Geometric methods for analysing quantum speed limits: Time-dependent controlled quantum systems with constrained control functions

Abstract

We are interested in fundamental limits to computation imposed by physical constraints. In particular, the physical laws of motion constrain the speed at which a computer can transition between well-defined states. Here, we discuss speed limits in the context of quantum computing. We derive some results in the familiar representation, then demonstrate that the same results may be derived more readily by transforming the problem description into an alternative representation. This transformed approach is more readily extended to time-dependent and constrained systems. We demonstrate the approach applied to a spin chain system. © 2013 Springer-Verlag Berlin Heidelberg.