{"paper":{"title":"The Grover search as a naturally occurring phenomenon","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","cs.DS"],"primary_cat":"quant-ph","authors_text":"Giuseppe Di Molfetta, Mathieu Roget, Pablo Arrighi, St\\'ephane Guillet","submitted_at":"2019-08-29T13:22:30Z","abstract_excerpt":"We provide first evidence that under certain conditions, 1/2-spin fermions may naturally behave like a Grover search, looking for topological defects in a material. The theoretical framework is that of discrete-time quantum walks (QW), i.e. local unitary matrices that drive the evolution of a single particle on the lattice. Some QW are well-known to recover the $(2+1)$--dimensional Dirac equation in continuum limit, i.e. the free propagation of the 1/2-spin fermion. We study two such Dirac QW, one on the square grid and the other on a triangular grid reminiscent of graphene-like materials. The"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.11213","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1908.11213/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}