Interfacing Gottesman-Kitaev-Preskill Qubits to Quantum Memories

Gottesman-Kitaev-Preskill (GKP) states have been demonstrated to pose significant advantages when utilized for fault-tolerant all-optical quantum computing and quantum communications links. However, interfacing these systems with long-lived solid-state quantum memories has remained an open problem. We propose an interface between quantum memories and GKP qubit states based on a cavity interaction-mediated controlled displacement gate. We characterize the quality of memory-GKP entanglement as a function of cavity parameters, suggesting optimal operation regimes for high-quality state transfer between either qubit states. We extend this protocol for creating GKP cluster states by avoiding the requirement of ancillary optical quadrature-squeezed light. Utilizing post-selected entanglement swapping operations for GKP qubits, we demonstrate the utility of our protocol for near-deterministic entanglement generation between quantum memories over low-loss quantum links. Extensions and derivatives of our proposal could enable various applications by utilizing the operational trade-offs for qubits encoded in memory and in the GKP basis.