wang, and Pawel Wocjan. ``Thermal State Preparation via Rounding Promises''. Quantum 7, 1132 (2023).","DOI":"10.22331\/q-2023-10-10-1132"},{"key":"31","unstructured":"Chi-Fang Chen, Michael J. Kastoryano, Fernando G. S. L. Brand\u00e3o, and Andr\u00e1s Gily\u00e9n. ``Quantum Thermal State Preparation'' (2023). arXiv:2303.18224."},{"key":"32","unstructured":"Chi-Fang Chen, Michael J. Kastoryano, and Andr\u00e1s Gily\u00e9n. ``An efficient and exact noncommutative quantum Gibbs sampler'' (2023). arXiv:2311.09207."},{"key":"33","doi-asserted-by":"publisher","unstructured":"Zhiyan Ding, Chi-Fang Chen, and Lin Lin. ``Single-ancilla ground state preparation via Lindbladians''. Phys. Rev. Research 6, 033147 (2024).","DOI":"10.1103\/PhysRevResearch.6.033147"},{"key":"34","doi-asserted-by":"publisher","unstructured":"Zhiyan Ding, Bowen Li, and Lin Lin. ``Efficient quantum Gibbs samplers with Kubo\u2013Martin\u2013Schwinger detailed balance condition''. Commun. Math. Phys. 406, 67 (2025). arXiv:2404.05998.","DOI":"10.1007\/s00220-025-05235-3"},{"key":"35","doi-asserted-by":"publisher","unstructured":"Zhiyan Ding, Xiantao Li, and Lin Lin. ``Simulating Open Quantum Systems Using Hamiltonian Simulations''. PRX Quantum 5, 020332 (2024).","DOI":"10.1103\/PRXQuantum.5.020332"},{"key":"36","unstructured":"Andr\u00e1s Gily\u00e9n, Chi-Fang Chen, Joao F. Doriguello, and Michael J. Kastoryano. ``Quantum generalizations of Glauber and Metropolis dynamics'' (2024). arXiv:2405.20322."},{"key":"37","unstructured":"Hongrui Chen, Bowen Li, Jianfeng Lu, and Lexing Ying. ``A Randomized Method for Simulating Lindblad Equations and Thermal State Preparation'' (2025). arXiv:2407.06594v3."},{"key":"38","doi-asserted-by":"publisher","unstructured":"Frank Verstraete, Michael M. Wolf, and J. Ignacio Cirac. ``Quantum computation and quantum-state engineering driven by dissipation''. Nat. Phys. 5, 633\u2013636 (2009).","DOI":"10.1038\/nphys1342"},{"key":"39","doi-asserted-by":"publisher","unstructured":"B. Kraus, H. P. B\u00fcchler, S. Diehl, A. Kantian, A. Micheli, and P. Zoller. ``Preparation of entangled states by quantum Markov processes''. Phys. Rev. A 78, 042307 (2008).","DOI":"10.1103\/PhysRevA.78.042307"},{"key":"40","doi-asserted-by":"publisher","unstructured":"Patrick M. Harrington, Erich J. Mueller, and Kater W. Murch. ``Engineered dissipation for quantum information science''. Nat. Rev. Phys. 4, 660\u2013671 (2022).","DOI":"10.1038\/s42254-022-00494-8"},{"key":"41","doi-asserted-by":"publisher","unstructured":"Sergey Bravyi, Anirban Chowdhury, David Gosset, and Pawel Wocjan. ``Quantum Hamiltonian complexity in thermal equilibrium''. Nat. Phys. 18, 1367\u20131370 (2022).","DOI":"10.1038\/s41567-022-01742-5"},{"key":"42","doi-asserted-by":"crossref","unstructured":"Cambyse Rouz\u00e9, Daniel Stilck Fran\u00e7a, and \u00c1lvaro M. Alhambra. ``Efficient thermalization and universal quantum computing with quantum Gibbs samplers'' (2024). arXiv:2403.12691.","DOI":"10.1145\/3717823.3718268"},{"key":"43","doi-asserted-by":"publisher","unstructured":"Thiago