In a nearly-adiabatic two-level (qubit) system, driving the control field so that its frequency tracks the instantaneous, time-dependent energy gap between the two levels - a 'time-dependent resonance' condition - reproduces the numerically optimal control that maximizes the probability of ending in the target eigenstate. An exact-WKB analysis in the complex time plane, using turning points, Stokes lines, and the Dykhne-Davis-Pechukas connection formula, shows analytically that this resonant protocol coincides with optimal adiabatic control, and unlike shortcut-to-adiabaticity it needs no extra counterdiabatic terms added to the Hamiltonian.
Theoretical single-author study of control in nearly-adiabatic two-level (qubit) quantum systems. The author analyzes a 'time-dependent resonance' protocol in which the drive frequency is made to fol…