Fault-tolerant Compass Codes

TL;DR

This paper introduces a fault-tolerant scheme for a class of gauge-fixed Bacon-Shor codes, including generalized surface codes, demonstrating improved performance under biased noise through optimized geometry and an efficient decoder.

Contribution

It presents a novel fault-tolerant measurement scheme for gauge-fixed Bacon-Shor codes and extends the union-find decoder to biased noise models, achieving a high threshold.

Findings

Fault tolerance achieved via direct stabilizer measurements.

Optimized surface code performance by stretching stabilizer geometry.

Union-find decoder adapted for biased noise with 0.83% threshold.

Abstract

We study a class of gauge fixings of the Bacon-Shor code at the circuit level, which includes a subfamily of generalized surface codes. We show that for these codes, fault tolerance can be achieved by direct measurements of the stabilizers. By simulating our fault-tolerant scheme under biased noise, we show the possibility of optimizing the performance of the surface code by stretching the bulk stabilizer geometry. To decode the syndrome efficiently and accurately, we generalize the union-find decoder to biased noise models. Our decoder obtains a $0.83\%$ threshold value for the surface code in quadratic time complexity.