{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1995:EDCPWQPUO6FO7KJYJ7UCPZNRVQ","short_pith_number":"pith:EDCPWQPU","canonical_record":{"source":{"id":"quant-ph/9511026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1995-11-20T20:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"fa185c89991489a57118af967fca74940d69c844b1c8d31a6963faf277e4c763","abstract_canon_sha256":"b74975f8f3ce0120af5e418a3f1ae905fc923dddf1f39446eb4b68635dbe15a5"},"schema_version":"1.0"},"canonical_sha256":"20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847","source":{"kind":"arxiv","id":"quant-ph/9511026","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9511026","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9511026v1","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9511026","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"EDCPWQPUO6FO","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_16","alias_value":"EDCPWQPUO6FO7KJY","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_8","alias_value":"EDCPWQPU","created_at":"2026-07-04T14:47:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1995:EDCPWQPUO6FO7KJYJ7UCPZNRVQ","target":"record","payload":{"canonical_record":{"source":{"id":"quant-ph/9511026","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"quant-ph","submitted_at":"1995-11-20T20:39:33Z","cross_cats_sorted":[],"title_canon_sha256":"fa185c89991489a57118af967fca74940d69c844b1c8d31a6963faf277e4c763","abstract_canon_sha256":"b74975f8f3ce0120af5e418a3f1ae905fc923dddf1f39446eb4b68635dbe15a5"},"schema_version":"1.0"},"canonical_sha256":"20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:47:03.526065Z","signature_b64":"hnB88YxtbN7guKw5FV4Iw5VyKkiz5+nFGESSvFyAXeYlPDTYxR2jt81J3xf6bv7WL/1VcDd7J+/YNQMdFlWvBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847","last_reissued_at":"2026-07-04T14:47:03.525645Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:47:03.525645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"quant-ph/9511026","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Ly9DrOh1q1n7BkwJGxFqzUDd0BCmsbCyX4CZW0y0Tn/Blt1v6cEdANpW9GurRDbbDJ6/+2DVOpG4J/NJHB2wBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:59:32.445861Z"},"content_sha256":"ed184a42f51fe6d13524d831d01abed6cfca0d7c52375caf62e9046ea4b3b031","schema_version":"1.0","event_id":"sha256:ed184a42f51fe6d13524d831d01abed6cfca0d7c52375caf62e9046ea4b3b031"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1995:EDCPWQPUO6FO7KJYJ7UCPZNRVQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quantum measurements and the Abelian Stabilizer Problem","license":"","headline":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"A.Yu.Kitaev (L.D.Landau Institute for Theoretical Physics, Moscow)","submitted_at":"1995-11-20T20:39:33Z","abstract_excerpt":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The group action (or the function whose stabilizer is sought) can be implemented as an efficient quantum circuit realizing the corresponding unitary operator.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Kitaev presents a polynomial quantum algorithm for the Abelian stabilizer problem based on measuring eigenvalues of unitary operators, generalizing Shor's factoring and discrete-log algorithms.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"4177f06e7d59b5b5fed412ba821b7d1db659b1f9762e90f772c4bb5604bee31d"},"source":{"id":"quant-ph/9511026","kind":"arxiv","version":1},"verdict":{"id":"185009bc-4285-4b3e-ab70-340eee4e978f","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T05:03:44.059564Z","strongest_claim":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm.","one_line_summary":"Kitaev presents a polynomial quantum algorithm for the Abelian stabilizer problem based on measuring eigenvalues of unitary operators, generalizing Shor's factoring and discrete-log algorithms.