English

Extending the Promise of the Deutsch--Jozsa--Hoyer Algorithm for Finite Groups

Quantum Physics 2007-05-23 v2

Abstract

Hoyer has given a generalisation of the Deutsch--Jozsa algorithm which uses the Fourier transform on a group G which is (in general) non-Abelian. His algorithm distinguishes between functions which are either perfectly balanced (m-to-one) or constant, with certainty, and using a single quantum query. Here, we show that this algorithm (which we call the Deutsch--Jozsa--Hoyer algorithm) can in fact deal with a broader range of promises, which we define in terms of the irreducible representations of G.

Keywords

Cite

@article{arxiv.quant-ph/0412067,
  title  = {Extending the Promise of the Deutsch--Jozsa--Hoyer Algorithm for Finite Groups},
  author = {Michael Batty and Samuel L. Braunstein and Andrew J. Duncan},
  journal= {arXiv preprint arXiv:quant-ph/0412067},
  year   = {2007}
}

Comments

24 pages, 5 figures, to appear in LMS JCM Updated on 9th August 2005 following the referees comments. Added: Overview of questions surrounding the Fourier transform; Appendix on group representations. Corrected typos and improved notation