Time optimal qubit computer

We present a number of new physical systems that may be addressed using methods of time dependent transformation. A recap of results available for two-state systems is given, with particular emphasis on the AC Stark effect. We give some results that are not well known, including the full solution for a two state system in a static electric field with arbitrary direction. Connection with established theorems in time optimal quantum control is given, and a full discussion outlines some advanced results in matrix calculus. In particular, we derive a set of matrix gates relevant to quantum information theory and computation using time optimal unitary operators, and define the hyperbolic equivalent of the quantum brachistochrone problem.