{"paper":{"title":"Vertices cannot be hidden from quantum spatial search for almost all random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Adam Glos, Aleksandra Krawiec, Ryszard Kukulski, Zbigniew Pucha{\\l}a","submitted_at":"2017-09-20T12:24:20Z","abstract_excerpt":"In this paper we show that all nodes can be found optimally for almost all random Erd\\H{o}s-R\\'enyi ${\\mathcal G}(n,p)$ graphs using continuous-time quantum spatial search procedure. This works for both adjacency and Laplacian matrices, though under different conditions. The first one requires $p=\\omega(\\log^8(n)/n)$, while the seconds requires $p\\geq(1+\\varepsilon)\\log (n)/n$, where $\\varepsilon>0$. The proof was made by analyzing the convergence of eigenvectors corresponding to outlying eigenvalues in the $\\|\\cdot\\|_\\infty $ norm. At the same time for $p<(1-\\varepsilon)\\log(n)/n$, the proper"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.06829","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"}