{"paper":{"title":"NAND-Trees, Average Choice Complexity, and Effective Resistance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Shelby Kimmel, Stacey Jeffery","submitted_at":"2015-11-06T21:01:07Z","abstract_excerpt":"We show that the quantum query complexity of evaluating NAND-tree instances with average choice complexity at most $W$ is $O(W)$, where average choice complexity is a measure of the difficulty of winning the associated two-player game. This generalizes a superpolynomial speedup over classical query complexity due to Zhan et al. [Zhan et al., ITCS 2012, 249-265]. We further show that the player with a winning strategy for the two-player game associated with the NAND-tree can win the game with an expected $\\widetilde{O}(N^{1/4}\\sqrt{{\\cal C}(x)})$ quantum queries against a random opponent, where"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.02235","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"}