{"paper":{"title":"Quantum DNF Learnability Revisited","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christino Tamon, Jeffrey C. Jackson, Tomoyuki Yamakami","submitted_at":"2002-02-12T17:29:08Z","abstract_excerpt":"We describe a quantum PAC learning algorithm for DNF formulae under the uniform distribution with a query complexity of $\\tilde{O}(s^{3}/\\epsilon + s^{2}/\\epsilon^{2})$, where $s$ is the size of DNF formula and $\\epsilon$ is the PAC error accuracy. If $s$ and $1/\\epsilon$ are comparable, this gives a modest improvement over a previously known classical query complexity of $\\tilde{O}(ns^{2}/\\epsilon^{2})$. We also show a lower bound of $\\Omega(s\\log n/n)$ on the query complexity of any quantum PAC algorithm for learning a DNF of size $s$ with $n$ inputs under the uniform distribution."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0202066","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"}