Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

Tailoring error correcting codes to the structure of the physical noise can reduce the overhead of fault-tolerant quantum computation. 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: phenomenological, ancilla Entangling Measurement (EM3), Single-step Depolarizing EM3 (SDEM3), and erasure. Under phenomenological noise, specific-logical threshold crossings occur near p_e approx 0.3--0.5\% for \{8,3\} $k=6$--$56$ and 0.15--0.2\% for \{10,3\} $k=12$--$146$. EM3 ancilla noise yields a threshold of {sim}1.5\% for all three families. SDEM3 is a depolarizing noise model motivated by Majorana tetron architectures; fine-grained codes achieve thresholds of {sim}1.0--1.2\% for all three families. The erasure model captures detected photon loss on spin-optical links; fine-grained codes achieve erasure thresholds of {sim}8.5--9\% for \{8,3\}, {sim}7--8\% for \{10,3\}, and {sim}6.5--8\% for \{12,3\}. Photon loss is the dominant error source in photon-mediated quantum computing. Under the full three-parameter SPOQC-2 noise model, the \{8,3\} codes achieve a 2D fault-tolerant area 2.2times that of the surface code compiled to pair measurements while encoding k = 10 logical qubits. In a companion paper, we evaluate the same code families in a distributed setting.