Experimental implementation of fault-tolerant error syndrome measurement for pair-cat code (1/2)

Stabilized quantum manifolds of a bosonic system can encode error-protected qubits. In particular, a single-mode manifold spanned by cat states can exponentially suppress against phase-flip errors. However, errors due to photon loss cannot be corrected without stopping the stabilization process, using existing microwave superconducting circuit technology. Phase-flip suppression can also be achieved by stabilizing a manifold spanned by pair-cat states, which are superpositions of the two-mode states called Barut-Girardello/pair-coherent states. Moreover, it is now possible to detect, in a fault-tolerant manner, photon-loss errors in either mode, simultaneously with the manifold stabilization, by monitoring the photon-number difference between them. In this talk, we will present an experimental implementation of cavities and superconducting devices that is compatible with such encoding. We will also report on techniques of continuous monitoring of the photon number difference between the modes. Part-one of this two-part presentation will introduce the basic theoretical concepts of pair-cat codes and the design parameters of our experimental implementation.