{"paper":{"title":"Quantum SAT Problems with Finite Sets of Projectors are Complete for a Plethora of Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Alex Meiburg, Daniel Nagaj, Ricardo Rivera Cardoso","submitted_at":"2025-06-08T17:59:55Z","abstract_excerpt":"Previously, all known variants of the Quantum Satisfiability (QSAT) problem, i.e. deciding whether a $k$-local ($k$-body) Hamiltonian is frustration-free, could be classified as being either in $\\mathsf{P}$; or complete for $\\mathsf{NP}$, $\\mathsf{MA}$, or $\\mathsf{QMA_1}$. Here, we demonstrate new qubit variants of this problem that are complete for $\\mathsf{BQP_1}$, $\\mathsf{coRP}$, $\\mathsf{QCMA}$, $\\mathsf{PI(coRP,NP)}$, $\\mathsf{PI(BQP_1,NP)}$, $\\mathsf{PI(BQP_1,MA)}$, $\\mathsf{SoPU(coRP,NP)}$, $\\mathsf{SoPU(BQP_1,NP)}$, and $\\mathsf{SoPU(BQP_1,MA)}$. Our result implies that a complete cl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.07244","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.07244/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}