{"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"}