Datadriven kvantfelskorrigering genom avkodning av repetitionskoden med grafneurala nätverk

Abstract

Quantum error correction is one challenge faced when implementing quantum computer systems. Repetition code is a simpler correcting decoder that detects bit- or phase-flip errors. To fully benefit from the repetition code, an appropriate decoder is required. Therefore, this report aims to compare two different decoding methods, a classical algorithm known as Minimum-Weight Perfect Matching, MWPM and a machine learning-based method using Graph Neural Networks, GNN. A modular phase-flip detecting repetition code is constructed and executed on an IBM Quantum processor. The measured syndromes are used as training data for GNN, which is trained on Chalmers high-performance computing cluster Alvis. The report also investigates how decoding time scales with increasing code area. Results showed that the GNN decoder achieved marginally higher logical accuracy αL compared to MWPM, particularly near the code area where optimization of the hyperparameters was performed. Furthermore, GNN achieved slightly higher logical accuracy compared to MWPM for code distance and time repetitions d,dt ≤ 9. This is because the decoder was tested on syndromes generated during the same quantum computer execution as the training data. However, GNN also showed consistently higher logical error probability pL and was less effective than MWPM when tested on different syndromes, which may hinder practical application in environments with varying error distributions.