Optimal control of two-level quantum systems
Dapos;Alessandro, D.; Dahleh, M.
American Control Conference, 2000. Proceedings of the 2000
Volume 6, Issue , 2000 Page(s):3893 - 3897 vol.6
Digital Object Identifier 10.1109/ACC.2000.876952
Summary:We study the manipulation of two-level quantum systems. This
research is motivated by the design of quantum mechanical logic gates
which perform prescribed logic operations on a two-level quantum system,
a quantum bit. We consider the problem of driving the evolution operator
to a desired state, while minimizing the energy-type cost.
Mathematically, this problem translates into an optimal control problem
for systems varying on the Lie group of special unitary matrices, with
cost that is quadratic in the control. We develop a comprehensive theory
of optimal control for two-level quantum systems. In particular, we
prove the `normality' of the given problem and the `regularity' of the
optimal control functions. The impact of the results of the paper on
nuclear magnetic resonance experiments and quantum computation is
discussed
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