Control, optimisation and transport problems in quantum information

Abstract

We present an investigation of optimal control techniques applied to computational and transport processes in the field of quantum information. We implement these processes using a range of different quantum systems: a harmonic oscillator, a pair of trapped Rydberg atoms, and a spin chain. In each case, we explore how application of analytic and numerical optimal control techniques (such as the Krotov method) can effect fast, efficient, and error-free unitary operations and information transfer processes, with particular attention to experimental uncertainties present in such systems and their implementations.

In the pursuit of fast quantum operations, we discover that in our spin chain system our optimal control algorithm will fail to find solutions as the total operation time falls below a critical value. We postulate a correspondence between this value and that of the quantum speed limit, which defines a physical bound on the allowed rate of information transfer in quantum sytems when given a fixed energy resource.

In conclusion, we assert that not only can optimal control be a powerful tool for implementing successful transport operations in quantum information, but it also has deeper application in the probing of fundamental limits on the dynamics of physical systems.