Remote Entanglement in Lattice Surgery: To Distill, or Not to Distill

Distributed quantum computing can potentially address the scalability challenge by networking processors through photon-mediated remote entanglement. Prior approaches assumed that remote Bell pairs require distillation before use, incurring substantial overhead, to achieve sufficiently high fidelity. However, recent results show that lattice-surgery operations at logical qubit boundaries tolerate significantly higher error rates than previously assumed. We quantify the resource trade-offs between distillation overhead and surface-code distance requirements under realistic constraints including probabilistic entanglement generation and memory decoherence. We identify the fidelity crossover point separating the two regimes. Below this threshold, the distillation strategy dominates, reducing resource overhead by up to two orders of magnitude. Above it, no-distillation becomes the more efficient choice, reducing resource overhead by more than half. We briefly describe the application of these methods to ion-trap and neutral-atom platforms. These results provide joint design guidelines for optimizing photonic interconnects and fault-tolerant architectures in distributed quantum computing.