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

Fernando Martínez-García¹, Francisco Revson F Pereira², Pedro Parrado-Rodríguez³

¹Instituto de Física Fundamental IFF-CSIC, Calle Serrano 113b, 28006 Madrid, Spain.

Entropy (Basel, Switzerland)

|January 28, 2026

Summary

This summary is machine-generated.

We developed a novel quantum error correction decoder using Population Annealing. This method efficiently identifies the best recovery operation, achieving near-optimal thresholds for key quantum noise models.

Keywords:

color codes decoder population annealing quantum error correction

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Area of Science:

Quantum Computing
Quantum Error Correction
Computational Physics

Background:

Large-scale quantum computing necessitates robust quantum error-correcting (QEC) codes.
Effective QEC relies on accurate syndrome decoding to determine recovery operations.
Current decoding methods face challenges with complex noise models.

Purpose of the Study:

To implement and evaluate a new decoder for quantum error correction.
To map the decoding problem to a spin system for analysis.
To assess decoder performance under various realistic noise conditions.

Main Methods:

Developed a decoder that maps QEC syndrome decoding to a spin system problem.
Utilized Population Annealing to estimate free energies of error classes.
Tested the decoder on a 4.8.8 color code lattice.

Main Results:

Achieved near-optimal performance thresholds for bit-flip and depolarizing noise models.
Reported the highest threshold to date for phenomenological noise, including measurement errors.
Demonstrated decoder effectiveness across different quantum error correction codes.

Conclusions:

The Population Annealing-based decoder offers high success probability for identifying quantum error recovery operations.
This approach is broadly applicable to various stabilizer codes like surface and qLDPC codes.
The decoder shows significant promise for advancing fault-tolerant quantum computation.