Universal quantum computation using the discrete-time quantum walk

Lovett, Neil B. and Cooper, Sally and Everitt, Matthew and Trevers, Matthew and Kendon, Viv (2010) Universal quantum computation using the discrete-time quantum walk. Physical Review A, 81 (4). 042330. ISSN 2469-9934 (https://doi.org/10.1103/PhysRevA.81.042330)

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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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