{"paper":{"title":"Learning junta distributions, quantum junta states, and QAC$^0$ circuits","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Francisco Escudero-Guti\\'errez, Jinge Bao","submitted_at":"2024-10-21T09:39:20Z","abstract_excerpt":"In this work, we consider the problems of learning junta distributions, their quantum counterparts (quantum junta states) and $\\mathsf{QAC}^0$ circuits, which we show to be close to juntas.\n  (1) Junta distributions. A probability distribution $p:\\{-1,1\\}^n\\to \\mathbb [0,1]$ is a $k$-junta if it only depends on $k$ bits. We show that they can be learned with to error $\\varepsilon$ in total variation distance from $O(2^k\\log(n)/\\varepsilon^2)$ samples, which quadratically improves the upper bound of Aliakbarpour et al. (COLT'16) and matches their lower bound in every parameter.\n  (2) Junta stat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.15822","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2410.15822/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}