Kvantfelskorrektion av bitfel i repetitionskoder med maskininlärning

Abstract

One of the biggest challenges with quantum computers is minimizing and correcting errors that arise due to the instability of quantum systems. The qubits in the system are sensitive to external factors and disturbances, which can lead to various types of quantum errors, including bit-flip errors. To address this, there are different methods for predicting and correcting quantum errors. Two such methods are Minimum Weight Perfect Matching (MWPM) and machine learning. This report investigates the effectiveness of a trained graph neural network (GNN) as a decoder by comparing the rate of bit-flip errors in re petition codes to MWPM on IBM’s quantum computers. The method is based on using Qiskit to construct a quantum circuit capable of detecting bit-flip errors without collapsing the state of the qubits, thereby obtaining the error rate in the form of syndromes. Data collected from runs on the quantum computer is used to train a GNN and is also applied to MWPM for code distances d ∈ [3, 21]. The performance of the decoders is then compared. The results showed that a larger GNN with seven graph convolutional layers generally performed better than both MWPM and a smaller network with three graph convolutio nal layers for all investigated code distances, except for d = 7. MWPM also outperformed the smaller network, which generally had the lowest performance among the decoders studied. The method and results are analyzed based on theory and the research question to provide a broader understanding of how a trained GNN and MWPM behave for diffe rent code distances. Relevant sources of error that may have affected the results are also presented, along with a discussion of societal and ethical aspects. In conclusion, the findings indicate that machine learning is an effective method to apply for decoding in quantum error correction, given sufficiently large and well-trained GNNs.