IEEE Conference on Decision and Control (CDC)

The controllability of infinite quantum systems

Roger W. Brockett, Chitra Rangan, Anthony M. Bloch

Published Jul 8, 2004• 17 citations

Abstract

Quantum phenomena of interest in connection with computation and communication often deal with transfers between eigenstates. For systems having only a finite number of states, the quantum evolution equation is finite-dimensional and the results on controllability on Lie groups as worked out decades ago provide most of what is needed in so far as controllability of dissipationless systems is concerned. However, for infinite-dimensional evolution of quantum systems, many difficulties, both conceptual and technical, remain. In this paper we organize some recent results from the physics literature in control theoretic terms and emphasize the type of analysis needed to go beyond what basic differential geometry can provide. In particular, we analyze from a controllability point of view the important results of Law and Eberly, and discuss the problem of controllability of quantum systems subject to the constraint that the trajectories must lie in pre-defined subspaces. The study of this problem is motivated by recent work on the design of quantum computers that avoid loss of coherence by operating in decoherence free subspaces.

DOI: 10.1109/cdc.2003.1272600

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