Sequential Graph-Based Decoding of the Surface Code using a Hybrid Graph and Recurrent Neural Network Model

Abstract

In order to achieve reliable quantum computation with noisy qubits, quantum error correction (QEC) is necessary. Quantum error correcting codes mitigate the inher ent noise in quantum systems by distributing the logical state over several qubits, thereby introducing redundancy. One such promising code is the surface code. It encodes the logical qubit using a two-dimensional lattice of physical data qubits and ancilla qubits. By taking and decoding measurements on the ancilla qubits of the surface code, one can deduce whether a logical bit- or phase-flip has occurred. However, this is a complex and potentially time-consuming task. Multiple decoding algorithms exist, such as the classical minimum-weight perfect matching (MWPM) decoder. In recent years, data-driven algorithms have been shown to decode the surface code with a high degree of accuracy. In this thesis, we present a machine learning approach to decoding the surface code using a combination of graph neural networks (GNN) and recurrent neural networks (RNN). Specifically, graph represen tations are constructed over a short, sliding time window of syndrome measurement data. Each representation is processed by a GNN and its output is used as a learned high-dimensional embedding for an RNN. This enables continuous decoding of mea surement patterns over longer time series. While the decoder is trained on relatively short syndromes, it is able to generalize for unseen syndromes and longer time se ries, outperforming the classical MWPM algorithm across both short and long time series. This work opens up a new approach to reliable and potentially fast decoding of QEC codes.