Rescaling decoder for 2D topological quantum color codes on 4.8.8 lattices

TL;DR

This paper introduces a rescaling decoder for 2D topological color codes on 4.8.8 lattices, demonstrating a threshold of 6.0% for code capacity noise, advancing scalable quantum error correction methods.

Contribution

It presents a novel rescaling decoding approach specifically designed for 2D topological color codes on 4.8.8 lattices, building on prior work for hexagonal lattices.

Findings

Achieved a 6.0% threshold for code capacity noise.

Demonstrated efficiency of the rescaling decoder for 2D color codes.

Extended decoding techniques to new lattice structures.

Abstract

Fault-tolerant quantum computation relies on scaling up quantum error correcting codes in order to suppress the error rate on the encoded quantum states. Topological codes, such as the surface code or color codes are leading candidates for practical scalable quantum error correction and require efficient and scalable decoders. In this work, we propose and study the efficiency of a decoder for 2D topological color codes on the 4.8.8 lattice, by building on the work of [1] for color codes on hexagonal lattices. The decoder is based on a rescaling approach, in which syndrome information on a part of the qubit lattice is processed locally, and then the lattice is rescaled iteratively to smaller sizes. We find a threshold of 6.0% for code capacity noise.