Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

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 1.5\%. With a native pair-measurement depolarizing model (SDEM3), thresholds are 1.0--1.2\%. For heralded photon loss, the \8,3\ family achieves 8.5--9\%, exceeding the planar honeycomb threshold of 6.3\%. In the multi-parameter SPOQC-2 noise model, the \8,3\ codes achieve a 2D fault-tolerant area 2.2× that of the surface code compiled to pair measurements. We present the first photon loss and SPOQC-2 thresholds for hyperbolic Floquet codes.