Quantum algorithms for some hidden shift problems

Wim Van Dam, Sean Hallgren, Lawrence Ip

Research output: Contribution to conferencePaper

40 Scopus citations

Abstract

Almost all of the most successful quantum algorithm discovered to date exploit the ability of the Fourier transform to recover subgroup structure of functions, especially periodicity. The fact that Fourier transform can also be used to capture shift structure has received far less attention in the context of quantum computation. In this paper, we present three examples of "unknown shift" problems that can be solved efficiently on a quantum computer using the quantum Fourier transform. We also define the hidden coset problem, which generalizes the hidden shift problem and the hidden subgroup problem. This framework provides a unified way of viewing the ability of the Fourier transform to capture subgroup and shift structure.

Original languageEnglish (US)
Pages489-498
Number of pages10
StatePublished - Jan 1 2003
EventConfiguralble Computing: Technology and Applications - Boston, MA, United States
Duration: Nov 2 1998Nov 3 1998

Other

OtherConfiguralble Computing: Technology and Applications
CountryUnited States
CityBoston, MA
Period11/2/9811/3/98

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

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    Van Dam, W., Hallgren, S., & Ip, L. (2003). Quantum algorithms for some hidden shift problems. 489-498. Paper presented at Configuralble Computing: Technology and Applications, Boston, MA, United States.