Entropy threshold: A simple proxy for performance of quantum error correction
Abstract
The rapidly growing landscape of quantum error-correction (QEC) protocols has produced a wealth of numerical data, but comparatively few heuristics for understanding and predicting their performance. Here, we develop a simple entropy-based proxy that predicts the thresholds of a variety of QEC protocols, ranging from the code-capacity setting of Clifford-deformed surface codes with biased Pauli or erasure noise to the circuit-level noise model of the surface or color codes with flag qubits. Our proxy estimates the threshold by locally comparing the noise entropy with the error information gained via stabilizer measurements (or spacetime detectors and flag outcomes in the circuit-level settings). Despite neglecting correlations between stabilizer outcomes and the contribution from code degeneracy, the proxy captures the main trends across diverse settings and yields threshold estimates in good agreement with numerical results. Our work develops much-needed phenomenology that enables simple back-of-the-envelope estimates of QEC performance, recovering and providing an explanation for the results of computationally intensive detailed simulations.
Related
- Ensemble Dependence of the Critical Exponent at a Quantum Error Correction Threshold
- Quantum error correction well below the color code threshold
- Logarithmic correction to the entropy of near-extremal higher-curvature black holes
- Bosonic quantum error correction with microwave cavities for quantum repeaters
- Error-Correction Transitions in Finite-Depth Quantum Channels
BibTeX
@misc{ruiz2026entropy,
title = {{Entropy threshold: A simple proxy for performance of quantum error correction}},
author = {Diego Ruiz and Aleksander Kubica},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39016},
eprint = {2609.39016},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39016},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Entropy threshold: A simple proxy for performance of quantum error correction
AU - Diego Ruiz
AU - Aleksander Kubica
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39016
UR - https://arxiv.org/abs/2609.39016
AB - The rapidly growing landscape of quantum error-correction (QEC) protocols has produced a wealth of numerical data, but comparatively few heuristics for understanding and predicting their performance. Here, we develop a simple entropy-based proxy that predicts the thresholds of a variety of QEC protocols, ranging from the code-capacity setting of Clifford-deformed surface codes with biased Pauli or erasure noise to the circuit-level noise model of the surface or color codes with flag qubits. Our proxy estimates the threshold by locally comparing the noise entropy with the error information gained via stabilizer measurements (or spacetime detectors and flag outcomes in the circuit-level settings). Despite neglecting correlations between stabilizer outcomes and the contribution from code degeneracy, the proxy captures the main trends across diverse settings and yields threshold estimates in good agreement with numerical results. Our work develops much-needed phenomenology that enables simple back-of-the-envelope estimates of QEC performance, recovering and providing an explanation for the results of computationally intensive detailed simulations.
ER -