{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HYFL5PHA6AYLUTZ74HT4IQ2DNY","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":"c064554c4b5b085e8d6e7022749e85578190bdcd3767e2c991a2df29b17a67a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-14T19:42:55Z","title_canon_sha256":"47b19e569e98aa13f974d388ccaba2d506df8114151beb81e6d57031a229ed6c"},"schema_version":"1.0","source":{"id":"1206.3223","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1206.3223","created_at":"2026-05-18T03:38:43Z"},{"alias_kind":"arxiv_version","alias_value":"1206.3223v1","created_at":"2026-05-18T03:38:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1206.3223","created_at":"2026-05-18T03:38:43Z"},{"alias_kind":"pith_short_12","alias_value":"HYFL5PHA6AYL","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HYFL5PHA6AYLUTZ7","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HYFL5PHA","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:04f8b50575cd290ba7b387ad64e8b89b4055953512af33811faaa4485af9d4c0","target":"graph","created_at":"2026-05-18T03:38:43Z","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":"Given an arbitrary single-qubit operation, an important task is to efficiently decompose this operation into an (exact or approximate) sequence of fault-tolerant quantum operations. We derive a depth-optimal canonical form for single-qubit quantum circuits, and the corresponding rules for exactly reducing an arbitrary single-qubit circuit to this canonical form. We focus on the single-qubit universal H,T basis due to its role in fault-tolerant quantum computing, and show how our formalism might be extended to other universal bases. We then extend our canonical representation to the family of S","authors_text":"Alex Bocharov, Krysta M. Svore","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-14T19:42:55Z","title":"A Depth-Optimal Canonical Form for Single-qubit Quantum Circuits"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.3223","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":"sha256:61dc9b9e3c484469d6ace582821c021ee1cc3f610f9bdbc302997edce9171f8f","target":"record","created_at":"2026-05-18T03:38:43Z","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":"c064554c4b5b085e8d6e7022749e85578190bdcd3767e2c991a2df29b17a67a8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"quant-ph","submitted_at":"2012-06-14T19:42:55Z","title_canon_sha256":"47b19e569e98aa13f974d388ccaba2d506df8114151beb81e6d57031a229ed6c"},"schema_version":"1.0","source":{"id":"1206.3223","kind":"arxiv","version":1}},"canonical_sha256":"3e0abebce0f030ba4f3fe1e7c443436e339ac6f013260366645c65bd183f4146","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3e0abebce0f030ba4f3fe1e7c443436e339ac6f013260366645c65bd183f4146","first_computed_at":"2026-05-18T03:38:43.765046Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:38:43.765046Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cQzIJTonNUvTPFt0G1BQnt26GAH7iJeGVQHoAip0Kp9WxEzLDUmfHHXmT6y6u7QG2xba3fN6jeuzr0bvO33kAg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:38:43.765620Z","signed_message":"canonical_sha256_bytes"},"source_id":"1206.3223","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:61dc9b9e3c484469d6ace582821c021ee1cc3f610f9bdbc302997edce9171f8f","sha256:04f8b50575cd290ba7b387ad64e8b89b4055953512af33811faaa4485af9d4c0"],"state_sha256":"aed88db07e23796146c0ad9d955d4aeab9e2b07921f4fdf81102129c6d4f1a48"}