Universal quantum computation using the discrete-time quantum walk

Neil B. Lovett, Sally Cooper, Matthew Everitt, Matthew Trevers, Viv Kendon

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Abstract

A proof that continuous-time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by A. M. Childs [Phys. Rev. Lett. 102, 180501 (2009)]. We present a version based instead on the discrete-time quantum walk. We show that the discrete-time quantum walk is able to implement the same universal gate set and thus both discrete and continuous-time quantum walks are computational primitives. Additionally, we give a set of components on which the discrete-time quantum walk provides perfect state transfer.
Original languageEnglish
Article number042330
Number of pages7
JournalPhysical Review A
Volume81
Issue number4
DOIs
Publication statusPublished - 30 Apr 2010

Keywords

  • continuous-time quantum walks
  • discrete-time
  • low degree
  • quantum computation
  • quantum walk
  • state transfer
  • universal gates
  • unweighted graphs
  • computational linguistics
  • continuous time systems
  • quantum computers
  • quantum theory

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