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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2506.07244","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2025-06-08T17:59:55Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"6ca8ea5227686c222d984af406a895339658ba5c95db8f6ab6bf245bb690f32a","abstract_canon_sha256":"b5d7a08f04c95827a51a6cb3bc4cf3fec2fe977d5ce83532a502f9fadede2ab2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:18:04.162924Z","signature_b64":"Nbzhi+0kBYu2yGuBmhKSUzxt3xqsFvdaTT9ZULInSDq10kdyHooqXl2zW39HSG3DhdU7+gzGFL3OcM7BHaPwCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"778f9b8c0ab110037a2b202c21adb248b6b962b43db9915999a7fdd94f53542d","last_reissued_at":"2026-07-05T11:18:04.162393Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:18:04.162393Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\mathsf{SoPU(BQP_1,MA)}$. 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