Labubu: Layer-Buffered Bundled Optimization for Efficient Remote Gate Scheduling in Distributed Quantum Computing

Distributed Quantum Computing (DQC) expands qubit capacity by interconnecting multiple Quantum Processing Units (QPUs), but remote gate execution introduces significant entanglement overhead. In this paper, we investigate the Remote Gate Scheduling problem in DQC (RGS-DQC) under a hybrid Telegate and Teledata model, provide a formal formulation, and establish its NP-hardness. To address this challenge, we propose LABUBU, a layer-buffered bundled optimization framework that integrates coordinate-wise pruned greedy refinement with bounded perturbation under QPU capacity constraints while maintaining linear complexity per iteration. Extensive simulations on both structured Quantum Fourier Transform circuits and unstructured random circuits show that Labubu consistently reduces entanglement cost compared with Telegate-SA, Telegate-RD, Teledata-ZS, and the competitive GateCover baseline. Experiments on QEC encoded circuits further confirm its potential for large scale fault tolerant distributed quantum computing.