Tailoring Fusion-Based Error Correction for High Thresholds to Biased Fusion Failures
Kaavya Sahay, Jahan Claes, Shruti Puri · Physical Review Letters · 2023
We introduce fault-tolerant (FT) architectures for error correction with the $XZZX$ cluster state based on performing measurements of two-qubit Pauli operators $Z\ensuremath{\bigotimes}Z$ and $X\ensuremath{\bigotimes}X$, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to effectively correct noise that predominantly causes faulty $X\ensuremath{\bigotimes}X$ measurements during fusions. This feature offers a practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase $X\ensuremath{\bigotimes}X$ 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.