Universal quantum computation using the discrete time quantum walk

TL;DR

This paper demonstrates that discrete time quantum walks can perform universal quantum computation, similar to continuous time quantum walks, and provides components for perfect state transfer, broadening the understanding of quantum computational primitives.

Contribution

It shows that discrete time quantum walks are capable of universal quantum computation and offers components for perfect state transfer, establishing their equivalence with continuous time walks.

Findings

Discrete time quantum walks can implement universal quantum gates.

Discrete and continuous time quantum walks are both computational primitives.

Provides components for perfect state transfer using discrete time quantum walks.

Abstract

A proof that continuous time quantum walks are universal for quantum computation, using unweighted graphs of low degree, has recently been presented by Childs [PRL 102 180501 (2009)]. We present a version based instead on the discrete time quantum walk. We show 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.