Scalable Neural Network Decoders for Higher Dimensional Quantum Codes

TL;DR

This paper introduces a scalable, low-depth convolutional neural network decoder for higher-dimensional quantum codes, demonstrating effective error correction with thresholds around 7.1% for 4D toric codes, even under noisy conditions.

Contribution

It presents a scalable neural network decoder for higher-dimensional quantum codes, overcoming previous limitations of non-scalability in machine learning approaches.

Findings

Achieves a 7.1% threshold for noiseless 4D toric code decoding.

Performs better at larger code sizes with low error probabilities under noisy syndrome measurements.

Provides theoretical and numerical analysis distinguishing CNN from baseline methods.

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.