Design rules for fault-tolerant multi-gate teleportation

2026-07-01

AI Summary

This work addresses the challenge of correlated errors induced by network failures in multi-gate teleportation, which can compromise fault tolerance. To preserve fault tolerance while maximizing the number of gates that can be batched together, the authors develop a correlation-aware, circuit-level noise model and derive an upper bound on the maximum batch size for fault-tolerant multi-gate teleportation under the rotated surface code: $n_{\text{max}}^{\text{corr}}(d) = \lceil d/2 \rceil$. This is the first theoretical bound that explicitly accounts for error correlations. The study further demonstrates that the standard minimum-weight perfect matching (MWPM) decoder suffices for effective error correction, obviating the need for customized decoding strategies. In noise regimes dominated by entanglement generation errors ($\gamma \gg 1$), the proposed approach significantly reduces resource overhead compared to gate-by-gate teleportation while maintaining or improving upon the original logical error rate.

Abstract

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. We derive a design rule for fault-tolerant packet sizes, $\nmax^{\text{corr}}(d) = \lceil d/2 \rceil$ for rotated surface codes of distance~$d$ with a correlation-aware decoder ($\nmax^{\text{naive}} = \lfloor d/2 \rfloor$ without), bounding how many gates can be packaged whilst preserving fault tolerance. Simulation with PyMatching shows that the standard MWPM decoder built from the packet circuit's noise model naturally corrects the correlated error: at network-to-local noise ratios $γ= \pnet/\pgate$ up to $100$, the packet matches or surpasses the per-link sequential LER at moderate-to-high $γ$, with the advantage growing with both $γ$ and $d$, whilst reducing the entanglement cost from $n$ ebits to~$1$. Packetisation wins when the network is the bottleneck ($γ\gg 1$); at $γ\approx 1$ the $n{-}1$ extra local fan-out gates offset the network savings. No custom decoder is required: the circuit-level noise model already encodes the correlation. These results enable noise-aware distributed circuit compilers to favour fan-out packetisation without sacrificing fault tolerance.

Problem

• fault tolerance
• multi-gate teleportation
• correlated errors
• quantum error correction
• entanglement cost

Innovation

• multi-gate teleportation
• fault tolerance
• correlated errors
• surface codes
• entanglement efficiency