Bergamaschi, Chi-Fang Chen, and Yunchao Liu. ``Quantum Computational Advantage with Constant-Temperature Gibbs Sampling''. In 2024 IEEE 65th Annual Symposium on Foundations of Computer Science (FOCS). Pages 1063\u20131085. (2024).","DOI":"10.1109\/FOCS61266.2024.00071"},{"key":"44","unstructured":"Joel Rajakumar and James D. Watson. ``Gibbs Sampling gives Quantum Advantage at Constant Temperatures with $O(1)$-Local Hamiltonians'' (2024). arXiv:2408.01516."},{"key":"45","doi-asserted-by":"publisher","unstructured":"Mark Srednicki. ``Chaos and Quantum Thermalization''. Phys. Rev. E 50, 888 (1994).","DOI":"10.1103\/PhysRevE.50.888"},{"key":"46","doi-asserted-by":"publisher","unstructured":"Mark Srednicki. ``Thermal fluctuations in quantized chaotic systems''. J. Phys. A: Math. Gen. 29, L75\u2013L79 (1996).","DOI":"10.1088\/0305-4470\/29\/4\/003"},{"key":"47","doi-asserted-by":"publisher","unstructured":"Mark Srednicki. ``The approach to thermal equilibrium in quantized chaotic systems''. J. Phys. A: Math. Gen. 32, 1163 (1999).","DOI":"10.1088\/0305-4470\/32\/7\/007"},{"key":"48","doi-asserted-by":"publisher","unstructured":"Luca D'Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol. ``From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics''. Adv. Phys. 65, 239\u2013362 (2016).","DOI":"10.1080\/00018732.2016.1198134"},{"key":"49","doi-asserted-by":"publisher","unstructured":"Herbert Spohn and Joel L. Lebowitz. ``Irreversible Thermodynamics for Quantum Systems Weakly Coupled to Thermal Reservoirs''. In Advances in Chemical Physics. Volume 38, pages 109\u2013142. John Wiley & Sons, Ltd (1978).","DOI":"10.1002\/9780470142578.ch2"},{"key":"50","doi-asserted-by":"publisher","unstructured":"Robert Alicki. ``On the detailed balance condition for non-hamiltonian systems''. Rept. Math. Phys. 10, 249\u2013258 (1976).","DOI":"10.1016\/0034-4877(76)90046-X"},{"key":"51","doi-asserted-by":"publisher","unstructured":"Andrzej Kossakowski, Alberto Frigerio, Vittorio Gorini, and Maurizio Verri. ``Quantum detailed balance and KMS condition''. Commun. Math. Phys. 57, 97\u2013110 (1977).","DOI":"10.1007\/BF01625769"},{"key":"52","doi-asserted-by":"publisher","unstructured":"Eric A. Carlen and Jan Maas. ``Gradient flow and entropy inequalities for quantum markov semigroups with detailed balance''. Journal of Functional Analysis 273, 1810\u20131869 (2017).","DOI":"10.1016\/j.jfa.2017.05.003"},{"key":"53","doi-asserted-by":"publisher","unstructured":"Franco Fagnola and Veronica Umanit\u00e0. ``Generators of Detailed Balance Quantum Markov Semigroups''. Infin. Dimens. Anal. Quantum Probab. Relat. Top. 10, 335\u2013363 (2007).","DOI":"10.1142\/S0219025707002762"},{"key":"54","doi-asserted-by":"publisher","unstructured":"Franco Fagnola and Veronica Umanit\u00e0. ``Generators of KMS Symmetric Markov Semigroups on $\\mathcal{B}({\\rm h)}$ Symmetry and Quantum Detailed Balance''. Commun. Math. Phys. 298, 523\u2013547 (2010).","DOI":"10.1007\/s00220-010-1011-1"},{"key":"55","doi-asserted-by":"publisher","unstructured":"K. Temme, M. J. Kastoryano, M. B. Ruskai, M. M. Wolf, and F. Verstraete. ``The $\\chi^2$-divergence and Mixing times of quantum Markov processes''. J. Math. Phys. 51, 122201 (2010).","DOI":"10.1063\/1.3511335"},{"key":"56","unstructured":"Michael M Wolf. ``Quantum Channels & Operations Guided Tour''. Lecture notes. Niels-Bohr Institute, Copenhagen (2012). url: https:\/\/mediatum.ub.tum.de\/doc\/1701036\/document.pdf."},{"key":"57","doi-asserted-by":"publisher","unstructured":"Matthew Pocrnic, Dvira Segal, and Nathan Wiebe. ``Quantum simulation of Lindbladian dynamics via repeated interactions''. J. Phys. A: Math. Theor. 58, 305302 (2025). arXiv:2312.05371.","DOI":"10.1088\/1751-8121\/adebc4"},{"key":"58","unstructured":"Akshar Ramkumar and Mehdi Soleimanifar. ``Mixing time of quantum Gibbs sampling for random sparse Hamiltonians'' (2024). arXiv:2411.04454."},{"key":"59","unstructured":"Chi-Fang Chen and Fernando G. S. L. Brand\u00e3o. ``Fast Thermalization from the Eigenstate Thermalization Hypothesis'' (2021). arXiv:2112.07646."},{"key":"60","unstructured":"Cambyse Rouz\u00e9, Daniel Stilck Fran\u00e7a, and \u00c1lvaro M. Alhambra. ``Optimal quantum algorithm for Gibbs state preparation'' (2024). arXiv:2411.04885."},{"key":"61","doi-asserted-by":"publisher","unstructured":"Marko Znidaric. ``Relaxation times of dissipative many-body quantum systems''. Phys. Rev. E 92, 042143 (2015).","DOI":"10.1103\/PhysRevE.92.042143"},{"key":"62","unstructured":"\u0160t\u011bp\u00e1n \u0160m\u00edd, Richard Meister, Mario Berta, and Roberto Bondesan. ``Polynomial Time Quantum Gibbs Sampling for Fermi-Hubbard Model at any Temperature'' (2025) arXiv:2501.01412."},{"key":"63","unstructured":"Matthew Hagan and Nathan Wiebe. ``The Thermodynamic Cost of Ignorance: Thermal State Preparation with One Ancilla Qubit'' (2025) arXiv:2502.03410."},{"key":"64","unstructured":"Hao-En Li, Yongtao Zhan, and Lin Lin. ``Dissipative ground state preparation in ab initio electronic structure theory'' (2024). arXiv:2411.01470."},{"key":"65","doi-asserted-by":"publisher","unstructured":"M. B. Plenio and P. L. Knight. ``The quantum-jump approach to dissipative dynamics in quantum optics''. Rev. Mod. Phys. 70, 101\u2013144 (1998).","DOI":"10.1103\/RevModPhys.70.101"},{"key":"66","doi-asserted-by":"publisher","unstructured":"Marko Znidaric. ``Dephasing-induced diffusive transport in the anisotropic Heisenberg model''. New J. Phys. 12, 043001 (2010).","DOI":"10.1088\/1367-2630\/12\/4\/043001"},{"key":"67","doi-asserted-by":"publisher","unstructured":"S. Finazzi, A. Le Boit\u00e9, F. Storme, A. Baksic, and C. Ciuti. ``Corner-Space Renormalization Method for Driven-Dissipative Two-Dimensional Correlated Systems''. Phys. Rev. Lett. 115, 080604 (2015).","DOI":"10.1103\/PhysRevLett.115.080604"},{"key":"68","doi-asserted-by":"publisher","unstructured":"Luca Gravina and Vincenzo Savona. ``Adaptive variational low-rank dynamics for open quantum