Section: New Results

Stabilization of quantum systems under continuous non-demolition measurements

Participants: Gerardo Cardona, Alain Sarlette and Pierre Rouchon

The stabilization of quantum states or quantum subspaces using feedback signals from quantum non-demolition measurements is a basic control task; in discrete-time, this is the fundamental control property shown in the first quantum feedback experiment by Serge Haroche. In continuous-time, the problem is harder. So-called Markovian feedback can stabilize some states, but in particular the quantum non-demolition eigenstates which would be marginally stable under measurements, cannot be stabilized asymptotically with this technique. Stochastic control techniques, based on feedback from a full state estimator, have been proposed and analyzed to stabilize such eigenstates, proving convergence but not much more. In [12], we prove how a relatively simple controller, feeding back Wiener noise with a gain that depends on eigenstate populations, allows to exponentially stabilize the target eigenstate. This generalizes our previous results about the qubit. In [24], we provide a similar scheme and convergence proof for stabilizing an invariant subspace of the measurement, namely the codespace of a repetition code for quantum error correction. To the best of our knowledge there was no convergence proof so far for stabilizing such subspaces on the basis of continuous measurements.