Abstract
Quantum error correction is an essential technique for constructing a scalable quantum computer. In order to implement quantum error correction with near-term quantum devices, a fast and near-optimal decoding method is demanded. A decoder based on machine learning is considered as one of the most viable solutions for this purpose, since its prediction is fast once training has been done, and it is applicable to any quantum error correcting code and any noise model. So far, various formulations of the decoding problem as the task of machine learning have been proposed. Here, we discuss general constructions of machine-learning-based decoders. We found several conditions to achieve near-optimal performance, and proposed a criterion which should be optimized when a size of training data set is limited. We also discuss preferable constructions of neural networks, and proposed a decoder using spatial structures of topological codes using a convolutional neural network. We numerically show that our method can improve the performance of machine-learning-based decoders in various topological codes and noise models.
Highlights
In order to build a scalable quantum computer, quantum error correction (QEC) [1,2,3] is a vital technique for achieving reliable computation
We propose the use of construction of neural networks which explicitly utilize the spatial structure of the topological codes
We review the basics of the supervised machine learning with neural networks
Summary
In order to build a scalable quantum computer, quantum error correction (QEC) [1,2,3] is a vital technique for achieving reliable computation. One approach is to use the most likely physical errors that are consistent with the observed syndrome value as a recovery operation This scheme is called the minimum-distance (MD) decoder. The machine-learning-based decoder using a neural network is called a neural decoder [24] All these existing methods numerically showed that the performance of the neural decoder is superior to the known efficient decoders when a sufficiently large amount of the training data set is supplied. We show that the performance of the neural decoder is improved with these techniques, and it shows better performance than that of a decoder using minimum-weight perfect matching with a 106 data set at a distance d = 11 in the surface code under a depolarizing noise. The neural decoder can be used as a fast, versatile, and high-performance decoder for decoding topological stabilizer codes
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