Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead
We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this...
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| Autores principales: | , |
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| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
American Physical Society
2021
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| Materias: | |
| Acceso en línea: | https://doaj.org/article/5219d68ce74b4240bc68f002e81b2d09 |
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| Sumario: | We introduce a technique that uses gauge fixing to significantly improve the quantum-error-correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be gained, and we introduce a new method for decoding which uses this information to improve performance. Applied to the subsystem toric code with three-qubit check operators, we increase the threshold under circuit-level depolarizing noise from 0.67% to 0.81%. The threshold increases further under a circuit-level noise model with small finite bias, up to 2.22% for infinite bias. Furthermore, we construct families of finite-rate subsystem low-density parity-check codes with three-qubit check operators and optimal-depth parity-check measurement schedules. To the best of our knowledge, these finite-rate subsystem codes outperform all known codes at circuit-level depolarizing error rates as high as 0.2%, where they have a qubit overhead that is 4.3× lower than the most efficient version of the surface code and 5.1× lower than the subsystem toric code. Their threshold and pseudo-threshold exceeds 0.42% for circuit-level depolarizing noise, increasing to 2.4% under infinite bias using gauge fixing. |
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