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

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