Erasure Thresholds for Hyperbolic and Semi-Hyperbolic Surface Codes

TL;DR

This paper extends erasure noise models to hyperbolic surface codes, demonstrating that they maintain an erasure advantage with thresholds up to 4.7%, similar to planar codes, under various noise models.

Contribution

It introduces a generalized noise model for hyperbolic surface codes and quantifies their erasure thresholds, showing they outperform Pauli noise ratios similar to planar codes.

Findings

Hyperbolic codes achieve thresholds up to 4.7%.

Erasure-to-Pauli ratios are consistent with surface code values.

Erasure advantage extends to hyperbolic surface codes.

Abstract

We extend the circuit-level erasure noise model and Wang et al.\ quadratic expansion fitting of Chang et al.\ from planar surface codes to hyperbolic CSS surface codes. Under Chang et al.'s noise models, the $\{8,3\}$ Bolza fine-grained family threshold reaches $3.6\%$ under the general-Pauli models (which coincide at temporal resolution $\eta = 1$) and $4.7\%$ under the tailored spatially perfect model at $R_e = 1$ (pure erasure). The corresponding erasure-to-Pauli ratios ($5.0\times$ and $6.5\times$) match the surface code values to within $5\%$. Per-observable crossing-point analysis at $R_e = 1$ (Models 1--3) independently yields an erasure-to-Pauli ratio of $5.3\times$. These results establish that the erasure advantage extends to hyperbolic codes.