A new statistical mechanical model called the random coupled-plaquette gauge model (RCPGM) is introduced to improve decoding of surface codes under noisy conditions. By optimally accounting for Y-errors in syndrome measurements, the model raises the fundamental error threshold from 4.3% (uncoupled RPGM) to 6% under phenomenological depolarizing noise. For circuit-level noise, an approximate reduction technique yields a threshold of 1.4% versus 0.7% for the uncoupled approach. Results are obtained via Parallel Tempering Monte Carlo simulations and expand the landscape of statistical mechanical mappings for quantum error correction, suggesting practical improvements for fault-tolerant quantum computation decoders.
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