A local-time algorithm for achieving quantum control

A local-time algorithm (LTA) is developed for designing electric fields to guide a quantum system toward a desired observable. The LTA is a noniterative forward marching procedure based on making a choice for the control field over the next immediate small time increment t_i+1 - t_i = Δ solely on the ability of the local field value εⁱ in that increment to take the system closer to the target goal. Each locally optimal field value εⁱ, i = 1, 2,... is chosen from a fixed toolkit of discretized members {ε_j} that sample the dynamic range ε_min ≤ ε ≤ ε_max of the control. Despite the strictly local myopic design process, the LTA is shown to be capable of achieving good quality control results in model systems. The LTA has no fixed time to reach the target, and the time it takes to produce good quality control primarily depends on the "distance" between the initial and target states, as measured by the number of intermediate state linkages connecting them and their strength. A comparison is made between the behavior of optimal control theory (OCT) and the LTA; each has different characteristics, and it is shown that the LTA can be computationally very efficient. LTA and traditional OCT methods can be viewed as extreme cases of a larger class of time-windowed approaches to control.