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, resulting in substantial overhead, to achieve sufficiently high fidelity before use. 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 and show that choosing the right strategy can reduce resource overhead by up to two orders of magnitude at low fidelities and up to 68% at high fidelities. We briefly describe the application of these methods to ion-trap and neutral-atom platforms. These results provide co-design principles for optimizing photonic interconnects and fault-tolerant architectures in distributed quantum computers.