1010.2805 (Ming Zhang et al.)

Trajectory-constrained optimal local time-continuous waveform controls
for state transitions in $N$-level quantum systems    [PDF]

Ming Zhang, Jia-Hua Wei, Weiwei Zhou, Hong-Yi Dai, Zairong Xi, S. G. Schirmer

Based on a parametrization of pure quantum states we explicitly construct a
sequence of (at most) $4N-5$ local time-continuous waveform controls to achieve
a specified state transition for $N$-level quantum systems when sufficient
controls of the Hamiltonian are available. The control magnitudes are further
optimized in terms of a time-energy performance, which is a generalization of
the time performance index. Trajectory-constrained optimal local
time-continuous waveform controls, including both local sine-waveforms and
$n^{\rm th}$-order-polynomial waveform controls are obtained in terms of
time-energy performance. It is demonstrated that constrained optimal local
$n^{\rm th}$-order-polynomial waveform controls approach constrained optimal
bang-bang controls when $n\rightarrow\infty$.

View original: http://arxiv.org/abs/1010.2805