Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing
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Abstract
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 ${\sim}1.5\%$. With a native pair-measurement depolarizing model (SDEM3), thresholds are ${\sim}1.0$--$1.2\%$. For heralded photon loss, the $\{8,3\}$ family achieves ${\sim}8.5$--$9\%$, exceeding the planar honeycomb threshold of ${\sim}6.3\%$. 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.