Almost Any Quantum Logic Gate is Universal

Abstract

It is shown that if one can apply some Hamiltonian repeatedly to a few variables at a time one can in general effect any desired unitary time evolution on an arbitrarily large number of variables. As a result, almost any quantum logic gate with two or more inputs is computationally universal in that copies of the gate can be ``wired together'' to effect any desired logic circuit, and to perform any desired unitary transformation on a set of quantum variables.