ResearchPod Summary
This paper investigates which quantum error-correcting code—the Raussendorf-Harrington-Goyal (RHG) code, the Foliated Floquet Color Code (FFCC), or the reduced FFCC—performs best in a compound photon-atom architecture. The authors specifically examine whether the lower graph degree of the FFCC variants provides a performance advantage when accounting for realistic circuit-level loss, including delayed heralding and correlated bond-loss propagation.
To compare these codes, the authors construct two hardware-compatible generation schemes: a bipartite scheme, where qubits maintain their physical type (photon or atom) throughout the entangling sequence, and a State Transfer from Atom to Photon (STAP) scheme, where qubits change type. They use a circuit-level loss model where photon loss is the dominant error mechanism, and they simulate logical error rates (LERs) using Stim and PyMatching. The study also evaluates the impact of excess loss on intermodule connections, simulating a modular hardware environment where long-range links are more prone to failure than local ones.
Under uniform loss conditions, the RHG code achieves the highest circuit-level threshold of 2.75%, outperforming both FFCC variants. While the FFCC variants have lower graph degrees, this benefit does not compensate for their lower intrinsic loss tolerance. However, the performance ranking is sensitive to the architecture's specific loss profile. When intermodule CZ connections are assigned excess loss, the RHG threshold degrades more rapidly than that of the reduced FFCC, eventually reversing the performance order. This demonstrates that the optimal code choice is not determined by graph degree alone, but by the interplay between the code's geometry, the generation schedule, and the physical distribution of loss across the hardware.
This work provides a critical benchmark for modular quantum architectures. It highlights that the theoretical benefits of low-degree codes, often touted in abstract settings, must be carefully weighed against the practical realities of hardware-specific gate ordering and loss propagation. The findings suggest that for modular systems with high intermodule loss, codes with fewer intermodule connections, such as the reduced FFCC, may be more robust than the standard RHG code, despite the latter's superior performance in uniform-loss scenarios.
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