{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"d3d2ff1f9b077479794eabb786b03498a59e016b7487ee76a0ee9fbead03e99e","created":"2026-10-15T23:43:22Z","files":[],"origin":{"assisted_by":["ai:gpt-5.5"],"kind":"seed"},"parents":["3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","ce59fb6cd812fc05906d0c60a71c75ea22bc686bcf38e7c3ef7010834d98ee7b"],"salt":"3558fac520b05762802b9c5e8da5fbc8770e772804fd79e49725f53e2f595ef5","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"yes-no","assisted_by":["ai:gpt-5.5"],"external_id":"cm.sign-problem-numerics.dynamical-sign-problem","kind":"well-posed","literature_status":"partially-resolved","n":"2","parents":[],"plain":"Simulating how electrons evolve in time requires summing complex phases that cancel more and more as time grows, so the cost rises exponentially with simulated time. For a single magnetic impurity, new methods reduced this to polynomial cost; whether this is possible for whole lattices is open.","posed_since":"","precise":"Real-time diagrammatic and path-integral Monte Carlo for nonequilibrium Green's functions have variance growing as $\\exp(c t)$. Inchworm Monte Carlo (Cohen et al. 2015) and related methods reach polynomial scaling in t for Anderson impurity models. Determine whether a classical algorithm computes local real-time correlators of the infinite 2D Hubbard model at $U/t \\sim 4$, starting from a thermal state at $T \\sim t$, up to time $t_{\\max}$ with error $\\epsilon$ at cost polynomial in $t_{\\mathrm{max}}$ and $1/\\epsilon$, or prove that this is hard (e.g. by a complexity reduction). An answer is an algorithm with proven scaling or a hardness proof.","problem_ref":"3aa3308ec11884f917f1766769579cd9607c5179cf7198157322768c02d06862","references":"","settled_by":"An algorithm with a proven polynomial cost bound verified against exact results, or a complexity-theoretic reduction showing such an algorithm would imply an unlikely collapse.","status_note":"Polynomial-cost methods exist for quantum impurity models since 2015; no such method is known for lattices.","title":"Polynomial-cost real-time simulation of interacting fermion lattices","topic_ref":null},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"57edeb3035979307c0c3b141afe26b93e5d0242e45833d2b8346f8262cc18507","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"624318360454cb3b5370f42e0524396b21a43d840e43cec3d82b5580fdcc675e","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"ZkZCMq-v0jn5jv4v4EdCVBUqD-4Cz_wmaTJACWJWl3mUsqssYVZmDubbRwaveHawQhYJ7gsVTWghtFdnkmqsCA"},"schema":"pubphys.envelope/1"},"record_hash":"57edeb3035979307c0c3b141afe26b93e5d0242e45833d2b8346f8262cc18507","leaf_index":3026}