Robustness Analysis for Quantum Systems Controlled by Continuous-Time Pulses

TL;DR

This paper extends differential sensitivity techniques to analyze the robustness of closed quantum systems controlled by continuous-time pulses, establishing bounds on sensitivity related to system parameters and control inputs.

Contribution

It generalizes sensitivity analysis methods to time-varying quantum controls and derives bounds based on system Hamiltonian and control input limits.

Findings

Vanishing sensitivity correlates with perfect fidelity.

Upper bounds on sensitivity depend on Hamiltonian and control input size.

The approach applies to continuously controlled quantum systems.

Abstract

Differential sensitivity techniques originally developed to study the robustness of energy landscape controllers are generalized to the important case of closed quantum systems subject to continuously varying controls. Vanishing sensitivity to parameter variation is shown to coincide with perfect fidelity, as was the case for time-invariant controls. Upper bounds on the magnitude of the differential sensitivity to any parameter variation are derived based simply on knowledge of the system Hamiltonian and the maximum size of the control inputs.