A Local-Time Algorithm for Achieving Quantum Control

Abstract

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 ti+1 − ti = 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 {εj} that sample the dynamic range εmin ≤ ε ≤ εmax 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.