{"paper":{"title":"Search by quantum walks on two-dimensional grid without amplitude amplification","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Alexander Rivosh, Andris Ambainis, Arturs Backurs, Nikolajs Nahimovs, Raitis Ozols","submitted_at":"2011-12-14T20:55:56Z","abstract_excerpt":"We study search by quantum walk on a finite two dimensional grid. The algorithm of Ambainis, Kempe, Rivosh (quant-ph/0402107) takes O(\\sqrt{N log N}) steps and finds a marked location with probability O(1/log N) for grid of size \\sqrt{N} * \\sqrt{N}. This probability is small, thus amplitude amplification is needed to achieve \\Theta(1) success probability. The amplitude amplification adds an additional O(\\sqrt{log N}) factor to the number of steps, making it O(\\sqrt{N} log N).\n  In this paper, we show that despite a small probability to find a marked location, the probability to be within an O("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.3337","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"}