Conservation-law-based global bounds to quantum optimal control

TL;DR

This paper introduces a conservation-law-based framework to establish fundamental limits on quantum control performance, providing tight bounds that improve understanding of achievable speeds and fidelities in quantum systems.

Contribution

It presents a novel integral-equation-based approach using conservation laws to derive fundamental bounds for various quantum control tasks, surpassing previous uncertainty-based limits.

Findings

Bounds are tight or nearly tight in three quantum control scenarios.

The framework reveals performance limits not apparent from local optimization.

Global bounds help identify achievable and impossible control performance levels.

Abstract

Active control of quantum systems enables diverse applications ranging from quantum computation to manipulation of molecular processes. Maximum speeds and related bounds have been identified from uncertainty principles and related inequalities, but such bounds utilize only coarse system information, and loosen significantly in the presence of constraints and complex interaction dynamics. We show that an integral-equation-based formulation of conservation laws in quantum dynamics leads to a systematic framework for identifying fundamental limits to any quantum control scenario. We demonstrate the utility of our bounds in three scenarios -- three-level driving, decoherence suppression, and maximum-fidelity gate implementations -- and show that in each case our bounds are tight or nearly so. Global bounds complement local-optimization-based designs, illuminating performance levels that may be possible as well as those that cannot be surpassed.