Comparing and correcting robustness metrics for quantum optimal control

TL;DR

This paper compares different numerical methods for assessing robustness in quantum optimal control, introduces a correction to improve estimations, and demonstrates the approach's effectiveness in realistic quantum systems.

Contribution

It systematically analyzes and corrects robustness metrics, providing a novel, constrained optimal control framework for more accurate, physics-informed robustness in quantum control.

Findings

Numerical differences identified between adjoint end-point and toggling-frame approaches.

Discretization correction significantly improves robustness estimation accuracy.

Method effectively handles control and fidelity constraints in quantum systems.

Abstract

Control pulses that nominally optimize fidelity are sensitive to routine hardware drift and modeling errors. Robust quantum optimal control seeks error-insensitive control pulses that maintain fidelity thresholds and obey hardware constraints. Distinct numerical approximations to the first-order error susceptibility include adjoint end-point and toggling-frame approaches. Although theoretically equivalent, we provide a novel, systematic study demonstrating important numerical differences between these two approaches. We also introduce a critical discretization correction to the widely-used toggling-frame robustness estimator, measurably improving its estimate of first-order error susceptibility. We accomplish our study by positioning robustness as a first-class objective within direct, constrained optimal control. Our approach uniquely handles control and fidelity constraints while cleanly isolating robustness for dedicated optimization. In both single- and two-qubit examples under realistic constraints, our approach provides an analytic edge for obtaining precise, physics-informed robustness.