systems''. Phys. Rev. Research 6, 023072 (2024).","DOI":"10.1103\/PhysRevResearch.6.023072"},{"key":"69","doi-asserted-by":"publisher","unstructured":"Hendrik Weimer, Augustine Kshetrimayum, and Rom\u00e1n Or\u00fas. ``Simulation methods for open quantum many-body systems''. Rev. Mod. Phys. 93, 015008 (2021).","DOI":"10.1103\/RevModPhys.93.015008"},{"key":"70","unstructured":"Aaron Sander, Maximilian Fr\u00f6hlich, Martin Eigel, Jens Eisert, Patrick Gel\u00df, Michael Hinterm\u00fcller, Richard M. Milbradt, Robert Wille, and Christian B. Mendl. ``Large-scale stochastic simulation of open quantum systems'' (2025) arXiv:2501.17913."},{"key":"71","unstructured":"Yongtao Zhan, Zhiyan Ding, Jakob Huhn, Johnnie Gray, John Preskill, Garnet Kin-Lic Chan, and Lin Lin. ``Rapid quantum ground state preparation via dissipative dynamics'' (2025) arXiv:2503.15827."},{"key":"72","doi-asserted-by":"publisher","unstructured":"A. R. Kolovsky and A. Buchleitner. ``Quantum chaos in the Bose-Hubbard model''. EPL 68, 632 (2004).","DOI":"10.1209\/epl\/i2004-10265-7"},{"key":"73","doi-asserted-by":"publisher","unstructured":"Y. Y. Atas and E. Bogomolny. ``Multifractality of eigenfunctions in spin chains''. Phys. Rev. E 86, 021104 (2012).","DOI":"10.1103\/PhysRevE.86.021104"},{"key":"74","doi-asserted-by":"publisher","unstructured":"Lukas Pausch, Edoardo G. Carnio, Alberto Rodr\u00edguez, and Andreas Buchleitner. ``Chaos and Ergodicity across the Energy Spectrum of Interacting Bosons''. Phys. Rev. Lett. 126, 150601 (2021).","DOI":"10.1103\/PhysRevLett.126.150601"},{"key":"75","doi-asserted-by":"publisher","unstructured":"Eric Brunner, Lukas Pausch, Edoardo G. Carnio, Gabriel Dufour, Alberto Rodr\u00edguez, and Andreas Buchleitner. ``Many-Body Interference at the Onset of Chaos''. Phys. Rev. Lett. 130, 080401 (2023).","DOI":"10.1103\/PhysRevLett.130.080401"},{"key":"76","doi-asserted-by":"publisher","unstructured":"Meghana Raghunandan, Fabian Wolf, Christian Ospelkaus, Piet O. Schmidt, and Hendrik Weimer. ``Initialization of quantum simulators by sympathetic cooling''. Sci. Adv. 6, eaaw9268 (2020).","DOI":"10.1126\/sciadv.aaw9268"},{"key":"77","doi-asserted-by":"publisher","unstructured":"Stefano Polla, Yaroslav Herasymenko, and Thomas E. O'Brien. ``Quantum digital cooling''. Phys. Rev. A 104, 012414 (2021).","DOI":"10.1103\/PhysRevA.104.012414"},{"key":"78","doi-asserted-by":"publisher","unstructured":"X. Mi et al. ``Stable quantum-correlated many-body states through engineered dissipation''. Science 383, adh9932 (2024).","DOI":"10.1126\/science.adh9932"},{"key":"79","unstructured":"Toby S. Cubitt. ``Dissipative ground state preparation and the Dissipative Quantum Eigensolver'' (2023). arXiv:2303.11962."},{"key":"80","unstructured":"Etienne Granet and Henrik Dreyer. ``A noise-limiting quantum algorithm using mid-circuit measurements for dynamical correlations at infinite temperature'' (2024). arXiv:2401.02207."