# Near-Optimal Decoding Algorithm for Color Codes Using Population Annealing

## TL;DR

This paper introduces a new decoding algorithm for quantum error correction that achieves high performance across various noise models.

## Contribution

A novel decoder using Population Annealing to estimate error recovery probabilities in quantum codes is proposed and evaluated.

## Key findings

- The decoder reaches near-optimal thresholds for bit-flip and depolarizing noise.
- It achieves the highest reported threshold for phenomenological noise in color codes.
- The algorithm is applicable to multiple stabilizer codes like surface and qLDPC codes.

## 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 for bit-flip and depolarizing noise, and the highest reported threshold for phenomenological noise. This decoding algorithm can be applied to a wide variety of stabilizer codes, including surface codes and quantum Low-Density Parity Check (qLDPC) codes.