Dartmouth College Time Optimal Control of Quantum Systems
The last 50 years have witnessed a steady increase in man's ability to manipulate and control phenomenon at quantum level. The revolution that began with spectroscopy has culminated in recent advances showing the possibility of harnessing quantum dynamics for processing, protecting and storing information. A central problem in the design of quantum information processors and coherent control of quantum phenomenon in general is the phenomenon of decoherence. It is therefore of utmost importance to control these systems in a time optimal manner before decoherence corrupts the system of interest. In this talk we will focus on the time optimal control of nuclear spins in NMR quantum computing and spectroscopy. Radio frequency pulses are used in coherent spectroscopy to implement a unitary transfer of state. Pulse sequences that accomplish a desired transfer should be as short as possible in order to minimize the effects of relaxation and to optimize the sensitivity of the experiments. We will give an analytical characterization of such time optimal pulse sequences applicable to coherence transfer experiments in multiple-spin systems. From a general control theory perspective, the problems we want to study have the following character: Suppose we are given a controllable right invariant system on a compact Lie group; what is the minimum time required to steer the system between points of interest.