Constructions and performance of hyperbolic and semi-hyperbolic Floquet codes

TL;DR

This paper introduces hyperbolic and semi-hyperbolic Floquet codes with high efficiency and improved scaling, demonstrating their advantages over traditional surface codes in quantum error correction.

Contribution

The authors construct new families of Floquet codes from hyperbolic surface tilings and semi-hyperbolic methods, achieving higher efficiency and better scaling than existing codes.

Findings

Semi-hyperbolic Floquet codes are up to 48 times more efficient than planar honeycomb codes.

These codes can encode multiple logical qubits with minimal physical qubits at low noise levels.

Significant improvements in error correction performance over surface codes at realistic noise rates.

Abstract

We construct families of Floquet codes derived from colour code tilings of closed hyperbolic surfaces. These codes have weight-two check operators, a finite encoding rate and can be decoded efficiently with minimum-weight perfect matching. We also construct semi-hyperbolic Floquet codes, which have improved distance scaling, and are obtained via a fine-graining procedure. Using a circuit-based noise model that assumes direct two-qubit measurements, we show that semi-hyperbolic Floquet codes can be $48\times$ more efficient than planar honeycomb codes and therefore over $100\times$ more efficient than alternative compilations of the surface code to two-qubit measurements, even at physical error rates of $0.3\%$ to $1\%$. We further demonstrate that semi-hyperbolic Floquet codes can have a teraquop footprint of only 32 physical qubits per logical qubit at a noise strength of $0.1\%$. For standard circuit-level depolarising noise at $p=0.1\%$, we find a $30\times$ improvement over planar honeycomb codes and a $5.6\times$ improvement over surface codes. Finally, we analyse small instances that are amenable to near-term experiments, including a Floquet code derived from the Bolza surface that encodes four logical qubits into 16 physical qubits.