Higgott, O; Breuckmann, NP; (2021) Subsystem Codes with High Thresholds by Gauge Fixing and Reduced Qubit Overhead. Physical Review X , 11 (3) , Article 031039. 10.1103/PhysRevX.11.031039.

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Abstract

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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