Optimality of qubit purification protocols in the presence of imperfections

TL;DR

This paper investigates how experimental imperfections like detector inefficiency and decoherence affect the optimality of qubit purification protocols, providing insights for real-world quantum control implementations.

Contribution

It analyzes the impact of imperfections on optimal control solutions and introduces a simplified verification theorem for assessing global optimality.

Findings

Optimal control solutions differ significantly with imperfections.

Imperfections can degrade the effectiveness of idealized protocols.

A simplified verification theorem helps evaluate protocol optimality.

Abstract

Quantum control is an essential tool for the operation of quantum technologies such as quantum computers, simulators, and sensors. Although there are sophisticated theoretical tools for developing quantum control protocols, formulating optimal protocols while incorporating experimental conditions remains a challenge. In this paper, motivated by recent advances in realization of real-time feedback control in circuit quantum electrodynamics systems, we study the effect of experimental imperfections on the optimality of qubit purification protocols. Specifically, we find that the optimal control solutions in the presence of detector inefficiency and non-negligible decoherence can be significantly different from the known solutions to idealized dynamical models. In addition, we present a simplified form of the verification theorem to examine the global optimality of a control protocol.