The Equations of Quantum Feedback Control in the Regime of Good Control

TL;DR

This paper derives the equations governing quantum feedback control in the regime of good control, revealing linear dynamics for single qubits but nonlinear behavior for larger systems, and analyzes steady-state performance of feedback protocols.

Contribution

It introduces the equations of motion for quantum feedback control in the good control regime, highlighting differences from classical systems and providing a first application to steady-state performance.

Findings

Single qubit dynamics are linear in this regime.

Larger systems exhibit nonlinear dynamics, unlike classical counterparts.

Steady-state performance of feedback protocols is characterized.

Abstract

We derive the equations of motion describing the feedback control of quantum systems in the regime of "good control", in which the control is sufficient to keep the system close to the desired state. One can view this regime as the quantum equivalent of the "linearized" regime for feedback control of classical nonlinear systems. Strikingly, while the dynamics of a single qubit in this regime is indeed linear, that of all larger systems remains nonlinear, in contrast to the classical case. As a first application of these equations, we determine the steady-state performance of feedback protocols for a single qubit that use unbiased measurements.