{"paper":{"title":"Finding structural anomalies in graphs by means of quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Daniel Reitzner, Edgar Feldman, Hai-Woong Lee, Hongjun Zheng, Mark Hillery, Vladimir Buzek","submitted_at":"2010-09-02T17:30:05Z","abstract_excerpt":"We explore the possibility of using quantum walks on graphs to find structural anomalies, such as extra edges or loops, on a graph. We focus our attention on star graphs, whose edges are like spokes coming out of a central hub. If there are $N$ spokes, we show that a quantum walk can find an extra edge connecting two of the spokes or a spoke with a loop on it in $O(\\sqrt{N})$ steps. We initially find that if all of the spokes have loops except one, the walk will not find the spoke without a loop, but this can be fixed if we choose the phase with which the particle is reflected from the vertex "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.0482","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"}