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We extend these results to show that this quantum advantage still occurs for Gibbs states of Hamiltonians with O(1)-local interactions at constant temperature by showing classical hardness-of-sampling and demonstrating such Gibbs states can be prepared efficiently using a quantum computer. In particular, we show hardness-of-sampling is maintained even for 5-local Hamiltonians on a 3D lattice. We additionally show that the hardness-of-sampling is robust when we are only able to make imperfect measurements.<\/jats:p>","DOI":"10.22331\/q-2026-01-22-1981","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T10:21:58Z","timestamp":1769077318000},"page":"1981","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":3,"title":["Gibbs Sampling gives Quantum Advantage at Constant Temperatures with O(1)-Local Hamiltonians"],"prefix":"10.22331","volume":"10","author":[{"given":"Joel","family":"Rajakumar","sequence":"first","affiliation":[{"name":"Joint Center for Quantum Information & Computer Science, National Institute of Standards & Technology and University of Maryland, College Park"},{"name":"Department of Computer Science and Institute for Advanced Computer Studies, University of Maryland, College Park"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"James 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