},{"key":"81","doi-asserted-by":"publisher","unstructured":"Vikram Kashyap, Georgios Styliaris, Sara Mouradian, J. Ignacio Cirac, and Rahul Trivedi. ``Accuracy Guarantees and Quantum Advantage in Analog Open Quantum Simulation with and without Noise''. Phys. Rev. X 15, 021017 (2025).","DOI":"10.1103\/PhysRevX.15.021017"},{"key":"82","doi-asserted-by":"publisher","unstructured":"Michael J. Kastoryano and Kristan Temme. ``Quantum logarithmic Sobolev inequalities and rapid mixing''. J. Math. Phys. 54, 052202 (2013).","DOI":"10.1063\/1.4804995"},{"key":"83","doi-asserted-by":"publisher","unstructured":"Earl Campbell. ``Random compiler for fast hamiltonian simulation''. Phys. Rev. Lett. 123, 070503 (2019).","DOI":"10.1103\/PhysRevLett.123.070503"},{"key":"84","doi-asserted-by":"publisher","unstructured":"Vadim Oganesyan and David A. Huse. ``Localization of interacting fermions at high temperature''. Phys. Rev. B 75, 155111 (2007).","DOI":"10.1103\/PhysRevB.75.155111"},{"key":"85","doi-asserted-by":"publisher","unstructured":"Y. Y. Atas, E. Bogomolny, O. Giraud, and G. Roux. ``Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles''. Phys. Rev. Lett. 110, 084101 (2013).","DOI":"10.1103\/PhysRevLett.110.084101"},{"key":"86","doi-asserted-by":"publisher","unstructured":"Joel J. Wallman and Joseph Emerson. ``Noise tailoring for scalable quantum computation via randomized compiling''. Phys. Rev. A 94, 052325 (2016).","DOI":"10.1103\/PhysRevA.94.052325"},{"key":"87","doi-asserted-by":"publisher","unstructured":"Samuel Duffield, Gabriel Matos, and Melf Johannsen. ``qujax: Simulating quantum circuits with JAX''. J. Open Source Softw. 8, 5504 (2023).","DOI":"10.21105\/joss.05504"},{"key":"88","unstructured":"James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang. ``JAX: composable transformations of Python+NumPy programs'' (2018). Version 0.3.13. http:\/\/github.com\/jax-ml\/jax (accessed 2024-12-21)."},{"key":"89","doi-asserted-by":"publisher","unstructured":"Seyon Sivarajah, Silas Dilkes, Alexander Cowtan, Will Simmons, Alec Edgington, and Ross Duncan. ``t$|$ket$\\rangle$: a retargetable compiler for NISQ devices''. Quantum Sci. Technol. 6, 014003 (2020).","DOI":"10.1088\/2058-9565\/ab8e92"},{"key":"90","doi-asserted-by":"publisher","unstructured":"Andrew M. Childs, Edward Farhi, and John Preskill. ``Robustness of adiabatic quantum computation''. Phys. Rev. A 65, 012322 (2001).","DOI":"10.1103\/PhysRevA.65.012322"},{"key":"91","doi-asserted-by":"publisher","unstructured":"J\u00e9r\u00e9mie Roland and Nicolas J. Cerf. ``Noise resistance of adiabatic quantum computation using random matrix theory''. Phys. Rev. A 71, 032330 (2005).","DOI":"10.1103\/PhysRevA.71.032330"},{"key":"92","doi-asserted-by":"publisher","unstructured":"Rahul Trivedi, Adrian Franco Rubio, and J. Ignacio Cirac. ``Quantum advantage and stability to errors in analogue quantum simulators''. Nature Commun. 