Hyperbolic and Semi-Hyperbolic Floquet Codes for Photonic Quantum Computing

TL;DR

This paper introduces new hyperbolic Floquet codes suitable for photonic quantum computing, demonstrating their thresholds under various noise models and showing advantages over traditional codes in certain scenarios.

Contribution

The authors construct novel hyperbolic and semi-hyperbolic Floquet codes from specific tessellations, evaluate their performance under multiple noise models, and establish the first photon loss and SPOQC-2 thresholds for these codes.

Findings

All code families achieve ~1.5% threshold under EM3 noise.

The {8,3} code exceeds planar honeycomb photon loss threshold (~8.5-9%).

The {8,3} codes outperform surface codes in fault-tolerant area in SPOQC-2 model.

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.