00931nas a2200121 4500008004100000245004200041210004200083260001300125490000800138520060300146100002300749856003700772 2009 eng d00aUniversal computation by quantum walk0 aUniversal computation by quantum walk c2009/5/40 v1023 a 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.
1 aChilds, Andrew, M. uhttp://arxiv.org/abs/0806.1972v1