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

Abstract

Based on a parametrization of pure quantum states we explicitly construct a sequence of (at most) 4N − 5 local time-continuous waveforms controls to achieve the specified state transition for N -level quantum system when sufficient controls of the Hamiltonian are available. The control magnitudes are further optimized in terms of the time-energy performance which is the generalization of the time performance, and then the trajectory-constrained optimal local time-continuous waveforms controls including both local sine-waveforms and n-order-polynomial-function-waveform controls are obtained in terms of time-energy performance. It is demonstrated that constrained optimal local nst-order-polynomial-function-waveform controls approach constrained optimal bang-bang controls when n → ∞.