Analytical determination of quantum error-correction thresholds

Determine analytical threshold values for quantum error-correction codes and noise models whose thresholds are not currently known analytically.

Background

The paper identifies the threshold as a central performance metric for quantum error-correction protocols: it is the physical error rate below which the logical error rate can be made arbitrarily small by increasing code size. Although numerical Monte Carlo simulations can estimate thresholds, such simulations are computationally intensive, motivating simpler analytical or heuristic approaches.

This unresolved issue is broader than any single code family or noise model. The paper proposes an entropy-based proxy that estimates thresholds across several settings, but it does not analytically determine the exact thresholds for the general class of codes and noise models referenced in the statement.

References

For most QEC codes and noise models, however, thresholds are not known analytically, and estimating them requires computationally intensive Monte Carlo simulations of logical error rates across multiple code sizes and noise strengths.

— Entropy threshold: A simple proxy for performance of quantum error correction  (2609.39016 - Ruiz et al., 30 Sep 2026) in Introduction, paragraph beginning “Quantum error correction (QEC) is essential...”