Transversal Fault Tolerant Distributed Quantum Computing Operations

Scalable quantum computing requires distributed architectures, but the performance of faulttolerant operations across noisy inter-module links remains poorly characterized. We present the first full-circuit simulations of two key distributed primitives: transversal non-local CNOT and logical teleportation using surface and bivariate-bicycle codes with imperfect inter-module links. Our results, enabled by a novel scalable library (TMCBS), demonstrate that both transversal operations outperform their lattice surgery counterparts. Notably, we find that the non-local CNOT achieves up to 100× lower logical error rates than teleportation at the same code distance and noise levels. We further show that a surface code distance of d ≈ 31 suffices to achieve logical error rates below 10^{−12} at practical physical error rates (p ∼ 10−3), enabling large-scale algorithms. These results provide critical guidance for architecture and code selection in distributed quantum computing.