{"paper":{"title":"Efficient Quantum Algorithms for (Gapped) Group Testing and Junta Testing","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["quant-ph"],"primary_cat":"cs.CC","authors_text":"Aleksandrs Belovs, Andris Ambainis, Oded Regev, Ronald de Wolf","submitted_at":"2015-07-11T16:53:57Z","abstract_excerpt":"In the $k$-junta testing problem, a tester has to efficiently decide whether a given function $f:\\{0,1\\}^n\\rightarrow \\{0,1\\}$ is a $k$-junta (i.e., depends on at most $k$ of its input bits) or is $\\epsilon$-far from any $k$-junta. Our main result is a quantum algorithm for this problem with query complexity $\\tilde O(\\sqrt{k/\\epsilon})$ and time complexity $\\tilde O(n\\sqrt{k/\\epsilon})$. This quadratically improves over the query complexity of the previous best quantum junta tester, due to At\\i c\\i\\ and Servedio. Our tester is based on a new quantum algorithm for a gapped version of the combi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03126","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"}