Efficient Decoding of Topological Color Codes

TL;DR

This paper introduces an efficient iterative decoder for topological color codes, demonstrating a 7.8% error threshold through numerical simulations on a hexagonal lattice, advancing fault-tolerant quantum computation.

Contribution

An alternative efficient iterative decoding method for topological color codes applied to hexagonal lattices, with demonstrated error threshold improvements.

Findings

Error threshold of 7.8% for the proposed decoder

Effective decoding on hexagonal lattice topological codes

Enhanced fault tolerance in quantum computation

Abstract

Color codes are a class of topological quantum codes with a high error threshold and large set of transversal encoded gates, and are thus suitable for fault tolerant quantum computation in two-dimensional architectures. Recently, computationally efficient decoders for the color codes were proposed. We describe an alternate efficient iterative decoder for topological color codes, and apply it to the color code on hexagonal lattice embedded on a torus. In numerical simulations, we find an error threshold of 7.8% for independent dephasing and spin flip errors.