15, 6507 (2024).","DOI":"10.1038\/s41467-024-50750-x"},{"key":"93","doi-asserted-by":"publisher","unstructured":"K. Kechedzhi, S. V. Isakov, S. Mandr\u00e0, B. Villalonga, X. Mi, S. Boixo, and V. Smelyanskiy. ``Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments''. Future Gener. Comput. Syst. 153, 431\u2013441 (2024).","DOI":"10.1016\/j.future.2023.12.002"},{"key":"94","unstructured":"Benjamin F. Schiffer, Adrian Franco Rubio, Rahul Trivedi, and J. Ignacio Cirac. ``The quantum adiabatic algorithm suppresses the proliferation of errors'' (2024). arXiv:2404.15397."},{"key":"95","doi-asserted-by":"publisher","unstructured":"Etienne Granet and Henrik Dreyer. ``Dilution of Error in Digital Hamiltonian Simulation''. PRX Quantum 6, 010333 (2025).","DOI":"10.1103\/PRXQuantum.6.010333"},{"key":"96","unstructured":"Eli Chertkov, Yi-Hsiang Chen, Michael Lubasch, David Hayes, and Michael Foss-Feig. ``Robustness of near-thermal dynamics on digital quantum computers'' (2024). arXiv:2410.10794."},{"key":"97","doi-asserted-by":"publisher","unstructured":"Akel Hashim. ``Randomized Compiling for Scalable Quantum Computing on a Noisy Superconducting Quantum Processor''. Phys. Rev. X 11, 041039 (2021).","DOI":"10.1103\/PhysRevX.11.041039"},{"key":"98","doi-asserted-by":"crossref","unstructured":"Ainesh Bakshi, Allen Liu, Ankur Moitra, and Ewin Tang. ``Learning quantum Hamiltonians at any temperature in polynomial time'' (2023) arXiv:2310.02243.","DOI":"10.1145\/3618260.3649619"},{"key":"99","doi-asserted-by":"publisher","unstructured":"Chaitanya Murthy and Mark Srednicki. ``Bounds on chaos from the eigenstate thermalization hypothesis''. Phys. Rev. Lett. 123, 230606 (2019).","DOI":"10.1103\/PhysRevLett.123.230606"},{"key":"100","doi-asserted-by":"publisher","unstructured":"E. B. Davies. ``Markovian master equations''. Commun. Math. Phys. 39, 91\u2013110 (1974).","DOI":"10.1007\/BF01608389"},{"key":"101","doi-asserted-by":"publisher","unstructured":"E. B. Davies. ``Markovian master equations. II''. Math. Ann. 219, 147\u2013158 (1976).","DOI":"10.1007\/BF01351898"},{"key":"102","doi-asserted-by":"publisher","unstructured":"Anatoly Dymarsky and Hong Liu. ``New characteristic of quantum many-body chaotic systems''. Phys. Rev. E 99, 010102 (2019).","DOI":"10.1103\/PhysRevE.99.010102"},{"key":"103","doi-asserted-by":"publisher","unstructured":"Mari Carmen Ba\u00f1uls, David A. Huse, and J. Ignacio Cirac. ``Entanglement and its relation to energy variance for local one-dimensional hamiltonians''. Phys. Rev. B 101, 144305 (2020).","DOI":"10.1103\/PhysRevB.101.144305"},{"key":"104","doi-asserted-by":"publisher","unstructured":"Sirui Lu, Mari Carmen Ba\u00f1uls, and J. Ignacio Cirac. ``Algorithms for quantum simulation at finite energies''. PRX Quantum 2, 020321 (2021).","DOI":"10.1103\/PRXQuantum.2.020321"},{"key":"105","doi-asserted-by":"publisher","unstructured":"W. Beugeling, A. Andreanov, and Masudul Haque. ``Global characteristics of all eigenstates of local many-body Hamiltonians: participation ratio and entanglement entropy''. J. Stat. Mech. 2015, P02002 (2015).","DOI":"10.1088\/1742-5468\/2015\/02\/P02002"},{"key":"106","doi-asserted-by":"publisher","unstructured":"Y. Y. Atas and E. Bogomolny. ``Quantum Ising model in transverse and longitudinal fields: chaotic wave functions''. J. Phys. A: Math. Theor. 