{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"27bc05741d5477f05a41ffaee408787450fcc0df2e28acbe9e95bcdd1bffe7e5","created":"2026-10-03T07:18:01Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"df25a8df1595620d92f6fa589cfda1042bd029b4f6f1f19d2f8e24b4f861dbe2","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"classification","assisted_by":[],"external_id":"cm.sign-problem-numerics.sign-free-criteria","kind":"well-posed","literature_status":"partially-resolved","n":"1","parents":[],"plain":"Some special electron models can be simulated without the sign problem thanks to hidden symmetries. A complete list of which models allow this, and whether clever changes of variables can remove the problem in others, is not known.","posed_since":"","precise":"Known sign-free classes of determinant quantum Monte Carlo include models with an antiunitary (Kramers-type) symmetry of the decoupled fermion matrix and models with Majorana time-reversal symmetry (2015 to 2016). Determine necessary and sufficient conditions on a local fermion Hamiltonian for the existence of an auxiliary-field decoupling or local basis change that makes all weights nonnegative, and the computational complexity of deciding it. An answer is a classification theorem or a hardness result for natural Hamiltonian classes.","problem_ref":null,"references":"","settled_by":"A proof giving necessary and sufficient conditions, or a reduction proving the decision problem NP-hard for local fermion Hamiltonians.","status_note":"Results from 2019 to 2020 showed that finding a sign-curing local basis is NP-hard for some qubit Hamiltonian classes; a fermionic classification is incomplete.","title":"Complete criteria for sign-free fermion quantum Monte Carlo","topic_ref":"91e71237aaab9c02133089fdeea13d2a6f819a14e160de99c6f929cdb211535a"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"8098914e7f4b02ebc6af9b73e881d5c785d666c1e1dffc257dd0b5c27dcb7631","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"f8c5402a92587ca904e6e0a2ae3150b8785ee9aaa4d49c195862a89ec5e78479","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"Klns-kJMg-RhIJ2WoOrVnqAr95Tt_Lcc49VeO3C9LQTmUqZKXm1e3F9yJXGr4s7LBKyd7I4ij8gTTLrHlHetDA"},"schema":"pubphys.envelope/1"},"record_hash":"8098914e7f4b02ebc6af9b73e881d5c785d666c1e1dffc257dd0b5c27dcb7631","leaf_index":1156}