{"paper":{"title":"On the Complexity of the Circuit Width Problem","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"Yinchen Liu, Zhengfeng Ji, Zhe'ou Zhou","submitted_at":"2026-06-16T17:31:50Z","abstract_excerpt":"Montanaro's polynomial representation expresses amplitudes of quantum circuits over the gates $H$, $Z$, $CZ$, and $CCZ$ as normalized gaps of degree-three polynomials over $\\mathbb{F}_2$. The normalization is governed by the circuit width $w(f)$, the minimum number of qubits in any circuit realizing a polynomial $f$. Thus, efficient width minimization would give an approximate-counting route toward a combinatorial characterization of $BQP$. We study the computational complexity of this parameter. For degree-three polynomials with no constant term, deciding whether $w(f)\\le k$ is $NP$-complete,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.18201","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.18201/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"}