The random coupled-plaquette gauge model and the surface code under circuit-level noise

Area of Science:

• Quantum Information Science
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Quantum error correction is crucial for fault-tolerant quantum computation.
• Surface codes are a leading architecture for quantum error correction.
• Accurate modeling of noise, especially Y-errors, is essential for decoder performance.

Purpose of the Study:

• Introduce the random coupled-plaquette gauge model (RCPGM) for improved quantum error correction.
• Determine fundamental error thresholds for surface codes with noisy syndrome measurements.
• Investigate the performance of RCPGM under different noise models.

Main Methods:

• Utilized Parallel Tempering Monte Carlo simulations.
• Analyzed phenomenological depolarizing data and bit-flip syndrome noise.
• Applied an approximate reduction technique for circuit-level noise scenarios.

Main Results:

• Achieved a 6% error threshold for depolarizing data and bit-flip noise, outperforming the uncoupled RPGM (4.3%).
• Found a 1.4% threshold for circuit-level noise, compared to 0.7% for the uncoupled RPGM.
• Demonstrated RCPGM's effectiveness in accounting for Y-errors.

Conclusions:

• The RCPGM significantly enhances the error thresholds of surface codes.
• Results expand statistical mechanical mappings for quantum error correction.
• The findings encourage practical decoder development for fault-tolerant quantum computation.