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   Roozbehani, Hajir; Polyanskiy, Yury (March 2018, 2018 Conf. Inform. Sciences and Syst. (CISS))

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5. Handling leakage with subsystem codes

   https://doi.org/10.1088/1367-2630/ab3372  

   Brown, Natalie C.; Newman, Michael; Brown, Kenneth R. (July 2019, New Journal of Physics)

   Abstract Leakage is a particularly damaging error that occurs when a qubit state falls out of its two-level computational subspace. Compared to independent depolarizing noise, leaked qubits may produce many more configurations of harmful correlated errors during error-correction. In this work, we investigate different local codes in the low-error regime of a leakage gate error model. When restricting to bare-ancilla extraction, we observe that subsystem codes are good candidates for handling leakage, as their locality can limit damaging correlated errors. As a case study, we compare subspace surface codes to the subsystem surface codes introduced by Bravyiet al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as ⪅ 7.5 × 10⁻⁴while offering better per-qubit distance protection. Furthermore, we show that at low to intermediate distances, Bacon–Shor codes offer better per-qubit error protection against leakage in an ion-trap motivated error model below error rates as high as ⪅ 1.2 × 10⁻³. For restricted leakage models, this advantage can be extended to higher distances by relaxing to unverified two-qubit cat state extraction in the surface code. These results highlight an intrinsic benefit of subsystem code locality to error-corrective performance. 

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