Quantum feedback for rapid state preparation in the presence of control imperfections

TL;DR

This paper analyzes the robustness of quantum feedback protocols for rapid state preparation against various control imperfections, highlighting the impact of delays, detection inefficiencies, and system noise.

Contribution

It provides a detailed analysis of how different control imperfections affect the performance of quantum feedback protocols using the Wiseman-Milburn formalism.

Findings

Time delays critically affect protocol performance.

Detection inefficiencies are more impactful in slow systems.

System noise like dephasing can be incorporated into the model.

Abstract

Quantum feedback control protocols can improve the operation of quantum devices. Here we examine the performance of a purification protocol when there are imperfections in the controls. The ideal feedback protocol produces an $x$ eigenstate from a mixed state in the minimum time, and is known as rapid state preparation. The imperfections we examine include time delays in the feedback loop, finite strength feedback, calibration errors, and inefficient detection. We analyse these imperfections using the Wiseman-Milburn feedback master equation and related formalism. We find that the protocol is most sensitive to time delays in the feedback loop. For systems with slow dynamics, however, our analysis suggests that inefficient detection would be the bigger problem. We also show how system imperfections, such as dephasing and damping, can be included in model via the feedback master equation.