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. © 2009 The American Physical Society.
CITATION STYLE
Childs, A. M. (2009). Universal computation by quantum walk. Physical Review Letters, 102(18). https://doi.org/10.1103/PhysRevLett.102.180501
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