An approach to control design for two-level quantum ensemble systems

TL;DR

This paper introduces a practical control strategy for two-level quantum systems, enabling accurate approximation of target states with proven convergence and demonstrated effectiveness through simulations.

Contribution

It provides the first fully implementable control method for a family of driftless two-level quantum systems with rigorous convergence guarantees.

Findings

Guarantees accurate approximation of target distributions on SU(2)

Proves convergence properties analytically

Demonstrates effectiveness via numerical simulations

Abstract

Quantum ensemble systems arise in a variety of applications, including NMR spectroscopy and robust quantum control. While their theoretical properties have been extensively studied, relatively little attention has been given to the explicit construction of control inputs. In this paper, we address this gap by presenting a fully implementable control strategy for a one-parameter family of driftless two-level quantum systems. The proposed method is supported by rigorous analysis that guarantees accurate approximation of target distributions on SU(2). Convergence properties are established analytically, and numerical simulations are provided to demonstrate the effectiveness of the approach.