Quantum Error Correction Using Graph Neural Networks

University essay from Göteborgs universitet / Institutionen för fysik

Abstract: A graph neural network (GNN) is constructed and trained with a purpose of usingit as a quantum error correction decoder for depolarized noise on the surface code.Since associating syndromes on the surface code with graphs instead of grid-likedata seemed promising, a previous decoder based on the Markov Chain Monte Carlomethod was used to generate data to create graphs. In this thesis the emphasis hasbeen on error probabilities, p = 0.05, 0.1 and surface code sizes d = 5, 7, 9. Twospecific network architectures have been tested using various graph convolutionallayers. While training the networks, evenly distributed datasets were used and thehighest reached test accuracy for p = 0.05 was 97% and for p = 0.1 it was 81.4%.Utilizing the trained network as a quantum error correction decoder for p = 0.05the performance did not achieve an error correction rate equal to the referencealgorithm Minimum Weight Perfect Matching. Further research could be done tocreate a custom-made graph convolutional layer designed with intent to make thecontribution of edge attributes more pivotal.

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