{"paper":{"title":"Stabilizer Circuits, Quadratic Forms, and Computing Matrix Rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Chaowen Guan, Kenneth W. Regan","submitted_at":"2019-03-29T21:58:39Z","abstract_excerpt":"We show that a form of strong simulation for $n$-qubit quantum stabilizer circuits $C$ is computable in $O(s + n^\\omega)$ time, where $\\omega$ is the exponent of matrix multiplication. Solution counting for quadratic forms over $\\mathbb{F}_2$ is also placed into $O(n^\\omega)$ time. This improves previous $O(n^3)$ bounds. Our methods in fact show an $O(n^2)$-time reduction from matrix rank over $\\mathbb{F}_2$ to computing $p = |\\langle \\; 0^n \\;|\\; C \\;|\\; 0^n \\;\\rangle|^2$ (hence also to solution counting) and a converse reduction that is $O(s + n^2)$ except for matrix multiplications used to "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00101","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"}