# Quantum-Control Theory

Control of quantum mechanical systems is emerging as a general theme at the fore-front of science, driven by developments and goals in femtosecond laser physics, state-selective chemistry, materials synthesis, nanotechnology, and quantum computation.

Professor Clark carried out early theoretical work in this interdisciplinary research area in collaboration with Professor T.J. Tarn of the Department of Systems Science and Mathematics in the School of Engineering and Applied Science and students. Based on spectral analysis and lie-algebraic methods within the conceptual framework of nonlinear control theory, they were able to prove fundamental theorems on the limits of controllability of quantum systems: given a set of admissible controls, under what circumstances can a system be steered to a desired quantum state at a given (or at some) later time? Further, a solution was offered for the inverse control problem in which the dynamical track of the expectation value of an observable quantity is specified and the required external control is to be generated. The practical implementation of these theorems and results are currently being explored in terms of models pertinent to laser control of molecular processes and to quantum computation.

Additionally, Clark and Tarn are investigating learning algorithms for adaptive control in which "bottom-up" signals form the physical system guide "top-down" determination of the appropriate control sequence.