Characterization of control noise effects in optimal quantum unitary dynamics

TL;DR

This paper introduces measures to quantify how field noise impacts targeted quantum unitary transformations, revealing the importance of noise statistics and control form for robustness in quantum control landscapes.

Contribution

It provides a new geometric interpretation of stochastic noise effects and links robustness to the overlap between landscape curvature and noise correlation functions.

Findings

Robust controls are associated with small overlap regions.

Distinct noise spectral regimes support robust control solutions.

Both noise statistics and control form are crucial for robustness.

Abstract

This work develops measures for quantifying the effects of field noise upon targeted unitary transformations. Robustness to noise is assessed in the framework of the quantum control landscape, which is the mapping from the control to the unitary transformation performance measure (quantum gate fidelity). Within that framework, a new geometric interpretation of stochastic noise effects naturally arises, where more robust optimal controls are associated with regions of small overlap between landscape curvature and the noise correlation function. Numerical simulations of this overlap in the context of quantum information processing reveal distinct noise spectral regimes that better support robust control solutions. This perspective shows the dual importance of both noise statistics and the control form for robustness, thereby opening up new avenues of investigation on how to mitigate noise effects in quantum systems.