  We address the standard quantum error correction using the three-qubit
bit-flip code, yet in continuous-time. This entails rendering a target manifold
of quantum states globally attractive. Previous feedback designs could feature
spurious equilibria, or resort to discrete kicks pushing the system away from
these equilibria to ensure global asymptotic stability. We present a new
approach that consists of introducing controls driven by Brownian motions.
Unlike the previous methods, the resulting closed-loop dynamics can be shown to
stabilize the target manifold exponentially. We further present a reduced-order
filter formulation with classical probabilities. The exponential property is
important to quantify the protection induced by the closed-loop
error-correction dynamics against disturbances. We study numerically the
performance of this control law and of the reduced filter.
