{"paper":{"title":"An efficient high dimensional quantum Schur transform","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.DM","math.CO"],"primary_cat":"quant-ph","authors_text":"Hari Krovi","submitted_at":"2018-03-30T21:04:30Z","abstract_excerpt":"The Schur transform is a unitary operator that block diagonalizes the action of the symmetric and unitary groups on an $n$ fold tensor product $V^{\\otimes n}$ of a vector space $V$ of dimension $d$. Bacon, Chuang and Harrow \\cite{BCH07} gave a quantum algorithm for this transform that is polynomial in $n$, $d$ and $\\log\\epsilon^{-1}$, where $\\epsilon$ is the precision. In a footnote in Harrow's thesis \\cite{H05}, a brief description of how to make the algorithm of \\cite{BCH07} polynomial in $\\log d$ is given using the unitary group representation theory (however, this has not been explained in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.00055","kind":"arxiv","version":2},"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"}