{"paper":{"title":"An efficient quantum algorithm for finding hidden parabolic subgroups in the general linear group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"G\\'abor Ivanyos, Miklos Santha, Raghav Kulkarni, Thomas Decker, Youming Qiao","submitted_at":"2014-06-25T09:53:58Z","abstract_excerpt":"In the theory of algebraic groups, parabolic subgroups form a crucial building block in the structural studies. In the case of general linear groups over a finite field $F_q$, given a sequence of positive integers $n_1, ..., n_k$, where $n=n_1+...+n_k$, a parabolic subgroup of parameter $(n_1, ..., n_k)$ in $GL_n(F_q)$ is a conjugate of the subgroup consisting of block lower triangular matrices where the $i$th block is of size $n_i$. Our main result is a quantum algorithm of time polynomial in $\\log q$ and $n$ for solving the hidden subgroup problem in $GL_n(F_q)$, when the hidden subgroup is "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.6511","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"}