{"paper":{"title":"Counting, Fanout, and the Complexity of Quantum ACC","license":"","headline":"","cross_cats":[],"primary_cat":"quant-ph","authors_text":"Christopher Pollett, Cristopher Moore, Frederic Green, Steven Homer","submitted_at":"2001-06-04T20:45:31Z","abstract_excerpt":"We propose definitions of $\\QAC^0$, the quantum analog of the classical class $\\AC^0$ of constant-depth circuits with AND and OR gates of arbitrary fan-in, and $\\QACC[q]$, the analog of the class $\\ACC[q]$ where $\\Mod_q$ gates are also allowed. We prove that parity or fanout allows us to construct quantum $\\MOD_q$ gates in constant depth for any $q$, so $\\QACC[2] = \\QACC$. More generally, we show that for any $q,p > 1$, $\\MOD_q$ is equivalent to $\\MOD_p$ (up to constant depth). This implies that $\\QAC^0$ with unbounded fanout gates, denoted $\\QACwf^0$, is the same as $\\QACC[q]$ and $\\QACC$ for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"quant-ph/0106017","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"}