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

Abstract

We introduce fault-tolerant (FT) architectures for error correction with the XZZX cluster state based on performing measurements of two-qubit Pauli operators $Z\otimes Z$ and $X\otimes X$, or fusions, on a collection of few-body entangled resource states. Our construction is tailored to be effective against noise that predominantly causes faulty $X\otimes X$ measurements during fusions. This feature offers practical advantage in linear optical quantum computing with dual-rail photonic qubits, where failed fusions only erase $X\otimes X$ measurement outcomes. By applying our construction to this 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.

7+6 pages, 4+6 figures, comments welcome

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• Tailoring fusion-based photonic quantum computing schemes to quantum emitters
• Encoded-Fusion-Based Quantum Computation for High Thresholds with Linear Optics
• Boosted Bell-state measurements for photonic quantum computation
• Linear-optical fusion boosted by high-dimensional entanglement
• Tailoring Dynamical Codes for Biased Noise: The X${}^3$Z${}^3$ Floquet Code
• Optomechanical resource for fault-tolerant quantum computing