Universal Computation by Quantum Walk

Andrew M. Childs
Phys. Rev. Lett. 102, 180501 – Published 4 May 2009

Abstract

In some of the earliest work on quantum computing, Feynman showed how to implement universal quantum computation with a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any quantum computation encoded in some graph. The main idea is to implement quantum gates by scattering processes.

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  • Received 11 June 2008

DOI:https://doi.org/10.1103/PhysRevLett.102.180501

©2009 American Physical Society

Authors & Affiliations

Andrew M. Childs

  • Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1

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Vol. 102, Iss. 18 — 8 May 2009

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