{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,11]],"date-time":"2026-07-11T13:04:28Z","timestamp":1783775068388,"version":"3.55.0"},"reference-count":27,"publisher":"Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften","license":[{"start":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T00:00:00Z","timestamp":1696896000000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Science Foundation","award":["CCF-2238766"],"award-info":[{"award-number":["CCF-2238766"]}]}],"content-domain":{"domain":["quantum-journal.org"],"crossmark-restriction":false},"short-container-title":["Quantum"],"abstract":"<jats:p>A promising avenue for the preparation of Gibbs states on a quantum computer is to simulate the physical thermalization process. The Davies generator describes the dynamics of an open quantum system that is in contact with a heat bath. Crucially, it does not require simulation of the heat bath itself, only the system we hope to thermalize. Using the state-of-the-art techniques for quantum simulation of the Lindblad equation, we devise a technique for the preparation of Gibbs states via thermalization as specified by the Davies generator.\nIn doing so, we encounter a severe technical challenge: implementation of the Davies generator demands the ability to estimate the energy of the system unambiguously. That is, each energy of the system must be deterministically mapped to a unique estimate. Previous work showed that this is only possible if the system satisfies an unphysical &amp;apos;rounding promise&amp;apos; assumption. We solve this problem by engineering a random ensemble of rounding promises that simultaneously solves three problems: First, each rounding promise admits preparation of a &amp;apos;promised&amp;apos; thermal state via a Davies generator. Second, these Davies generators have a similar mixing time as the ideal Davies generator. Third, the average of these promised thermal states approximates the ideal thermal state.<\/jats:p>","DOI":"10.22331\/q-2023-10-10-1132","type":"journal-article","created":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T15:39:11Z","timestamp":1696952351000},"page":"1132","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":47,"title":["Thermal State Preparation via Rounding Promises"],"prefix":"10.22331","volume":"7","author":[{"given":"Patrick","family":"Rall","sequence":"first","affiliation":[{"name":"IBM Quantum, MIT-IBM Watson AI Lab, Cambridge, Massachusetts 02142, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Chunhao","family":"Wang","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Pennsylvania State University"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pawel","family":"Wocjan","sequence":"additional","affiliation":[{"name":"IBM Quantum, Thomas J Watson Research Center, Yorktown Heights, New York 10598, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2023,10,10]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"\u00c1lvaro M Alhambra. Quantum many-body systems in thermal equilibrium. arXiv:2204.08349, 2022.","DOI":"10.48550\/arXiv.2204.08349"},{"key":"1","doi-asserted-by":"publisher","unstructured":"Sergey Bravyi, Anirban Chowdhury, David Gosset, and Pawel Wocjan. On the complexity of quantum partition functions. arXiv:2110.15466, 2021.","DOI":"10.1038\/s41567-022-01742-5"},{"key":"2","doi-asserted-by":"publisher","unstructured":"Fernando G. S. L. Brand\u00e3o, Amir Kalev, Tongyang Li, Cedric Yen-Yu Lin, Krysta M. Svore, and Xiaodi Wu. Quantum SDP solvers: Large speed-ups, optimality, and applications to quantum learning. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2017), volume 132, page 27, 2019.","DOI":"10.4230\/LIPIcs.ICALP.2019.27"},{"key":"3","doi-asserted-by":"publisher","unstructured":"Heinz-Peter Breuer and Francesco Petruccione. The Theory of Open Quantum Systems. Oxford University Press, 2002.","DOI":"10.1093\/acprof:oso\/9780199213900.001.0001"},{"key":"4","doi-asserted-by":"publisher","unstructured":"Chi-Fang Chen and Fernando GSL Brand\u00e3o. Fast thermalization from the eigenstate thermalization hypothesis. arXiv:2112.07646, 2021.","DOI":"10.48550\/arXiv.2112.07646"},{"key":"5","doi-asserted-by":"publisher","unstructured":"Chi-Fang Chen, Michael J. Kastoryano, Fernando G. S. L. Brand\u00e3o, and Andr\u00e1s Gily\u00e9n. Quantum thermal state preparation. arXiv:2303.18224, 2023.","DOI":"10.48550\/arXiv.2212.02051"},{"key":"6","doi-asserted-by":"publisher","unstructured":"Anirban Narayan Chowdhury and Rolando D Somma. Quantum algorithms for Gibbs sampling and hitting-time estimation. Quantum Information & Computation, 17(1-2):41\u201364, 2017.","DOI":"10.26421\/QIC17.1-2-3"},{"key":"7","doi-asserted-by":"publisher","unstructured":"Richard Cleve and Chunhao Wang. Efficient quantum algorithms for simulating Lindblad evolution. arXiv:1612.09512 Proceedings of the 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017), 2017.","DOI":"10.48550\/arXiv.1612.09512"},{"key":"8","unstructured":"Edward Brian Davies. Quantum Theory of Open Systems. Academic Press, 1976."},{"key":"9","doi-asserted-by":"publisher","unstructured":"Edward Brian Davies. Generators of dynamical semigroups. Journal of Functional Analysis, 34(3):421\u2013432, 1979.","DOI":"10.1016\/0022-1236(79)90085-5"},{"key":"10","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 (STOC 2019), pages 193\u2013204, 2019.","DOI":"10.1145\/3313276.3316366"},{"key":"11","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, October 2022.","DOI":"10.22331\/q-2022-10-06-825"},{"key":"12","doi-asserted-by":"publisher","unstructured":"M\u00e1ria Kieferov\u00e1 and Nathan Wiebe. Tomography and generative training with quantum Boltzmann machines. Physical Review A, 96(6):062327, 2017.","DOI":"10.1103\/PhysRevA.96.062327"},{"key":"13","doi-asserted-by":"publisher","unstructured":"Guang Hao Low and Isaac L Chuang. Hamiltonian simulation by uniform spectral amplification. arXiv:1707.05391, 2017.","DOI":"10.48550\/arXiv.1707.05391"},{"key":"14","doi-asserted-by":"publisher","unstructured":"Goran Lindblad. On the generators of quantum dynamical semigroups. Communications in Mathematical Physics, 48(2):119\u2013130, 1976.","DOI":"10.1007\/BF01608499"},{"key":"15","doi-asserted-by":"publisher","unstructured":"Xiantao Li and Chunhao Wang. Simulating Markovian open quantum systems using higher-order series expansion. 2212.02051, 2022.","DOI":"10.48550\/arXiv.2212.02051"},{"key":"16","doi-asserted-by":"publisher","unstructured":"John M Martyn, Zane M Rossi, Andrew K Tan, and Isaac L Chuang. Grand unification of quantum algorithms. PRX Quantum, 2(4):040203, 2021.","DOI":"10.1103\/PRXQuantum.2.040203"},{"key":"17","doi-asserted-by":"publisher","unstructured":"Davide Nigro. On the uniqueness of the steady-state solution of the Lindblad\u2013gorini\u2013Kossakowski\u2013Sudarshan equation. Journal of Statistical Mechanics: Theory and Experiment, 2019(4):043202, 2019.","DOI":"10.1088\/1742-5468\/ab0c1c"},{"key":"18","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. Physical Review Letters, 103(22):220502, 2009.","DOI":"10.1103\/PhysRevLett.103.220502"},{"key":"19","doi-asserted-by":"publisher","unstructured":"Patrick Rall. Faster coherent quantum algorithms for phase, energy, and amplitude estimation. Quantum, 5:566, 2021.","DOI":"10.22331\/q-2021-10-19-566"},{"key":"20","unstructured":"S. Slezak and E. Crosson. Eigenstate thermalization and quantum Metropolis sampling, 2022. Presentation at QIP 2022. https:\/\/youtu.be\/by4rvu7RMtY."},{"key":"21","doi-asserted-by":"publisher","unstructured":"Herbert Spohn. An algebraic condition for the approach to equilibrium of an open $n$-level system. Letters in Mathematical Physics, 2(1):33\u201338, 1977.","DOI":"10.1007\/BF00420668"},{"key":"22","doi-asserted-by":"publisher","unstructured":"Kristan Temme, Tobias J Osborne, Karl G Vollbrecht, David Poulin, and Frank Verstraete. 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