Single-shot error correction on toric codes with high-weight stabilizers
Abstract
For quantum error correction codes the required number of measurement rounds typically increases with the code distance when measurements are faulty. Single-shot error correction allows for an error threshold with only one round of noisy syndrome measurements regardless of the code size. Here we implement single-shot check operators for toric codes. The single-shot checks are constructed by Gaussian elimination following Campbell [Campbell, Quantum Sci. Technol. 4, 025006 (2019), 10.1088/2058-9565/aafc8f]. The single-shot check operators result in a sustainable threshold at 5.62% for an error model with noisy measurements, outperforming the conventional toric code-check operators with multiple rounds of noisy measurement. The cost of the transformation is nonlocal high-weight stabilizer generators. We then consider a gate-based error model that leads to increased measurement error with stabilizer weight. Here we find no single-shot threshold behavior and instead find the code family will have an optimal code size for a fixed error rate. For this error model the conventional check operators with multiple measurements yields a lower logical error rate.
- Publication:
-
Physical Review A
- Pub Date:
- May 2024
- DOI:
- 10.1103/PhysRevA.109.052438
- arXiv:
- arXiv:2310.16160
- Bibcode:
- 2024PhRvA.109e2438L
- Keywords:
-
- Quantum Physics