Abstract
Machine learning has the potential to become an important tool in quantum error correction as it allows the decoder to adapt to the error distribution of a quantum chip. An additional motivation for using neural networks is the fact that they can be evaluated by dedicated hardware which is very fast and consumes little power. Machine learning has been previously applied to decode the surface code. However, these approaches are not scalable as the training has to be redone for every system size which becomes increasingly difficult. In this work the existence of local decoders for higher dimensional codes leads us to use a low-depth convolutional neural network to locally assign a likelihood of error on each qubit. For noiseless syndrome measurements, numerical simulations show that the decoder has a threshold of around 7.1% when applied to the 4D toric code. When the syndrome measurements are noisy, the decoder performs better for larger code sizes when the error probability is low. We also give theoretical and numerical analysis to show how a convolutional neural network is different from the 1-nearest neighbor algorithm, which is a baseline machine learning method.
Highlights
A full-featured quantum computer will rely on some form of error correction as physical qubits are prone to the effects of environmental noise.The authors contribute to this work.When using error correcting codes, decoders play a large role in the performance of the faulttolerant protocols
An issue that has not been addressed so far is scalability: in previous approaches, the neural networks have to be re-trained for every system size, despite the fact that in general machine learning methods become problematic when the input space becomes too large
To provide a positive answer to this question, we introduce a decoder for the four-dimensional version of the toric code based on neural networks for which the training only has to be performed once on a small system size
Summary
A full-featured quantum computer will rely on some form of error correction as physical qubits are prone to the effects of environmental noise. In Appendix D, we give a toy example which shows how a baseline machine learning model can fail at a task similar to decoding when the system size becomes large. This highlights the importance of choosing a translational invariant model as we do. In Appendix E, we observed and analyzed one property of multilayer convolutional neural networks, and show it fits nicely to the task of assigning likelihood of qubit errors for high dimensional toric code
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