Design rules for fault-tolerant multi-gate teleportation

arXiv:2607.01342v2 Announce Type: replace 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 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 $\gamma$, with the crossover $\gamma^\star$ decreasing as $d$ grows (from $\gamma^\star{\approx}17$ at $d{=}5$ to $\gamma^\star{<}1$ at $d{=}9$, extrapolated), whilst reducing the entanglement cost from $n$ ebits to~$1$. Packetisation wins when the network is the bottleneck ($\gamma \gg 1$); at $\gamma \approx 1$ the packet is marginally worse ($\leq1.13\times$ at $d\in\{5,7\}$, 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.

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 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 $\gamma$, with the crossover $\gamma^\star$ decreasing as $d$ grows (from $\gamma^\star{\approx}17$ at $d{=}5$ to $\gamma^\star{<}1$ at $d{=}9$, extrapolated), whilst reducing the entanglement cost from $n$ ebits to~$1$. Packetisation wins when the network is the bottleneck ($\gamma \gg 1$); at $\gamma \approx 1$ the packet is marginally worse ($\leq1.13\times$ at $d\in\{5,7\}$, 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.

Quantum Physics (quant-ph); Distributed, Parallel, and Cluster Computing (cs.DC)

arXiv:2607.01342 [quant-ph]

(or arXiv:2607.01342v2 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2607.01342 Focus to learn more arXiv-issued DOI via DataCite

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Design rules for fault-tolerant multi-gate teleportation

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