Near-optimal decoding algorithm for color codes using Population Annealing

TL;DR

This paper presents a near-optimal decoding algorithm for quantum color codes using Population Annealing, improving error correction performance across various noise models in quantum computing.

Contribution

Introduces a decoding method that maps quantum error correction to a spin system and employs Population Annealing for near-optimal decoding in color codes.

Findings

Achieves near-optimal thresholds under different noise models

Applicable to various stabilizer codes including surface and qLDPC codes

Demonstrates high success probability in decoding performance

Abstract

The development and use of large-scale quantum computers relies on integrating quantum error-correcting (QEC) schemes into the quantum computing pipeline. A fundamental part of the QEC protocol is the decoding of the syndrome to identify a recovery operation with a high success rate. In this work, we implement a decoder that finds the recovery operation with the highest success probability by mapping the decoding problem to a spin system and using Population Annealing to estimate the free energy of the different error classes. We study the decoder performance on a 4.8.8 color code lattice under different noise models, including code capacity with bit-flip and depolarizing noise, and phenomenological noise, which considers noisy measurements, with performance reaching near-optimal thresholds. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum low-density parity-check (qLDPC) codes.