{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:C4IEBMYFNL3ZYLIWGDWCQOXL66","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":"d791945c69b1a6cd04b417ce31c97ed1290ec540b750aec67cb296fb5966c061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-13T21:09:22Z","title_canon_sha256":"a97f761eadfe7396da75e87a4643cd5267cae7ce3255fa7aca775ec08c96362e"},"schema_version":"1.0","source":{"id":"1803.05047","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1803.05047","created_at":"2026-07-04T23:58:02Z"},{"alias_kind":"arxiv_version","alias_value":"1803.05047v2","created_at":"2026-07-04T23:58:02Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1803.05047","created_at":"2026-07-04T23:58:02Z"},{"alias_kind":"pith_short_12","alias_value":"C4IEBMYFNL3Z","created_at":"2026-07-04T23:58:02Z"},{"alias_kind":"pith_short_16","alias_value":"C4IEBMYFNL3ZYLIW","created_at":"2026-07-04T23:58:02Z"},{"alias_kind":"pith_short_8","alias_value":"C4IEBMYF","created_at":"2026-07-04T23:58:02Z"}],"graph_snapshots":[{"event_id":"sha256:a6c841d69dc74690dffda1c821e48e0c59156ae0d9fe0ce31597ea784d4dd6ec","target":"graph","created_at":"2026-07-04T23:58:02Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1803.05047/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We introduce canonical forms for single qutrit Clifford+T circuits and prove that every single-qutrit Clifford+T operator admits a unique such canonical form. We show that our canonical forms are T-optimal in the sense that among all the single-qutrit Clifford+T circuits implementing a given operator our canonical form uses the least number of T gates. Finally, we provide an algorithm which inputs the description of an operator (as a matrix or a circuit) and constructs the canonical form for this operator. The algorithm runs in time linear in the number of T gates. Our results provide a higher","authors_text":"Andrew N. Glaudell, Jacob M. Taylor, Neil J. Ross","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-13T21:09:22Z","title":"Canonical forms for single-qutrit Clifford+T operators"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.05047","kind":"arxiv","version":2},"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":"sha256:526e1d338293a58f14044769ad93a8d0c300be89510688ac9bc21744e4602a58","target":"record","created_at":"2026-07-04T23:58:02Z","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":"d791945c69b1a6cd04b417ce31c97ed1290ec540b750aec67cb296fb5966c061","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2018-03-13T21:09:22Z","title_canon_sha256":"a97f761eadfe7396da75e87a4643cd5267cae7ce3255fa7aca775ec08c96362e"},"schema_version":"1.0","source":{"id":"1803.05047","kind":"arxiv","version":2}},"canonical_sha256":"171040b3056af79c2d1630ec283aebf7bacb9288c2a634aa46116d60bf635109","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"171040b3056af79c2d1630ec283aebf7bacb9288c2a634aa46116d60bf635109","first_computed_at":"2026-07-04T23:58:02.982587Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T23:58:02.982587Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UOSExkR4tytLM2NHdFuXU8R66Eh0Jy2exzWfvHGJD5VCZUFzdl0ZlxKfbIoa/Mzvra3Ah+UB/BCEwDEeE8deDA==","signature_status":"signed_v1","signed_at":"2026-07-04T23:58:02.983000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1803.05047","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:526e1d338293a58f14044769ad93a8d0c300be89510688ac9bc21744e4602a58","sha256:a6c841d69dc74690dffda1c821e48e0c59156ae0d9fe0ce31597ea784d4dd6ec"],"state_sha256":"40b08f0367fd82801f5e8fc51a18d0c58607f9a946742269ca64012318fe934d"}