{"paper":{"title":"Optimizing the Number of Gates in Quantum Search","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DS"],"primary_cat":"quant-ph","authors_text":"Ronald de Wolf (CWI, Srinivasan Arunachalam (CWI), University of Amsterdam)","submitted_at":"2015-12-23T17:23:26Z","abstract_excerpt":"$ $In its usual form, Grover's quantum search algorithm uses $O(\\sqrt{N})$ queries and $O(\\sqrt{N} \\log N)$ other elementary gates to find a solution in an $N$-bit database. Grover in 2002 showed how to reduce the number of other gates to $O(\\sqrt{N}\\log\\log N)$ for the special case where the database has a unique solution, without significantly increasing the number of queries. We show how to reduce this further to $O(\\sqrt{N}\\log^{(r)} N)$ gates for any constant $r$, and sufficiently large $N$. This means that, on average, the gates between two queries barely touch more than a constant numbe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.07550","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"}