{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2005:S47RBZTMDBNDPWFYWJLP5YOH7R","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":"39687d0c5a3f6662843cb40cdd2033cd36c5bc306a4c69ddeacd21f252186d40","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-05-06T00:55:45Z","title_canon_sha256":"b8091acb90d09aea916aae465723d784e3fb175d84171aa153f6c6d41a19453c"},"schema_version":"1.0","source":{"id":"quant-ph/0505030","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/0505030","created_at":"2026-07-04T14:46:57Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/0505030v2","created_at":"2026-07-04T14:46:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/0505030","created_at":"2026-07-04T14:46:57Z"},{"alias_kind":"pith_short_12","alias_value":"S47RBZTMDBND","created_at":"2026-07-04T14:46:57Z"},{"alias_kind":"pith_short_16","alias_value":"S47RBZTMDBNDPWFY","created_at":"2026-07-04T14:46:57Z"},{"alias_kind":"pith_short_8","alias_value":"S47RBZTM","created_at":"2026-07-04T14:46:57Z"}],"graph_snapshots":[{"event_id":"sha256:d9a865a2766e4e617137ec819f5ab17271e89bc242a804a40497235750c92180","target":"graph","created_at":"2026-07-04T14:46:57Z","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/0505030/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This pedagogical review presents the proof of the Solovay-Kitaev theorem in the form of an efficient classical algorithm for compiling an arbitrary single-qubit gate into a sequence of gates from a fixed and finite set. The algorithm can be used, for example, to compile Shor's algorithm, which uses rotations of $\\pi / 2^k$, into an efficient fault-tolerant form using only Hadamard, controlled-{\\sc not}, and $\\pi / 8$ gates. The algorithm runs in $O(\\log^{2.71}(1/\\epsilon))$ time, and produces as output a sequence of $O(\\log^{3.97}(1/\\epsilon))$ quantum gates which is guaranteed to approximate ","authors_text":"Christopher M. Dawson, Michael A. Nielsen","cross_cats":[],"headline":"","license":"","primary_cat":"quant-ph","submitted_at":"2005-05-06T00:55:45Z","title":"The Solovay-Kitaev algorithm"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0505030","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":"sha256:0d08cf6820b7a7dd1e5a0fd39267de65be4b9ea1dc586949a23f0c4cfe7643af","target":"record","created_at":"2026-07-04T14:46:57Z","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":"39687d0c5a3f6662843cb40cdd2033cd36c5bc306a4c69ddeacd21f252186d40","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"2005-05-06T00:55:45Z","title_canon_sha256":"b8091acb90d09aea916aae465723d784e3fb175d84171aa153f6c6d41a19453c"},"schema_version":"1.0","source":{"id":"quant-ph/0505030","kind":"arxiv","version":2}},"canonical_sha256":"973f10e66c185a37d8b8b256fee1c7fc7f3e97186a4ff6603ef254be69812069","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"973f10e66c185a37d8b8b256fee1c7fc7f3e97186a4ff6603ef254be69812069","first_computed_at":"2026-07-04T14:46:57.990304Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:46:57.990304Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ywr7aVpr7BajjxNG8Hr2S0rP72PwdU5G5iMDM6oij8CtPCR2YCDoWqaYhJmv57j6o6NTs+y3JJPyOxB2RLkZAw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:46:57.990659Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/0505030","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:0d08cf6820b7a7dd1e5a0fd39267de65be4b9ea1dc586949a23f0c4cfe7643af","sha256:d9a865a2766e4e617137ec819f5ab17271e89bc242a804a40497235750c92180"],"state_sha256":"0895ee68a16eef51dfa37fdb78b245aebac082d80cdf4748a1f6f33dbf25eb23"}