Di\ufb00erence sets are basic combinatorial structures that have applications in signal processing, coding theory, and cryptography. We consider the problem of identifying a shifted version of the characteristic function of a (known) di\ufb00erence set. We present a generic quantum algorithm that can be used to tackle any hidden shift problem for any di\ufb00erence set in any abelian group. We discuss special cases of this framework where the resulting quantum algorithm is e\ufb03cient. This includes: a) Paley di\ufb00erence sets based on quadratic residues in \ufb01nite \ufb01elds, which allows to recover the shifted Legendre function quantum algorithm, b) Hadamard di\ufb00erence sets, which allows to recover the shifted bent function quantum algorithm, and c) Singer di\ufb00erence sets based on \ufb01nite geometries. The latter class allows us to de\ufb01ne instances of the dihedral hidden subgroup problem that can be e\ufb03ciently solved on a quantum computer<\/p>\n","protected":false},"excerpt":{"rendered":"
Di\ufb00erence sets are basic combinatorial structures that have applications in signal processing, coding theory, and cryptography. We consider the problem of identifying a shifted version of the characteristic function of a (known) di\ufb00erence set. We present a generic quantum algorithm that can be used to tackle any hidden shift problem for any di\ufb00erence set in […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik","msr_publisher_other":"","msr_booktitle":"Proceedings of the 11th Conference on the Theory of Quantum Computation, Communication and Cryptography (TQC 2016)","msr_chapter":"","msr_edition":"Leibniz International Proceedings in Informatics (LIPIcs)","msr_editors":"","msr_how_published":"","msr_isbn":"","msr_issue":"","msr_journal":"","msr_number":"","msr_organization":"","msr_pages_string":"8:1--8:16","msr_page_range_start":"8:01","msr_page_range_end":"8:16","msr_series":"","msr_volume":"","msr_copyright":"","msr_conference_name":"Proceedings of the 11th 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