English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Difference sets are basic combinatorial structures that have applications insignal processing, coding theory, and cryptography. We consider the problem ofidentifying a shifted version of the characteristic function of a (known)difference set. We present a generic quantum algorithm that can be used totackle any hidden shift problem for any difference set in any abelian group. Wediscuss special cases of this framework where the resulting quantum algorithmis efficient. This includes: a) Paley difference sets based on quadraticresidues in finite fields, which allows to recover the shifted Legendrefunction quantum algorithm, b) Hadamard difference sets, which allows torecover the shifted bent function quantum algorithm, and c) Singer differencesets based on finite geometries. The latter class allows us to define instancesof the dihedral hidden subgroup problem that can be efficiently solved on aquantum computer.

Quantum algorithms for abelian difference sets and applications to dihedral hidden subgroups