Universal computation by quantum walk

Details Universal computation by quantum walk Universal computation by quantum walk

2008-06-12

arxiv.org/abs/0806.1972v1

Phys. Rev. Lett. 102, 180501 (2009)

Physics

Quantum Physics

9 pages

Scientific paper

10.1103/PhysRevLett.102.180501

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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