@article {1205, title = {Universal computation by quantum walk}, journal = {Physical Review Letters}, volume = {102}, year = {2009}, month = {2009/5/4}, 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. }, doi = {10.1103/PhysRevLett.102.180501}, url = {http://arxiv.org/abs/0806.1972v1}, author = {Andrew M. Childs} }