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The group action (or the function whose stabilizer is sought) can be implemented as an efficient quantum circuit realizing the corresponding unitary operator.","pith_extraction_headline":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/9511026/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":16,"sample":[{"doi":"","year":1982,"title":"Quantum mechanical Hamiltonian models of Tu ring machines","work_id":"a256f939-6742-4be5-acde-7c9d3859a159","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Reversible logic and quantum computers","work_id":"635876e5-ce2f-46c0-8d19-262288427b4e","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Quantum mechanical computers","work_id":"2c781a02-e4f7-48a7-8e7d-89cbb7c3c442","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1985,"title":"Quantum theory, the Church-Turing princip le and the universal quantum computer","work_id":"694267f2-cae1-4c38-b054-30d03d1ae2d7","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1989,"title":"Quantum computational networks","work_id":"f3cd17dd-674c-4b1a-be60-869f32a001ca","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":16,"snapshot_sha256":"f5ba4ff3a496a975a4fb69a6d75ca13582174f1223d9473193ba9f250f0bec84","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"91cc3ecd0b470423f41a28207f1450a66e165d18ff24f3bd81462895af52a30c"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":"185009bc-4285-4b3e-ab70-340eee4e978f"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T14:47:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"01CYN/jlp29FhNZUGAhsYN5Kvm2lx5JvvQ9smkjaQ8M74XXYT0QxbJ7NskAkt5ZbsfXKVZa8TpVH1Jjoq8B7Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-13T23:59:32.446549Z"},"content_sha256":"561ad7b887252075d9b49195198a6b739e4c65a50c1c0a586baed83b02d93ad9","schema_version":"1.0","event_id":"sha256:561ad7b887252075d9b49195198a6b739e4c65a50c1c0a586baed83b02d93ad9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/bundle.json","state_url":"https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-13T23:59:32Z","links":{"resolver":"https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ","bundle":"https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/bundle.json","state":"https://pith.science/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/EDCPWQPUO6FO7KJYJ7UCPZNRVQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1995:EDCPWQPUO6FO7KJYJ7UCPZNRVQ","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":"b74975f8f3ce0120af5e418a3f1ae905fc923dddf1f39446eb4b68635dbe15a5","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1995-11-20T20:39:33Z","title_canon_sha256":"fa185c89991489a57118af967fca74940d69c844b1c8d31a6963faf277e4c763"},"schema_version":"1.0","source":{"id":"quant-ph/9511026","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"quant-ph/9511026","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"arxiv_version","alias_value":"quant-ph/9511026v1","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.quant-ph/9511026","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_12","alias_value":"EDCPWQPUO6FO","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_16","alias_value":"EDCPWQPUO6FO7KJY","created_at":"2026-07-04T14:47:03Z"},{"alias_kind":"pith_short_8","alias_value":"EDCPWQPU","created_at":"2026-07-04T14:47:03Z"}],"graph_snapshots":[{"event_id":"sha256:561ad7b887252075d9b49195198a6b739e4c65a50c1c0a586baed83b02d93ad9","target":"graph","created_at":"2026-07-04T14:47:03Z","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":4,"items":[{"attestation":"unclaimed","claim_id":"C1","kind":"strongest_claim","source":"verdict.strongest_claim","status":"machine_extracted","text":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm."},{"attestation":"unclaimed","claim_id":"C2","kind":"weakest_assumption","source":"verdict.weakest_assumption","status":"machine_extracted","text":"The group action (or the function whose stabilizer is sought) can be implemented as an efficient quantum circuit realizing the corresponding unitary operator."},{"attestation":"unclaimed","claim_id":"C3","kind":"one_line_summary","source":"verdict.one_line_summary","status":"machine_extracted","text":"Kitaev presents a polynomial quantum algorithm for the Abelian stabilizer problem based on measuring eigenvalues of unitary operators, generalizing Shor's factoring and discrete-log algorithms."},{"attestation":"unclaimed","claim_id":"C4","kind":"headline","source":"verdict.pith_extraction.headline","status":"machine_extracted","text":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm."