Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

Hyperbolic Floquet codes use only weight-2 measurements and can be implemented directly on hardware with native pair measurements. 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. The $\{10,3\}$ and $\{12,3\}$ families are new to hyperbolic Floquet codes. We evaluate these codes under four noise models. Under ancilla-based Entangling Measurement (EM3) noise, all three families achieve a threshold of $\sim 1.5\mathrm{\%}$. With a native pair-measurement depolarizing model (SDEM3), thresholds are $\sim 1.0$–$1.2\mathrm{\%}$. For heralded photon loss, the $\{8,3\}$ family achieves $\sim 8.5$–$9\mathrm{\%}$, exceeding the planar honeycomb threshold of $\sim 6.3\mathrm{\%}$. In the multi-parameter SPOQC-2 noise model, the $\{8,3\}$ codes achieve a 2D fault-tolerant area $2.2\times$ that of the surface code compiled to pair measurements. We present the first photon loss and SPOQC-2 thresholds for hyperbolic Floquet codes.