Universal computation by quantum walk.


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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@article{Childs2009UniversalCB, title={Universal computation by quantum walk.}, author={Andrew M. Childs}, journal={Physical review letters}, year={2009}, volume={102 18}, pages={180501} }