Efficient near-optimal decoding of the surface code through ensembling (2401.12434v3)
Abstract: We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual counterparts on repetition and surface code benchmarks, approaching maximum-likelihood accuracy at large ensemble sizes. We can use the degree of consensus among the ensemble as a confidence measure for a layered decoding scheme, in which a small ensemble flags high-risk cases to be checked by a larger, more accurate ensemble. This layered scheme can realize the accuracy improvements of large ensembles with a relatively small constant factor of computational overhead. We conclude that harmonization provides a viable path towards highly accurate real-time decoding.
- Google Quantum AI. Suppressing quantum errors by scaling a surface code logical qubit. Nature, 614(7949):676–681, 2023.
- Efficient algorithms for maximum likelihood decoding in the surface code. Physical Review A, 90(3):032326, 2014.
- Statistical mechanical models for quantum codes with correlated noise. Annales de l’Institut Henri Poincaré D, 8(2):269–321, 2021.
- Christopher T Chubb. General tensor network decoding of 2d pauli codes. arXiv preprint arXiv:2101.04125, 2021.
- Decoding algorithms for surface codes. arXiv e-prints, pages arXiv–2307, 2023.
- Topological quantum memory. Journal of Mathematical Physics, 43(9):4452–4505, 2002.
- Toward a union-find decoder for quantum ldpc codes. IEEE Transactions on Information Theory, 68(5):3187–3199, 2022.
- Linear programming decoder for hypergraph product quantum codes. In IEEE ITW 2020 - IEEE Information theory workshop 2020, Riva del Garda / Virtual, Italy, April 2021.
- Austin G Fowler. Optimal complexity correction of correlated errors in the surface code. arXiv preprint arXiv:1310.0863, 2013.
- Using linear programming to decode binary linear codes. IEEE Transactions on Information Theory, 51(3):954–972, 2005.
- Craig Gidney. Stim: a fast stabilizer circuit simulator. Quantum, 5:497, 2021.
- Yoked surface codes. arXiv preprint arXiv:2312.04522, 2023.
- Improved decoding of circuit noise and fragile boundaries of tailored surface codes. Physical Review X, 13(3):031007, 2023.
- Sparse blossom: correcting a million errors per core second with minimum-weight matching. arXiv preprint arXiv:2303.15933, 2023.
- Fault-tolerant weighted union-find decoding on the toric code. Physical Review A, 102(1):012419, 2020.
- Fault-tolerant quantum computing with color codes. arXiv preprint arXiv:1108.5738, 2011.
- Lp decoding of quantum stabilizer codes. In 2018 IEEE International Symposium on Information Theory (ISIT), page 1306–1310. IEEE Press, 2018.
- Tensor network decoding beyond 2d. arXiv preprint arXiv:2310.10722, 2023.
- Guifré Vidal. Efficient classical simulation of slightly entangled quantum computations. Physical review letters, 91(14):147902, 2003.