Neural Network Decoders for Large-Distance 2D Toric Codes

Xiaotong Ni

doi:10.22331/q-2020-08-24-310

Neural Network Decoders for Large-Distance 2D Toric Codes

QuTech, Delft University of Technology, P.O.Box 5046, 2600 GA Delft, The Netherlands.

Published:	2020-08-24, volume 4, page 310
Eprint:	arXiv:1809.06640v3
Doi:	https://doi.org/10.22331/q-2020-08-24-310
Citation:	Quantum 4, 310 (2020).

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Abstract

We still do not have perfect decoders for topological codes that can satisfy all needs of different experimental setups. Recently, a few neural network based decoders have been studied, with the motivation that they can adapt to a wide range of noise models, and can easily run on dedicated chips without a full-fledged computer. The later feature might lead to fast speed and the ability to operate at low temperatures. However, a question which has not been addressed in previous works is whether neural network decoders can handle 2D topological codes with large distances. In this work, we provide a positive answer for the toric code [1]. The structure of our neural network decoder is inspired by the renormalization group decoder [2,3]. With a fairly strict policy on training time, when the bit-flip error rate is lower than $9\%$ and syndrome extraction is perfect, the neural network decoder performs better when code distance increases. With a less strict policy, we find it is not hard for the neural decoder to achieve a performance close to the minimum-weight perfect matching algorithm. The numerical simulation is done up to code distance $d=64$. Last but not least, we describe and analyze a few failed approaches. They guide us to the final design of our neural decoder, but also serve as a caution when we gauge the versatility of stock deep neural networks. The source code of our neural decoder can be found at [4].

► BibTeX data

@article{Ni2020neuralnetwork,
  doi = {10.22331/q-2020-08-24-310},
  url = {https://doi.org/10.22331/q-2020-08-24-310},
  title = {Neural {N}etwork {D}ecoders for {L}arge-{D}istance 2{D} {T}oric {C}odes},
  author = {Ni, Xiaotong},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {4},
  pages = {310},
  month = aug,
  year = {2020}
}

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