{"paper":{"title":"A 3-Stranded Quantum Algorithm for the Jones Polynomial","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"jr, Louis H. Kauffman, Samuel J. Lomonaco","submitted_at":"2007-05-31T21:06:32Z","abstract_excerpt":"Let K be a 3-stranded knot (or link), and let L denote the number of crossings in K. Let $\\epsilon_{1}$ and $\\epsilon_{2}$ be two positive real numbers such that $\\epsilon_{2}$ is less than or equal to 1.\n  In this paper, we create two algorithms for computing the value of the Jones polynomial of K at all points $t=exp(i\\phi)$ of the unit circle in the complex plane such that the absolute value of $\\phi$ is less than or equal to $\\pi/3$.\n  The first algorithm, called the classical 3-stranded braid (3-SB) algorithm, is a classical deterministic algorithm that has time complexity O(L). The secon"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0706.0020","kind":"arxiv","version":1},"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"}