We investigate the time and the energy minimum optimal solutions for the
robust control of two-level quantum systems against offset or control field
uncertainties. Using the Pontryagin Maximum Principle, we derive the global
optimal pulses for the first robustness orders. We show that the dimension of
the control landscape is lower or equal to 2N for a field robust to the N th
order, which leads to an estimate of its complexity.Comment: 30 pages, 15 figures, submitted to Phys. Rev.
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