Universal quantum computation using the discrete-time quantum walk

Authors:
  • NLNeil B. Lovett
    Neil B. Lovett
  • SCSally Cooper
    Sally Cooper
  • MEMatthew Everitt
    Matthew Everitt
  • MTMatthew Trevers
    Matthew Trevers
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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.

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