Almost Any Quantum Logic Gate is Universal

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.