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Control of Quantum Systems

John W. Clark·Dennis G. Lucarelli·Tzyh-Jong Tarn
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Abstract

A quantum system subject to external fields is said to be controllable if these fields can be adjusted to guide the state vector to a desired destination in the state space of the system. Fundamental results on controllability are reviewed against the background of recent ideas and advances in two seemingly disparate endeavors: (i) laser control of chemical reactions and (ii) quantum computation. Using Lie-algebraic methods, sufficient conditions have been derived for global controllability on a finite-dimensional manifold of an infinite-dimensional Hilbert space, in the case that the Hamiltonian and control operators, possibly unbounded, possess a common dense domain of analytic vectors. Some simple examples are presented. A synergism between quantum control and quantum computation is creating a host of exciting new opportunities for both activities. The impact of these developments on computational many-body theory could be profound.

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John W. Clark, Dennis G. Lucarelli, Tzyh-Jong Tarn. 2002-05-01. Control of Quantum Systems. https://doi.org/10.1142/s021797920302051x

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