Constrained Minimum-Energy Optimal Control of the Dissipative Bloch Equations

TL;DR

This paper develops optimal control strategies for designing minimum-energy pulses in the dissipative Bloch equations, accounting for relaxation effects and control constraints, to improve quantum control precision.

Contribution

It introduces a Pontryagin's Maximum Principle-based method to derive optimal feedback laws with switchings for the dissipative Bloch system under control constraints.

Findings

Derived explicit optimal control laws with switchings.

Analyzed the impact of control bounds on pulse design.

Provided insights into energy-efficient quantum control in dissipative systems.

Abstract

In this letter, we apply optimal control theory to design minimum-energy $\pi/2$ and $\pi$ pulses for the Bloch system in the presence of relaxation with constrained control amplitude. We consider a commonly encountered case in which the transverse relaxation rate is much larger than the longitudinal one so that the latter can be neglected. Using the Pontryagin's Maximum Principle, we derive optimal feedback laws which are characterized by the number of switches, depending on the control bound and the coordinates of the desired final state.