Programmable Quantum Gate Arrays

We show how to construct quantum gate arrays that can be programmed to perform different unitary operations on a data register, depending on the input to some program register. It is shown that a universal quantum gate array-a gate array which can be programmed to perform any unitary operation-exists only if one allows the gate array to operate in a probabilistic fashion. Thus it is not possible to build a fixed, general purpose quantum computer which can be programmed to perform an arbitrary quantum computation.