}],"snapshot_sha256":"4177f06e7d59b5b5fed412ba821b7d1db659b1f9762e90f772c4bb5604bee31d"},"formal_canon":{"evidence_count":2,"snapshot_sha256":"91cc3ecd0b470423f41a28207f1450a66e165d18ff24f3bd81462895af52a30c"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/quant-ph/9511026/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm. Thus we extend famous Shor's results. Our method is based on a procedure for measuring an eigenvalue of a unitary operator. Another application of this procedure is a polynomial quantum Fourier transform algorithm for an arbitrary finite Abelian group. The paper also contains a rather detailed introduction to the theory of quantum computation.","authors_text":"A.Yu.Kitaev (L.D.Landau Institute for Theoretical Physics, Moscow)","cross_cats":[],"headline":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm.","license":"","primary_cat":"quant-ph","submitted_at":"1995-11-20T20:39:33Z","title":"Quantum measurements and the Abelian Stabilizer Problem"},"references":{"count":16,"internal_anchors":0,"resolved_work":16,"sample":[{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":1,"title":"Quantum mechanical Hamiltonian models of Tu ring machines","work_id":"a256f939-6742-4be5-acde-7c9d3859a159","year":1982},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":2,"title":"Reversible logic and quantum computers","work_id":"635876e5-ce2f-46c0-8d19-262288427b4e","year":1985},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":3,"title":"Quantum mechanical computers","work_id":"2c781a02-e4f7-48a7-8e7d-89cbb7c3c442","year":1985},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":4,"title":"Quantum theory, the Church-Turing princip le and the universal quantum computer","work_id":"694267f2-cae1-4c38-b054-30d03d1ae2d7","year":1985},{"cited_arxiv_id":"","doi":"","is_internal_anchor":false,"ref_index":5,"title":"Quantum computational networks","work_id":"f3cd17dd-674c-4b1a-be60-869f32a001ca","year":1989}],"snapshot_sha256":"f5ba4ff3a496a975a4fb69a6d75ca13582174f1223d9473193ba9f250f0bec84"},"source":{"id":"quant-ph/9511026","kind":"arxiv","version":1},"verdict":{"created_at":"2026-05-13T05:03:44.059564Z","id":"185009bc-4285-4b3e-ab70-340eee4e978f","model_set":{"reader":"grok-4.3"},"one_line_summary":"Kitaev presents a polynomial quantum algorithm for the Abelian stabilizer problem based on measuring eigenvalues of unitary operators, generalizing Shor's factoring and discrete-log algorithms.","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"A quantum algorithm solves the Abelian stabilizer problem in polynomial time, covering factoring and discrete logarithm.","strongest_claim":"We present a polynomial quantum algorithm for the Abelian stabilizer problem which includes both factoring and the discrete logarithm.","weakest_assumption":"The group action (or the function whose stabilizer is sought) can be implemented as an efficient quantum circuit realizing the corresponding unitary operator."}},"verdict_id":"185009bc-4285-4b3e-ab70-340eee4e978f"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ed184a42f51fe6d13524d831d01abed6cfca0d7c52375caf62e9046ea4b3b031","target":"record","created_at":"2026-07-04T14:47:03Z","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":"b74975f8f3ce0120af5e418a3f1ae905fc923dddf1f39446eb4b68635dbe15a5","cross_cats_sorted":[],"license":"","primary_cat":"quant-ph","submitted_at":"1995-11-20T20:39:33Z","title_canon_sha256":"fa185c89991489a57118af967fca74940d69c844b1c8d31a6963faf277e4c763"},"schema_version":"1.0","source":{"id":"quant-ph/9511026","kind":"arxiv","version":1}},"canonical_sha256":"20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"20c4fb41f4778aefa9384fe827e5b1ac0cb36dfbedc5824e4a914218acffb847","first_computed_at":"2026-07-04T14:47:03.525645Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:47:03.525645Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hnB88YxtbN7guKw5FV4Iw5VyKkiz5+nFGESSvFyAXeYlPDTYxR2jt81J3xf6bv7WL/1VcDd7J+/YNQMdFlWvBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T14:47:03.526065Z","signed_message":"canonical_sha256_bytes"},"source_id":"quant-ph/9511026","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ed184a42f51fe6d13524d831d01abed6cfca0d7c52375caf62e9046ea4b3b031","sha256:561ad7b887252075d9b49195198a6b739e4c65a50c1c0a586baed83b02d93ad9"],"state_sha256":"be50805cb20dade14e69fed8809ae1ec4aa82e83b00300b05bde60986ef2f4ac"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"7ASalJ3tXHHUpyptpcyQCYMFINgsP1Igc79SNUu746VdrwuUcvVmK87nE9+DQRNiIr0WdbthCY28IwuV3MipBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-13T23:59:32.477980Z","bundle_sha256":"d25566c16ec188e3370c4160ab2dc4f24e9abe1f6466559b08992b7487c87ff0"}}