Correlated Errors in the Surface Code

Pejman Jouzdani, Eduardo R. Mucciolo, E. Novais

Physics and Astronomy, REU/FRI Program, Thakur, Pritesh

Siying Wang, Yue Yan, ZhiXin Xia +1 more

Surface codes are promising for practical quantum error correction due to their high threshold and experimental feasibility. However, their performance under realistic noise conditions, particularly those involving correlated errors, requires further investigation. In this study, we systematically investigate the effect of several distinct types of correlated errors that could potentially arise from next-nearest-neighbor coupling in quantum systems. Our analytical results reveal that these correlated errors exhibit lower logical error rates due to their inherent structural symmetries. We further perform circuit-level simulations that incorporate realistic circuit level errors alongside correlated noise components, demonstrating that surface code performance is intimately related to the structural characteristics of the correlation patterns. This deepens our insights into the threshold of surface code and hence facilitates a more robust design of quantum circuits with a higher noise threshold.

SiYing Wang, ZhiXin Xia, Yue Yan +1 more

The surface code represents a promising candidate for fault-tolerant quantum computation due to its high error threshold and experimental accessibility with nearest-neighbor interactions. However, current exact surface code threshold analyses are based on the assumption of independent and identically distributed (i.i.d.) errors. Though there are numerical studies for the threshold with correlated error, they are only the lower bound rather than the exact value, which offers potential for higher error thresholds. Here, we establish an error-edge map, which allows for the mapping of quantum error correction to a square-octagonal random bond Ising model. We then present the maximum-likelihood threshold under a realistic noise model that combines independent single-qubit errors with correlated errors between nearest-neighbor data qubits. Our method is applicable for any ratio of nearest-neighbor correlated errors to i.i.d. errors. We present analytical constraints for the error correction threshold of surface codes, and by applying these constraints, we numerically obtain the error threshold higher than the existing values. Our error threshold is both an upper bound and achievable.

Austin G. Fowler

Natalie C. Brown, Michael Newman, Kenneth R. Brown

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 Bravyi et al. In contrast to depolarizing noise, subsystem surface codes outperform same-distance subspace surface codes below error rates as high as ⪅ 7.5 × 10−4 while 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.