Performance Bounds for Quantum Feedback Control

TL;DR

This paper develops a hierarchy of convex optimization bounds for quantum feedback control performance, providing fundamental limits, optimality certificates, and near-optimal controller design for quantum systems.

Contribution

It introduces a novel method combining quantum filtering and sum-of-squares techniques to compute bounds on quantum feedback control performance.

Findings

Bounds converge to optimal performance under certain conditions

Designed near-optimal controllers for a qubit in a cavity

Provides a framework for certifying quantum control performance

Abstract

The limits of quantum feedback control have immediate consequences for quantum information science at large, yet remain largely unexplored. Here, we combine quantum filtering theory and moment-sum-of-squares techniques to construct a hierarchy of convex optimization problems that furnish monotonically improving, computable bounds on the best attainable performance for a broad class of quantum feedback control problems. These bounds may serve as witnesses of fundamental limitations, optimality certificates, or performance targets. We prove convergence of the bounds to the optimal control performance under technical conditions and demonstrate the practical utility of our approach by designing certifiably near-optimal controllers for a qubit in a cavity subjected to photon counting and homodyne detection measurements.