50, 385102 (2017).","DOI":"10.1088\/1751-8121\/aa81f6"},{"key":"107","doi-asserted-by":"publisher","unstructured":"Wouter Beugeling, Arnd B\u00e4cker, Roderich Moessner, and Masudul Haque. ``Statistical properties of eigenstate amplitudes in complex quantum systems''. Phys. Rev. E 98, 022204 (2018).","DOI":"10.1103\/PhysRevE.98.022204"},{"key":"108","doi-asserted-by":"publisher","unstructured":"Hyungwon Kim and David A. Huse. ``Ballistic Spreading of Entanglement in a Diffusive Nonintegrable System''. Phys. Rev. Lett. 111, 127205 (2013).","DOI":"10.1103\/PhysRevLett.111.127205"},{"key":"109","doi-asserted-by":"publisher","unstructured":"Di Fang, Jianfeng Lu, and Yu Tong. ``Mixing Time of Open Quantum Systems via Hypocoercivity''. Phys. Rev. Lett. 134, 140405 (2025). arXiv:2404.11503.","DOI":"10.1103\/PhysRevLett.134.140405"},{"key":"110","doi-asserted-by":"publisher","unstructured":"Jean Dalibard, Yvan Castin, and Klaus M\u00f8lmer. ``Wave-function approach to dissipative processes in quantum optics''. Phys. Rev. Lett. 68, 580\u2013583 (1992).","DOI":"10.1103\/PhysRevLett.68.580"},{"key":"111","doi-asserted-by":"publisher","unstructured":"R. Dum, P. Zoller, and H. Ritsch. ``Monte Carlo simulation of the atomic master equation for spontaneous emission''. Phys. Rev. A 45, 4879\u20134887 (1992).","DOI":"10.1103\/PhysRevA.45.4879"},{"key":"112","doi-asserted-by":"publisher","unstructured":"Klaus M\u00f8lmer, Yvan Castin, and Jean Dalibard. ``Monte Carlo wave-function method in quantum optics''. J. Opt. Soc. Am. B 10, 524\u2013538 (1993).","DOI":"10.1364\/JOSAB.10.000524"},{"key":"113","doi-asserted-by":"publisher","unstructured":"J. R. Johansson, P. D. Nation, and Franco Nori. ``QuTiP 2: A Python framework for the dynamics of open quantum systems''. Comput. Phys. Commun. 184, 1234\u20131240 (2013).","DOI":"10.1016\/j.cpc.2012.11.019"},{"key":"114","unstructured":"Neill Lambert, Eric Gigu\u00e8re, Paul Menczel, Boxi Li, Patrick Hopf, Gerardo Su\u00e1rez, Marc Gali, Jake Lishman, Rushiraj Gadhvi, Rochisha Agarwal, Asier Galicia, Nathan Shammah, Paul Nation, J. R. Johansson, Shahnawaz Ahmed, Simon Cross, Alexander Pitchford, and Franco Nori. ``QuTiP 5: The Quantum Toolbox in Python'' (2024) arXiv:2412.04705."}],"container-title":["Quantum"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/quantum-journal.org\/papers\/q-2025-08-29-1843\/pdf\/","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2025,8,29]],"date-time":"2025-08-29T08:57:50Z","timestamp":1756457870000},"score":1,"resource":{"primary":{"URL":"https:\/\/quantum-journal.org\/papers\/q-2025-08-29-1843\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,29]]},"references-count":115,"URL":"https:\/\/doi.org\/10.22331\/q-2025-08-29-1843","archive":["CLOCKSS"],"relation":{},"ISSN":["2521-327X"],"issn-type":[{"value":"2521-327X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,29]]},"article-number":"1843"}}