{"paper":{"title":"Exponential-time quantum algorithms for graph coloring problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.DS","authors_text":"Kazuya Shimizu, Ryuhei Mori","submitted_at":"2019-07-01T03:35:48Z","abstract_excerpt":"The fastest known classical algorithm deciding the $k$-colorability of $n$-vertex graph requires running time $\\Omega(2^n)$ for $k\\ge 5$. In this work, we present an exponential-space quantum algorithm computing the chromatic number with running time $O(1.9140^n)$ using quantum random access memory (QRAM). Our approach is based on Ambainis et al's quantum dynamic programming with applications of Grover's search to branching algorithms. We also present a polynomial-space quantum algorithm not using QRAM for the graph $20$-coloring problem with running time $O(1.9575^n)$. In the polynomial-space"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.00529","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"}