{"paper":{"title":"Simon's problem for linear functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC","cs.DS"],"primary_cat":"quant-ph","authors_text":"Joran van Apeldoorn, Sander Gribling","submitted_at":"2018-10-29T09:47:30Z","abstract_excerpt":"Simon's problem asks the following: determine if a function $f: \\{0,1\\}^n \\rightarrow \\{0,1\\}^n$ is one-to-one or if there exists a unique $s \\in \\{0,1\\}^n$ such that $f(x) = f(x \\oplus s)$ for all $x \\in \\{0,1\\}^n$, given the promise that exactly one of the two holds. A classical algorithm that can solve this problem for every $f$ requires $2^{\\Omega(n)}$ queries to $f$. Simon showed that there is a quantum algorithm that can solve this promise problem for every $f$ using only $\\mathcal O(n)$ quantum queries to $f$. A matching lower bound on the number of quantum queries was given by Koiran e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.12030","kind":"arxiv","version":2},"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"}