We study a new paradigm for encoding, protecting and manipulating quantum information in a quantum harmonic oscillator (e.g. a high-Q mode of a 3D superconducting cavity) instead of a multi-qubit register . The infinite dimensional Hilbert space of such a system can be used to redundantly encode quantum information. The power of this idea lies in the fact that the dominant decoherence channel in a cavity is photon damping, and (as opposed to multi-qubit quantum error correcting codes) no more decay channels are added if we increase the number of photons we insert in the cavity. Hence, only a single error syndrome needs to be measured to identify if an error has occurred or not.

                        

(a) A protected logical qubit: a register of many physical qubits (case of Steane code). (b) Minimal architecture adapted to circuit QED experiments

In the context of quantum information, the decoherence, caused by the coupling of a system to uncontrolled external degrees of freedom, is generally considered as the main obstacle to synthesize quantum states and to observequantum effects. Paradoxically, it is possible to intentionally engineer a particular coupling to a reservoir in the aim of maintaining the coherence of some particular quantum states. In a general viewpoint, these approaches could be understood in the following manner: by coupling the quantum system to be stabilized to a strongly dissipative ancillary quantum system, one evacuates the entropy of the main system through the dissipation of the ancillary one. By building the feedback loop into the Hamiltonian, this type of autonomous feedback obviates the need for a complicated external control loop to correct errors.

In parallel and in strong interactions with the above experimental goals, we will develop systematic mathematical methods for dynamical analysis, control and estimation of composite and open quantum systems. Here is a list of some of the subjects of interest:

Quantum input-output theory

Stabilization by measurement-based quantum feedback

Filtering, quantum state and parameter estimations

Stabilization by interconnections and stabililty analysis using standard tools: Lyapunov functions, passivity, contraction and invariance principles

Systematic perturbation methods for model reduction

Numerical methods for high-dimensional open quantum systems