Applying classical control techniques to quantum systems: entanglement versus stability margin and other limitations

TL;DR

This paper explores the application of classical control techniques to quantum systems, focusing on entanglement and stability margins, highlighting both potential benefits and current limitations in understanding quantum robustness.

Contribution

It demonstrates how classical robust control concepts can be applied to open quantum systems and discusses the challenges and insights gained from such approaches.

Findings

Classical stability margins can be applied to open quantum systems with Lindbladian dynamics.

Entanglement between qubits can be analyzed using classical control tools.

Identifies limitations and areas for further development in quantum robust control.

Abstract

Development of robust quantum control has been challenging and there are numerous obstacles to applying classical robust control to quantum system including bilinearity, marginal stability, state preparation errors, nonlinear figures of merit. The requirement of marginal stability, while not satisfied for closed quantum systems, can be satisfied for open quantum systems where Lindbladian behavior leads to non-unitary evolution, and allows for nonzero classical stability margins, but it remains difficult to extract physical insight when classical robust control tools are applied to these systems. We consider a straightforward example of the entanglement between two qubits dissipatively coupled to a lossy cavity and analyze it using the classical stability margin and structured perturbations. We attempt, where possible, to extract physical insight from these analyses. Our aim is to highlight where classical robust control can assist in the analysis of quantum systems and identify areas where more work needs to be done to develop specific methods for quantum robust control.