Analytic Solutions of Control Mechanism in Single-Qubit Systems

TL;DR

This paper introduces analytic methods to understand the control mechanisms in single-qubit quantum systems, clarifying their evolution driven by pathway interference under piecewise constant controls.

Contribution

It provides novel analytic techniques to compute the underlying mechanisms of single-qubit evolution, enhancing interpretability of controlled quantum dynamics.

Findings

Analytic solutions for single-qubit control mechanisms are derived.

The methods clarify how pathway interference influences quantum state evolution.

Results improve understanding of quantum control processes.

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.