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arXiv · 0806.1972

Universal computation by quantum walk

Andrew M. Childs
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Abstract

In some of the earliest work on quantum mechanical computers, Feynman showed how to implement universal quantum computation by the dynamics of a time-independent Hamiltonian. I show that this remains possible even if the Hamiltonian is restricted to be a sparse matrix with all entries equal to 0 or 1, i.e., the adjacency matrix of a low-degree graph. Thus quantum walk can be regarded as a universal computational primitive, with any desired quantum computation encoded entirely in some underlying graph. The main idea of the construction is to implement quantum gates by scattering processes.

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Andrew M. Childs. 2008-06-12. Universal computation by quantum walk. https://doi.org/10.1103/physrevlett.102.180501

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