{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:ULL6FADINTW6WPKLM3G55URISL","short_pith_number":"pith:ULL6FADI","canonical_record":{"source":{"id":"1602.04145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-12T18:17:26Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"deafbb582dd15ec462af9894dc12f4d1953124f68f6bf8fa886779cfb1b49f0d","abstract_canon_sha256":"ca7790e27f4f397379613bb53d71efc76eb6b5bddf8555cbaefa0b5b202a21cd"},"schema_version":"1.0"},"canonical_sha256":"a2d7e280686cedeb3d4b66cdded22892dd35fb85e69aa3c2c4fe8f8485aed501","source":{"kind":"arxiv","id":"1602.04145","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04145","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04145v1","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04145","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULL6FADINTW6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULL6FADINTW6WPKL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULL6FADI","created_at":"2026-05-18T12:30:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:ULL6FADINTW6WPKLM3G55URISL","target":"record","payload":{"canonical_record":{"source":{"id":"1602.04145","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-12T18:17:26Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"deafbb582dd15ec462af9894dc12f4d1953124f68f6bf8fa886779cfb1b49f0d","abstract_canon_sha256":"ca7790e27f4f397379613bb53d71efc76eb6b5bddf8555cbaefa0b5b202a21cd"},"schema_version":"1.0"},"canonical_sha256":"a2d7e280686cedeb3d4b66cdded22892dd35fb85e69aa3c2c4fe8f8485aed501","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:20:54.442401Z","signature_b64":"Db+UHpDkNmOCCqPeW6ipEB7IYNUsh6MZSU5E/3TS5woWkH8PoEtStrNxqQ78tYfuPjSrI3Hq66cCQP2+rbj6Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a2d7e280686cedeb3d4b66cdded22892dd35fb85e69aa3c2c4fe8f8485aed501","last_reissued_at":"2026-05-18T01:20:54.441724Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:20:54.441724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1602.04145","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NJiggnOEt+aypcxSjKyLXFagGxYr1LDsg3e5KrdkGM+1jHytcrZRpJxXX7uLyFs070pROI9LmVbvkcFaxlPAAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:00:44.645498Z"},"content_sha256":"b206fcc09519e41d75a26e18731032222d996285517c6d5990e86e8700ef4050","schema_version":"1.0","event_id":"sha256:b206fcc09519e41d75a26e18731032222d996285517c6d5990e86e8700ef4050"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:ULL6FADINTW6WPKLM3G55URISL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Complexity classification of two-qubit commuting hamiltonians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Adam Bouland, Laura Man\\v{c}inska, Xue Zhang","submitted_at":"2016-02-12T18:17:26Z","abstract_excerpt":"We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one to sample from probability distributions which cannot be sampled from classically unless the polynomial hierarchy collapses. Furthermore, the only simulable Hamiltonians are those which fail to generate entanglement. This shows that generic two-qubit commuting Hamiltonians"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04145","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":""},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:20:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Pkheu6IURhbBp1QADkVApbOTTtPKwJplADvw/RxuN1gzJovinxN8WgTJKSSH/g3qEJDhsDmm/YXhzyfbOKF/Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T15:00:44.646167Z"},"content_sha256":"a16f311182b4edc1af1324d7a497080062bf060ee88a0ed24efc266193828859","schema_version":"1.0","event_id":"sha256:a16f311182b4edc1af1324d7a497080062bf060ee88a0ed24efc266193828859"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/ULL6FADINTW6WPKLM3G55URISL/bundle.json","state_url":"https://pith.science/pith/ULL6FADINTW6WPKLM3G55URISL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/ULL6FADINTW6WPKLM3G55URISL/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-26T15:00:44Z","links":{"resolver":"https://pith.science/pith/ULL6FADINTW6WPKLM3G55URISL","bundle":"https://pith.science/pith/ULL6FADINTW6WPKLM3G55URISL/bundle.json","state":"https://pith.science/pith/ULL6FADINTW6WPKLM3G55URISL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/ULL6FADINTW6WPKLM3G55URISL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:ULL6FADINTW6WPKLM3G55URISL","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"ca7790e27f4f397379613bb53d71efc76eb6b5bddf8555cbaefa0b5b202a21cd","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-12T18:17:26Z","title_canon_sha256":"deafbb582dd15ec462af9894dc12f4d1953124f68f6bf8fa886779cfb1b49f0d"},"schema_version":"1.0","source":{"id":"1602.04145","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1602.04145","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"arxiv_version","alias_value":"1602.04145v1","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1602.04145","created_at":"2026-05-18T01:20:54Z"},{"alias_kind":"pith_short_12","alias_value":"ULL6FADINTW6","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_16","alias_value":"ULL6FADINTW6WPKL","created_at":"2026-05-18T12:30:46Z"},{"alias_kind":"pith_short_8","alias_value":"ULL6FADI","created_at":"2026-05-18T12:30:46Z"}],"graph_snapshots":[{"event_id":"sha256:a16f311182b4edc1af1324d7a497080062bf060ee88a0ed24efc266193828859","target":"graph","created_at":"2026-05-18T01:20:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We classify two-qubit commuting Hamiltonians in terms of their computational complexity. Suppose one has a two-qubit commuting Hamiltonian H which one can apply to any pair of qubits, starting in a computational basis state. We prove a dichotomy theorem: either this model is efficiently classically simulable or it allows one to sample from probability distributions which cannot be sampled from classically unless the polynomial hierarchy collapses. Furthermore, the only simulable Hamiltonians are those which fail to generate entanglement. This shows that generic two-qubit commuting Hamiltonians","authors_text":"Adam Bouland, Laura Man\\v{c}inska, Xue Zhang","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-12T18:17:26Z","title":"Complexity classification of two-qubit commuting hamiltonians"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.04145","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:b206fcc09519e41d75a26e18731032222d996285517c6d5990e86e8700ef4050","target":"record","created_at":"2026-05-18T01:20:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"ca7790e27f4f397379613bb53d71efc76eb6b5bddf8555cbaefa0b5b202a21cd","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2016-02-12T18:17:26Z","title_canon_sha256":"deafbb582dd15ec462af9894dc12f4d1953124f68f6bf8fa886779cfb1b49f0d"},"schema_version":"1.0","source":{"id":"1602.04145","kind":"arxiv","version":1}},"canonical_sha256":"a2d7e280686cedeb3d4b66cdded22892dd35fb85e69aa3c2c4fe8f8485aed501","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2d7e280686cedeb3d4b66cdded22892dd35fb85e69aa3c2c4fe8f8485aed501","first_computed_at":"2026-05-18T01:20:54.441724Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:20:54.441724Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Db+UHpDkNmOCCqPeW6ipEB7IYNUsh6MZSU5E/3TS5woWkH8PoEtStrNxqQ78tYfuPjSrI3Hq66cCQP2+rbj6Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:20:54.442401Z","signed_message":"canonical_sha256_bytes"},"source_id":"1602.04145","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b206fcc09519e41d75a26e18731032222d996285517c6d5990e86e8700ef4050","sha256:a16f311182b4edc1af1324d7a497080062bf060ee88a0ed24efc266193828859"],"state_sha256":"ca296d76ca14c0159429d7817865bf2d303d5699d2d9156f9d380e3d0fc42d42"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5gjUjrmzBm9pIUpXz+ZEGddZlhmkfalKMRXn9R3zZn2ZqARr17drVHGyz3D99b1L7u/UKWiHbjaVKzAuKeJaCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T15:00:44.649731Z","bundle_sha256":"0697cbf0c12557b41d084593cca2c93848da1f19e0692d1946dd7d1c16c116b5"}}