{"paper":{"title":"Sedentary quantum walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Chris Godsil","submitted_at":"2017-10-30T18:57:57Z","abstract_excerpt":"Let $X$ be a graph with adjacency matrix $A$. The \\textsl{continuous quantum walk} on $X$ is determined by the unitary matrices $U(t)=\\exp(itA)$. If $X$ is the complete graph $K_n$ and $a\\in V(X)$, then \\[1-|U(t)_{a,a}|\\le2/n. \\] In a sense, this means that a quantum walk on a complete graph stay home with high probability. In this paper we consider quantum walks on cones over an $\\ell$-regular graph on $n$ vertices. We prove that if $\\ell^2/n\\to\\infty$ as $n$ increases, than a quantum walk that starts on the apex of the cone will remain on it with probability tending to $1$ as $n$ increases. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11192","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"}