Distributed Hyperbolic Floquet Codes under Depolarizing and Erasure Noise

Abstract: Distributing qubits across quantum processing units (QPUs) connected by shared entanglement enables scaling beyond monolithic architectures. Hyperbolic Floquet codes use only weight-2 measurements and are good candidates for distributed quantum error correcting codes. We construct hyperbolic and semi-hyperbolic Floquet codes from ${8,3}$, ${10,3}$, and ${12,3}$ tessellations via the Wythoff kaleidoscopic construction with the Low-Index Normal Subgroups (LINS) algorithm and distribute them across QPUs via spectral bisection. The ${10,3}$ and ${12,3}$ families are new to hyperbolic Floquet codes. We simulate these distributed codes under four noise models: depolarizing, SDEM3, correlated EM3, and erasure. With depolarizing noise ($p_{\text{local}} = 0.03\%$), fine-grained codes achieve non-local pseudo-thresholds up to 3.0\% for ${8,3}$, 3.0\% for ${10,3}$, and 1.75\% for ${12,3}$. Correlated EM3 yields pseudo-thresholds up to 0.75\% for ${8,3}$, 0.75\% for ${10,3}$, and 0.50\% for ${12,3}$; crossing-based thresholds from same-$k$ families are ${\sim}1.75$--$2.9\%$ across all tessellations. Using the SDEM3 model, fine-grained codes achieve distributed pseudo-thresholds of 1.75\% for ${8,3}$, 1.25\% for ${10,3}$, and 1.00\% for ${12,3}$. Under erasure noise motivated by spin-optical architectures, thresholds at 1\% local loss are 35--40\% for ${8,3}$, 30--35\% for ${10,3}$, and 25--30\% for ${12,3}$.