Proposal for a Logical Qubit Encoded into a Stabilized Manifold in Two Bosonic Modes.*

We introduce a driven-dissipative two-mode bosonic system whose reservoir causes simultaneous loss of two photons in each mode and whose steady states are superpositions of Barut-Girardello pair-coherent states. Quantum information encoded in a manifold spanned by these states is exponentially immune to phase drifts (cavity dephasing) in both modes. It is also possible to protect the encoded information from photon loss in either mode by continuously monitoring an error syndrome given by the photon number difference of the two modes. Furthermore, this monitoring can be done with current circuit QED technology without turning off the dissipative stabilizing process. In this talk, we will briefly introduce the general concept of this approach to quantum error correction as well as the specific encoding used. An overview of a potential implementation for this system in the framework of circuit QED will also be presented.