Coherent versus measurement-based feedback for controlling a single qubit

Abstract

We compare the performance of continuous coherent feedback, implemented using an ideal single-qubit controller, to that of continuous measurement-based feedback (MBF) for the task of controlling the state of a single qubit. We take as the basic dynamical resource the ability to couple the system to a quadrature of a traveling-wave field (for example, a transmission line) via a system observable, and the fundamental limitation is the maximum rate that is available for this coupling. We focus on the question of the best achievable control given ideal controllers. To obtain a fair comparison we acknowledge that the amplification involved in measurement-based control allows the controller to use macroscopic fields to apply feedback forces to the system, so it is natural to allow these feedback forces to be much larger than the mesoscopic coupling to the transmission line that mediates both the measurement for measurement-based control and the coupling to the mesoscopic controller for coherent control. Interestingly our numerical results indicate that under the above platform for comparison, coherent feedback can achieve exactly the performance of MBF given ideal controllers. We also discuss two control mechanisms available to coherent feedback.