Analytic Solutions of Control Mechanism in Single-Qubit Systems

Abstract: The mechanism governing the evolution of controlled quantum systems is often obscured, making their dynamics hard to interpret. Mitra and Rabitz {[Phys. Rev. A 67, 033407 (2003)]} define mechanism via a perturbative expansion of pathways between eigenstates; the evolution of the system is driven by the constructive and destructive interference of these pathway amplitudes. In this paper, we explore mechanism in controlled single-qubit systems and describe novel analytic methods for computing the mechanism underlying the evolution of a single qubit under a piecewise constant control.