Quantum Error Correction Using Graph Neural Networks

Abstract

A graph neural network (GNN) is constructed and trained with a purpose of using it 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-like data seemed promising, a previous decoder based on the Markov Chain Monte Carlo method was used to generate data to create graphs. In this thesis the emphasis has been on error probabilities, p = 0.05, 0.1 and surface code sizes d = 5, 7, 9. Two specific network architectures have been tested using various graph convolutional layers. While training the networks, evenly distributed datasets were used and the highest 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 = 0.05 the performance did not achieve an error correction rate equal to the reference algorithm Minimum Weight Perfect Matching. Further research could be done to create a custom-made graph convolutional layer designed with intent to make the contribution of edge attributes more pivotal.