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 continuous-variable quantum computing as well as for quantum communications links for entanglement distribution. However interfacing these systems to long-lived solid-state quantum memories has remained an open problem. Here we propose an interface between quantum memories and GKP qubit states based on a cavity-mediated controlled displacement gate. We characterize the quality of memory-GKP entanglement as a function of cavity parameters suggesting optimal regimes of operation for high-quality state transfer between either qubit states. We further extend this protocol to demonstrate the creation of 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 high-rate entanglement generation between quantum memories. Extensions and derivatives of our proposal could enable a wide variety of applications by utilizing the operational trade-offs for qubits encoded in memory and in the GKP basis.