Circuit-Level Loss Performance of FFCC and RHG Codes in a Compound Photon-Atom Quantum Architecture
We compare the Raussendorf-Harrington-Goyal (RHG) code, the Foliated Floquet Color Code (FFCC), and the reduced FFCC in a compound photon-atom architecture that directly generates measurement-based quantum computation (MBQC) resources with near-deterministic photon-atom CZ gates. RHG serves as a natural benchmark, while the FFCC variants allow us to study whether reduced graph degree improves performance under an architecture-aware circuit-level loss model with delayed heralding and correlated bond-loss propagation. We construct two generation schemes compatible with the compound hardware and evaluate circuit-level thresholds under periodic boundary conditions. RHG achieves the highest circuit-level threshold, 2.75%, and its threshold falls below that of reduced FFCC only for large excess loss on intermodule CZ connections. RHG also achieves the lowest logical error rate in most resource-matched comparisons, but some low-loss windows favor reduced FFCC. Overall, we show that when the hardware supports the native gates and connectivity required for MBQC, the benefits of lower graph degree must be weighed against each code's intrinsic IID loss tolerance, generation-scheme details, and hardware-aware resource overhead.