We propose an interface between solid-state quantum memories and Gottesman-Kitaev-Preskill encoded photonic qubits using cavity-assisted controlled phase gates [1, 2]. Our protocol yields capacity-approaching high rate of heralded entanglement among quantum memory registers in the low-loss regime.
Entangling quantum memories, mediated by optical-frequency or microwave channels, at high rates and fidelities is key for linking qubits across short and long ranges. All well-known protocols encode up to one qubit per optical mode, entangling one pair of memory qubits per transmitted mode over the channel, with probability η, the channel’s transmissivity. The rate is proportional to η ideal Bell states (ebits) per mode. The quantum capacity, C(η)=−log2(1−η) ebits per mode, which ≈1.44η for high loss, thereby making these schemes near rate-optimal. However, C(η)→∞ as η→1, making the known schemes highly rate-suboptimal for shorter ranges. We propose a cavity-assisted memory–photon interface that can be used to entangle matter memories with Gottesman–Kitaev–Preskill (GKP) photonic qudits, which, along with dual-homodyne entanglement swaps that retain analog information, enables entangling memories at capacity-approaching rates at low loss. We benefit from the loss resilience of GKP-encoded states and the ability to encode multiple qubits in one mode. Our memory–photon interface further supports the preparation of needed ancilla GKP qudits. We expect our result to spur research in low-loss, high-cooperativity cavity-coupled qubits with high-efficiency optical coupling and demonstrations of high-rate short-range quantum links.
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.
Distributing entanglement directly between error-corrected logical qubits is an important capability for scalable quantum networks. We propose a heralded protocol for generating remote entanglement between Gottesman--Kitaev--Preskill qubits encoded in the motional modes of spatially separated trapped ions, using the internal electronic states to interface the motional qubits with emitted photons. We derive the protocol for single-rail and polarization photonic encodings and evaluate the effects of finite GKP squeezing, photon loss, photon recoil, motional heating, and motional dephasing on the decoded logical state. Moreover, we numerically analysed the fidelity of distributed logical Bell-pair fidelity. We find that one can achieve more than 95% of fidelity in the realistic situation. The protocol combines motional-control and photonic-networking operations that have already been demonstrated in trapped-ion experiments.
There are various approaches to long-range quantum communication based on conceptually different forms of quantum repeaters. Here, we explore a quantum repeater scheme that employs quantum error correction (QEC) both on the flying (light) qubits and on the stationary (matter) qubits. The idea is to combine the benefits of encoded one-way and two-way schemes where effective channel transmission and loss scaling are enhanced by means of photon loss codes and encoded quantum memories, respectively, while sacrificing some of their advantages, such as high clock rates, independent of classical communication times (one-way), and potentially large segment lengths (two-way). More specifically, we illustrate, propose, and analyze such a quantum repeater using the bosonic Gottesman-Kitaev-Preskill (GKP) code, which naturally enables encoding and QEC of qudits, protecting them against transmission and memory loss, the latter, for instance, occurring on collective spin modes of atomic ensembles. While the encoded one-way and two-way schemes on their own either require very high repeater link coupling efficiencies and GKP squeezing or allow for experimentally more feasible, small values of these parameters, respectively, we find that there are intermediate parameter regimes where the combined repeater protocol is superior.