GKP state preparation via a driven, dissipative superconducting circuit

The Gottesman-Kitaev-Preskill (GKP) code is a scheme for encoding a qubit in a harmonic oscillator that enjoys significant robustness against noise. In spite of the theoretical advantages, implementing this code experimentally remains challenging. To that end, we propose a novel protocol to prepare, stabilize, and manipulate GKP qubit states in a driven, dissipative superconducting circuit consisting of an LC circuit in parallel with a Josephson junction and resistor. We demonstrate numerically and analytically how this protocol is able to efficiently realize GKP states for a wide range of experimentally accessible parameters, and passively correct against errors taking the system out of the codespace. Our proposal has the additional advantage that it does not rely on frequency combs, greatly simplifying the experimental setup.