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Many efforts have been made to realise certain forms of quantum advantage in this problem, for instance, the development of variational quantum algorithms. A recent work by Huggins et al. [1] reports a novel candidate, i.e. a quantum-classical hybrid Monte Carlo algorithm with a reduced bias in comparison to its fully-classical counterpart. In this paper, we propose a family of scalable quantum-assisted Monte Carlo algorithms where the quantum computer is used at its minimal cost and still can reduce the bias. By incorporating a Bayesian inference approach, we can achieve this quantum-facilitated bias reduction with a much smaller quantum-computing cost than taking empirical mean in amplitude estimation. Besides, we show that the hybrid Monte Carlo framework is a general way to suppress errors in the ground state obtained from classical algorithms. Our work provides a Monte Carlo toolkit for achieving quantum-enhanced calculation of fermion systems on near-term quantum devices.<\/jats:p>","DOI":"10.22331\/q-2023-08-03-1072","type":"journal-article","created":{"date-parts":[[2023,8,3]],"date-time":"2023-08-03T14:01:51Z","timestamp":1691071311000},"page":"1072","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":15,"title":["Quantum-assisted Monte Carlo algorithms for fermions"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4894-8322","authenticated-orcid":false,"given":"Xiaosi","family":"Xu","sequence":"first","affiliation":[{"name":"Graduate School of China Academy of Engineering Physics, Beijing 100193, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1705-2494","authenticated-orcid":false,"given":"Ying","family":"Li","sequence":"additional","affiliation":[{"name":"Graduate School of China Academy of Engineering Physics, Beijing 100193, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"9598","published-online":{"date-parts":[[2023,8,3]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"William J Huggins, Bryan A O\u2019Gorman, Nicholas C Rubin, David R Reichman, Ryan Babbush, and Joonho Lee. 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