{"paper":{"title":"Periodic Fourier representation of Boolean functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"quant-ph","authors_text":"Ryuhei Mori","submitted_at":"2018-03-27T08:10:44Z","abstract_excerpt":"In this work, we consider a new type of Fourier-like representation of Boolean function $f\\colon\\{+1,-1\\}^n\\to\\{+1,-1\\}$ \\[ f(x) = \\cos\\left(\\pi\\sum_{S\\subseteq[n]}\\phi_S \\prod_{i\\in S} x_i\\right). \\] This representation, which we call the periodic Fourier representation, of Boolean function is closely related to a certain type of multipartite Bell inequalities and non-adaptive measurement-based quantum computation with linear side-processing ($\\mathrm{NMQC}_\\oplus$). The minimum number of non-zero coefficients in the above representation, which we call the periodic Fourier sparsity, is equal "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.09947","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":""},"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"}