Quantum

Surface codes with coherent errors: optimal decoding and finite-size crossovers

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Based on a feed excerpt; full article content has not been acquired. Source evidence retrieved 11/11/2026, 05:13:25 UTC.

Briefings

Research on surface codes with coherent errors identifies a ballistic-crossover scale where Pauli decoding and coherent information exhibit distinct finite-size behaviors. The study derives a quartic interaction in replicated Majorana theory, leading to a scaling variable X4 that explains the collapse of decoding measures in free-fermion simulations. These findings support a Pauli-decoding threshold at theta_c=pi/4 in the thermodynamic limit, with even system sizes showing maximum-likelihood decoding maximizes entanglement fidelity.

Key points

• Surface codes with uniform coherent Z rotations followed by perfect syndrome measurements exhibit strong finite-size effects complicating asymptotic decoding threshold extraction.
• The study derives a leading inter-flavor quartic interaction of order beta_R^2 in replicated Majorana theory, providing a route to the class-D nonlinear sigma model.

Context

This research addresses the challenge of extracting the asymptotic decoding threshold for surface codes under uniform coherent Z rotations, which typically show strong finite-size effects. The findings are significant for quantum error correction protocols where coherent errors are common, as they establish the microscopic basis for the crossover behavior between ballistic and renormalization-group scales.

Limitations

The evidence is limited to a preprint (arXiv:2611.13098v1) with no peer-reviewed validation. Results are based on free-fermion simulations and theoretical derivations rather than experimental verification. Uncertainty exists regarding the exact crossover behavior at the SWAP point and the precise conditions for maximum-likelihood decoding optimization.

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