{"paper":{"title":"Search of clustered marked states with lackadaisical quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Amit Saha, Amlan Chakrabarti, Debasri Saha, Ritajit Majumdar, Susmita Sur-Kolay","submitted_at":"2018-04-04T14:48:04Z","abstract_excerpt":"Nature of quantum walk in presence of multiple marked state has been studied by Nahimovs and Rivosh \\cite{10.1007/978-3-662-49192-8_31}. They have shown that if the marked states are arranged in a $\\sqrt{k} \\times \\sqrt{k}$ cluster in a $\\sqrt{N} \\times \\sqrt{N}$ grid, then to find a single marked state among the multiple ones, quantum walk requires $\\Omega(\\sqrt{N} - \\sqrt{k})$ time. In this paper, we show that using lackadaisical quantum walk with the weight of the self-loop as $\\frac{4}{N(k + \\lfloor{\\frac{\\sqrt{{k}}}{2}}\\rfloor)}$, where $k$ is odd, the probability of finding a marked stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.01446","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"}