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We address the standard quantum error correction using the three-qubitbit-flip code, yet in continuous-time. This entails rendering a target manifoldof quantum states globally attractive. Previous feedback designs could featurespurious equilibria, or resort to discrete kicks pushing the system away fromthese equilibria to ensure global asymptotic stability. We present a newapproach that consists of introducing controls driven by Brownian motions.Unlike the previous methods, the resulting closed-loop dynamics can be shown tostabilize the target manifold exponentially. We further present a reduced-orderfilter formulation with classical probabilities. The exponential property isimportant to quantify the protection induced by the closed-looperror-correction dynamics against disturbances. We study numerically theperformance of this control law and of the reduced filter.

Continuous-time Quantum Error Correction with Noise-assisted Quantum Feedback