Stabilization and logical operation of GKP qubits in a fully 2D architecture

Gottesman-Kitaev-Preskill qubits represent a promising avenue for bosonic quantum error correction, with break-even performance demonstrated in microwave 3D cavities controlled by ancilla transmon qubits. Fault-tolerant quantum computation could be achieved through the concatenation of stabilized GKP qubits with a quantum error-correcting code, provided the logical error rate of GKP qubits could be maintained below the threshold of such codes. We envision that at least two key modifications to existing stabilization protocols will be required to unlock that goal. On the one hand, replacing ancilla transmons by protected qubits to mitigate ancilla error backpropagation would lift the current primary limitation on observed logical lifetime. On the other hand, developing fully-2D architectures would enhance the scalability of multi-qubit devices.

In this work, we focus on a recent proposal for stabilizing a GKP qubit in the high-quality mode of a planar resonator coupled to a protected heavy fluxonium ancilla qubit. We analyze the performance of a new stabilization protocol adapted to this 2D architecture, utilizing a microwave-activated three-wave mixing coupler, and present our progress towards extending this architecture to multi-qubit settings.