On the generation of sequential unitary gates from continuous time Schrodinger equations driven by external fields

In most of the proposals for quantum computers, a common feature is that the quantum circuits are expected to be made of cascades of unitary transformations acting on the quantum states. Such unitary gates are normally assumed to belong to a given discrete set of transformations. However, arbitrary superposition of quantum states may be achieved by utilizing a fixed number of transformations, each depending on a parameter. A framework is proposed to dynamically express these parameters directly in terms of the control inputs entering into the continuous time forced Schrouml;dinger equation.