2-D Compass Codes

TL;DR

This paper investigates a broad class of 2-D compass codes, exploring their threshold behavior under asymmetric noise and their fault-tolerance properties, revealing higher thresholds in certain noise models.

Contribution

It introduces a framework for analyzing 2-D compass codes with varying locality and gauge degrees of freedom, highlighting their improved thresholds against asymmetric noise.

Findings

Higher thresholds against asymmetric noise in idealized models

Codes inherit fault-tolerance features of Bacon-Shor code

Trade-offs between locality, asymmetry, and gauge degrees of freedom

Abstract

The compass model on a square lattice provides a natural template for building subsystem stabilizer codes. The surface code and the Bacon-Shor code represent two extremes of possible codes depending on how many gauge qubits are fixed. We explore threshold behavior in this broad class of local codes by trading locality for asymmetry and gauge degrees of freedom for stabilizer syndrome information. We analyze these codes with asymmetric and spatially inhomogeneous Pauli noise in the code capacity and phenomenological models. In these idealized settings, we observe considerably higher thresholds against asymmetric noise. At the circuit level, these codes inherit the bare-ancilla fault-tolerance of the Bacon-Shor code.