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We introduce fault-tolerant (FT) architectures for error correction with theXZZX cluster state based on performing measurements of two-qubit Paulioperators $Z\otimes Z$ and $X\otimes X$, or fusions, on a collection offew-body entangled resource states. Our construction is tailored to beeffective against noise that predominantly causes faulty $X\otimes X$measurements during fusions. This feature offers practical advantage in linearoptical quantum computing with dual-rail photonic qubits, where failed fusionsonly erase $X\otimes X$ measurement outcomes. By applying our construction tothis platform, we find a record high FT threshold to fusion failures exceeding$25\%$ in the experimentally relevant regime of non-zero loss rate per photon,considerably simplifying hardware requirements.

Tailoring fusion-based error correction for high thresholds to biased fusion failures