Decoding 3D color codes with boundaries

TL;DR

This paper extends 2D color code decoders to 3D, achieving near-optimal error correction thresholds and providing tools for visualization, thereby advancing the practicality of 3D color codes in fault-tolerant quantum computing.

Contribution

It introduces a 3D restriction decoder with boundaries for color codes, achieving higher thresholds and optimal scaling, along with a visualization package for analysis.

Findings

Achieved a threshold of 1.55(6)% for 3D color codes.

Demonstrated optimal scaling of logical error rates.

Provided a Python visualization tool for 3D color codes.

Abstract

Practical large-scale quantum computation requires both efficient error correction and robust implementation of logical operations. Three-dimensional (3D) color codes are a promising candidate for fault-tolerant quantum computation due to their transversal non-Clifford gates, but efficient decoding remains challenging. In this work, we extend previous decoders for two-dimensional color codes [1], which are based on the restriction of the decoding problem to a subset of the qubit lattice, to three dimensions. Including boundaries of 3D color codes, we demonstrate that the 3D restriction decoder achieves optimal scaling of the logical error rate and a threshold value of 1.55(6)% for code-capacity bit- and phase-flip noise, which is almost a factor of two higher than previously reported for this family of codes [2, 3]. We furthermore present qCodePlot3D, a Python package for visualizing 2D and 3D color codes, error configurations, and decoding paths, which supports the development and analysis of such decoders. These advancements contribute to making 3D color codes a more practical option for exploring fault-tolerant quantum computation.