  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.
