{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:LASEHB4JCM7N77PW3MM7WLUI7Y","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":"cbec04e0c862370b5b720437ba5ca14da1f077e75b8f9ea17dfba666649bf328","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-03-19T02:36:28Z","title_canon_sha256":"b848ecf7341ab2ae3a030f57e250703c81378f146697075e95c82ed8d12a43a6"},"schema_version":"1.0","source":{"id":"quant-ph/0603161","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0603161","created_at":"2026-07-04T17:02:58Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0603161v2","created_at":"2026-07-04T17:02:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0603161","created_at":"2026-07-04T17:02:58Z"},{"alias_kind":"pith_short_12","alias_value":"LASEHB4JCM7N","created_at":"2026-07-04T17:02:58Z"},{"alias_kind":"pith_short_16","alias_value":"LASEHB4JCM7N77PW","created_at":"2026-07-04T17:02:58Z"},{"alias_kind":"pith_short_8","alias_value":"LASEHB4J","created_at":"2026-07-04T17:02:58Z"}],"graph_snapshots":[{"event_id":"sha256:6d3fdb9eea65369c2a1862405d59151db792949b5221d4461036aae659da6061","target":"graph","created_at":"2026-07-04T17:02:58Z","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/quant-ph/0603161/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"Quantum computers hold great promise, but it remains a challenge to find efficient quantum circuits that solve interesting computational problems. We show that finding optimal quantum circuits is essentially equivalent to finding the shortest path between two points in a certain curved geometry. By recasting the problem of finding quantum circuits as a geometric problem, we open up the possibility of using the mathematical techniques of Riemannian geometry to suggest new quantum algorithms, or to prove limitations on the power of quantum computers.","authors_text":"Andrew C. Doherty, Mark R. Dowling, Michael A. Nielsen, Mile Gu","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2006-03-19T02:36:28Z","title":"Quantum Computation as Geometry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0603161","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":"sha256:326a22ed71b99fe44b755bd4ac61525bb00641824096501bd477bf6a71dfe32f","target":"record","created_at":"2026-07-04T17:02:58Z","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":"cbec04e0c862370b5b720437ba5ca14da1f077e75b8f9ea17dfba666649bf328","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2006-03-19T02:36:28Z","title_canon_sha256":"b848ecf7341ab2ae3a030f57e250703c81378f146697075e95c82ed8d12a43a6"},"schema_version":"1.0","source":{"id":"quant-ph/0603161","kind":"arxiv","version":2}},"canonical_sha256":"5824438789133edffdf6db19fb2e88fe3e3444b6dab3dfb525b8dce0c0d8e7d7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5824438789133edffdf6db19fb2e88fe3e3444b6dab3dfb525b8dce0c0d8e7d7","first_computed_at":"2026-07-04T17:02:58.144192Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:02:58.144192Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DAXxVed9NsZiOT1em+67L0yt6jKtX/Ucb//mz5gOqB8FozoMv637ZstYvVGfzU1I/7eJ0jvT1XMPiLPHSCTkCA==","signature_status":"signed_v1","signed_at":"2026-07-04T17:02:58.144680Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0603161","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:326a22ed71b99fe44b755bd4ac61525bb00641824096501bd477bf6a71dfe32f","sha256:6d3fdb9eea65369c2a1862405d59151db792949b5221d4461036aae659da6061"],"state_sha256":"41eb8e64129d66524ba2b7d0bcb8d8b582fc04f007e706cb4fe487673b559962"}