Analysing correlated noise on the surface code using adaptive decoding algorithms

Naomi H. Nickerson1 and Benjamin J. Brown2,3

1Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, Prince Consort Road, London SW7 2AZ, United Kingdom
2Niels Bohr International Academy, Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark
3Centre for Engineered Quantum Systems, School of Physics, University of Sydney, Sydney, New South Wales 2006, Australia

Laboratory hardware is rapidly progressing towards a state where quantum error-correcting codes can be realised. As such, we must learn how to deal with the complex nature of the noise that may occur in real physical systems. Single qubit Pauli errors are commonly used to study the behaviour of error-correcting codes, but in general we might expect the environment to introduce correlated errors to a system. Given some knowledge of structures that errors commonly take, it may be possible to adapt the error-correction procedure to compensate for this noise, but performing full state tomography on a physical system to analyse this structure quickly becomes impossible as the size increases beyond a few qubits. Here we develop and test new methods to analyse blue a particular class of spatially correlated errors by making use of parametrised families of decoding algorithms. We demonstrate our method numerically using a diffusive noise model. We show that information can be learnt about the parameters of the noise model, and additionally that the logical error rates can be improved. We conclude by discussing how our method could be utilised in a practical setting blue and propose extensions of our work to study more general error models.

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Cited by

[1] Nishad Maskara, Aleksander Kubica, and Tomas Jochym-O'Connor, "Advantages of versatile neural-network decoding for topological codes", arXiv:1802.08680 (2018).

[2] Andrew S. Darmawan and David Poulin, "Linear-time general decoding algorithm for the surface code", Physical Review E 97 5, 051302 (2018).

[3] Christopher T. Chubb and Steven T. Flammia, "Statistical mechanical models for quantum codes with correlated noise", arXiv:1809.10704 (2018).

[4] Muyuan Li, Daniel Miller, Michael Newman, Yukai Wu, and Kenneth R. Brown, "2-D Compass Codes", arXiv:1809.01193 (2018).

[5] Aleksander Kubica and John Preskill, "Cellular-automaton decoders with provable thresholds for topological codes", arXiv:1809.10145 (2018).

[6] Benjamin J. Brown and Dominic J. Williamson, "Parallelized quantum error correction with fracton topological codes", arXiv:1901.08061 (2019).

[7] Benjamin J. Brown, "A fault-tolerant non-Clifford gate for the surface code in two dimensions", arXiv:1903.11634 (2019).

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