{"paper":{"title":"The Heisenberg Representation of Quantum Computers","license":"","headline":"The Heisenberg representation describes quantum computers by tracking the evolution of operators rather than states.","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daniel Gottesman","submitted_at":"1998-07-01T19:34:39Z","abstract_excerpt":"Since Shor's discovery of an algorithm to factor numbers on a quantum computer in polynomial time, quantum computation has become a subject of immense interest. Unfortunately, one of the key features of quantum computers - the difficulty of describing them on classical computers - also makes it difficult to describe and understand precisely what can be done with them. A formalism describing the evolution of operators rather than states has proven extremely fruitful in understanding an important class of quantum operations. States used in error correction and certain communication protocols can"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"That the relevant quantum operations preserve the stabilizer structure and that the class of states and operations considered is representative of useful quantum computation tasks.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The Heisenberg representation describes quantum computers by tracking the evolution of operators rather than states.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"63dc3f041a6631f09937277d7a1b39559e453f2dc7efc4e28c03d56ea5eff365"},"source":{"id":"quant-ph/9807006","kind":"arxiv","version":1},"verdict":{"id":"c84339a2-9010-4d1d-86ed-96beb75893da","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-13T00:38:09.741838Z","strongest_claim":"States used in error correction and certain communication protocols can be described by their stabilizer, a group of tensor products of Pauli matrices. Even this simple group structure is sufficient to allow a rich range of quantum effects, although it falls short of the full power of quantum computation.","one_line_summary":"Quantum states for error correction are described by their stabilizer, a commuting group of tensor products of Pauli matrices, enabling analysis of a rich class of quantum effects short of full quantum computation.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"That the relevant quantum operations preserve the stabilizer structure and that the class of states and operations considered is representative of useful quantum computation tasks.","pith_extraction_headline":"The Heisenberg representation describes quantum computers by tracking the evolution of operators rather than states."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/quant-ph/9807006/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":13,"sample":[{"doi":"","year":1997,"title":"Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer","work_id":"6a74da59-fa0f-48a3-954d-517437ba8ffc","ref_index":1,"cited_arxiv_id":"quant-ph/9508027","is_internal_anchor":false},{"doi":"","year":1998,"title":"A Theory of Fault-Tolerant Quantum Computation","work_id":"2df86b67-dd85-4fff-81f4-6ac83e64e3d4","ref_index":2,"cited_arxiv_id":"quant-ph/9702029","is_internal_anchor":false},{"doi":"","year":1998,"title":"Expressing the operations of quantum computing in multiparticle geome tric algebra","work_id":"36eaf9e6-d524-4186-bc8b-902b6dbbbf57","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1996,"title":"Class of quantum error-correcting c odes saturating the quantum Hamming bound","work_id":"619d99ba-e7fb-451e-843b-0422be7a35d4","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1997,"title":"Quantum Error Correction and Orthogonal Geometry","work_id":"b8f53128-cae3-40ea-b2d0-eaa9166103b8","ref_index":5,"cited_arxiv_id":"quant-ph/9605005","is_internal_anchor":false}],"resolved_work":13,"snapshot_sha256":"18716bc37beaedcf7b569771d94fce4cada29d426e5227e43695ac066d0bc402","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"f83085fe39c71faf51ae09cfa857f731ecd5b524219332d940d571fd6c74b86f"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}