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Quantum systems can be controlled by other quantum systems in a reversibleway, without any information leaking to the outside of the system-controllercompound. Such coherent quantum control is deterministic, is less noisy thanmeasurement-based feedback control, and has potential applications in a varietyof quantum technologies, including quantum computation, quantum communicationand quantum metrology. Here we introduce a coherent feedback protocol,consisting of a sequence of identical interactions with controlling quantumsystems, that steers a quantum system from an arbitrary initial state towards atarget state. We determine the broad class of such coherent feedback channelsthat achieve convergence to the target state, and then stabilise as well asprotect it against noise. Our results imply that also weak system-controllerinteractions can counter noise if they occur with suitably high frequency. Weprovide an example of a control scheme that does not require knowledge of thetarget state encoded in the controllers, which could be the result of a quantumcomputation. It thus provides a mechanism for autonomous, purely quantumclosed-loop control.

Robust control of quantum systems by quantum systems