2026/07/27 by Mathys Rennela
#quant-ph #cs.DC
Multi-gate teleportation (MGT) packages n remote gates into a single ebit via a 1-ebit fan-out quantum circuit, saving n-1 entangled pairs relative to sequential gate teleportation. The cost is a correlated failure mode: a single network fault propagates through the fan-out tree, injecting a weight-n Pauli error on the target register (weight n+1 including the control). We establish a design rule for fault-tolerant packet sizes in rotated surface codes of odd distance~d: a rigorous decoder-independent floor \lfloor d/2 \rfloor, extended to \lceil d/2 \rceil by a local weight argument confirmed by simulation when the decoder is correlation-aware. Simulation with PyMatching shows the standard MWPM decoder built from the packet circuit's detector error model (DEM) naturally corrects the correlated error: at n=\lfloor d/2\rfloor the packet matches or surpasses the per-link sequential LER for moderate-to-high γ, with the crossover γ^⋆ decreasing as d grows (from γ^⋆≈17 at d=5 to γ^⋆<1 at d=9, extrapolated), whilst reducing the entanglement cost from n ebits to~1. Packetisation wins when the network is the bottleneck (γ≫ 1); at γ≈ 1 the packet is marginally worse (≤1.13× at d∈\5,7\, reversing by d=9) as the n-1 extra local fan-out gates offset the network savings. No custom decoding algorithm is required: the standard MWPM decoder, built from the packet circuit's DEM, already encodes the correlation.