{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:N5D3NW3OHSGOJRITEHAOEWYCHV","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":"456bfc6cf717036a60e73519a3434a5e40af8776a25dc6434e8a4e6e067df062","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-20T10:40:00Z","title_canon_sha256":"acbe035b2ae28910abb4abf33fdcf8141d9554fe93efa7f717c3242ff590593c"},"schema_version":"1.0","source":{"id":"1206.4451","kind":"arxiv","version":5}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.4451","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"arxiv_version","alias_value":"1206.4451v5","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.4451","created_at":"2026-05-18T03:00:39Z"},{"alias_kind":"pith_short_12","alias_value":"N5D3NW3OHSGO","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"N5D3NW3OHSGOJRIT","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"N5D3NW3O","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:efe712ac354ebbca0fd0b99077dd7688f366a981f5f1cbba839c458177857d65","target":"graph","created_at":"2026-05-18T03:00:39Z","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 study efficient generations of random diagonal-unitary matrices, an ensemble of unitary matrices diagonal in a given basis with randomly distributed phases for their eigenvalues. Despite the simple algebraic structure, they cannot be achieved by quantum circuits composed of a few-qubit diagonal gates. We introduce diagonal-unitary $t$-designs and present two quantum circuits that implement diagonal-unitary $2$-designs with the computational basis in $N$-qubit systems. One is composed of single-qubit diagonal gates and controlled-phase gates with randomized phases, which achieves an exact di","authors_text":"Mio Murao, Yoshifumi Nakata","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-20T10:40:00Z","title":"Diagonal-unitary 2-designs and their implementations by quantum circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.4451","kind":"arxiv","version":5},"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":"sha256:637d8d163b62b89c595c20a5e061750406727bf0904bfccc966d82fcf6291e0e","target":"record","created_at":"2026-05-18T03:00:39Z","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":"456bfc6cf717036a60e73519a3434a5e40af8776a25dc6434e8a4e6e067df062","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-20T10:40:00Z","title_canon_sha256":"acbe035b2ae28910abb4abf33fdcf8141d9554fe93efa7f717c3242ff590593c"},"schema_version":"1.0","source":{"id":"1206.4451","kind":"arxiv","version":5}},"canonical_sha256":"6f47b6db6e3c8ce4c51321c0e25b023d70958e7409e79698908a4bb5dcb54ea3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6f47b6db6e3c8ce4c51321c0e25b023d70958e7409e79698908a4bb5dcb54ea3","first_computed_at":"2026-05-18T03:00:39.874266Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:00:39.874266Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"vfL5mnuZmc8ciIDQzSE9q2Ubr7TSlwWMDKlxrwgECaz9FG1+afC0s1IFdWbp8ASsGuxt3xWlL2SZ+FwUNFWEDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:00:39.875211Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.4451","source_kind":"arxiv","source_version":5}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:637d8d163b62b89c595c20a5e061750406727bf0904bfccc966d82fcf6291e0e","sha256:efe712ac354ebbca0fd0b99077dd7688f366a981f5f1cbba839c458177857d65"],"state_sha256":"e77444dd486ac52a0cb8d53508e9069e108608a326a4c8f77d662f55d79e82ba"}