{"paper":{"title":"The Jones polynomial: quantum algorithms and applications in quantum complexity theory","license":"","headline":"","cross_cats":["math.GT"],"primary_cat":"quant-ph","authors_text":"Jon Yard, Pawel Wocjan","submitted_at":"2006-03-08T17:43:33Z","abstract_excerpt":"We analyze relationships between quantum computation and a family of generalizations of the Jones polynomial. Extending recent work by Aharonov et al., we give efficient quantum circuits for implementing the unitary Jones-Wenzl representations of the braid group. We use these to provide new quantum algorithms for approximately evaluating a family of specializations of the HOMFLYPT two-variable polynomial of trace closures of braids. We also give algorithms for approximating the Jones polynomial of a general class of closures of braids at roots of unity. Next we provide a self-contained proof o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0603069","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}