Determining quantum Monte Carlo simulability with geometric phases

Although stoquastic Hamiltonians are known to be simulable via sign-problem-free quantum Monte Carlo (QMC) techniques, the nonstoquasticity of a Hamiltonian does not necessarily imply existence QMC sign problem. We give sufficient and necessary condition for QMC-simulability in given basis: prove that simulation will if only all overall total phases along chordless cycles weighted graph whose adjacency matrix is zero (modulo 2π). use our findings provide construction nonstoquastic, yet hence QMC-simulable, many-body models. also demonstrate why truly sign-problematic models using weights stoquasticized generally suboptimal. offer superior alternative.Received 18 December 2020Accepted 12 April 2021DOI:https://doi.org/10.1103/PhysRevResearch.3.023080Published by American Physical Society under terms Creative Commons Attribution 4.0 International license. Further distribution this work must maintain attribution author(s) published article's title, journal citation, DOI.Published SocietyPhysics Subject Headings (PhySH)TechniquesQuantum CarloQuantum InformationCondensed Matter, Materials & Applied Physics