Tailoring Fusion-Based Error Correction for High Thresholds to Biased Fusion Failures

We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators Z⊗Z and X⊗X, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to effectively correct noise that predominantly causes faulty X⊗X measurements during fusions. This feature offers a practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase X⊗X measurement outcomes. By applying our construction to this platform, we find a record-high threshold to fusion failures exceeding 25% in the experimentally relevant regime of nonzero loss rate per photon, considerably simplifying hardware requirements.