{"paper":{"title":"Toward an Optimal Quantum Algorithm for Polynomial Factorization over Finite Fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","math.NT","quant-ph"],"primary_cat":"cs.SC","authors_text":"Javad Doliskani","submitted_at":"2018-07-25T15:49:49Z","abstract_excerpt":"We present a randomized quantum algorithm for polynomial factorization over finite fields. For polynomials of degree $n$ over a finite field $\\F_q$, the average-case complexity of our algorithm is an expected $O(n^{1 + o(1)} \\log^{2 + o(1)}q)$ bit operations. Only for a negligible subset of polynomials of degree $n$ our algorithm has a higher complexity of $O(n^{4 / 3 + o(1)} \\log^{2 + o(1)}q)$ bit operations. This breaks the classical $3/2$-exponent barrier for polynomial factorization over finite fields \\cite{guo2016alg}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.09675","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"}