Machine Learning Assisted Quantum Error Correction Using Scalable Neural Network Decoders

Examensarbete för masterexamen
Master's Thesis
Physics (MPPHS), MSc
Havstöm, Pontus
Heuts, Olivia
A necessary condition for fault-tolerant quantum computers is the implementation of quantum error correction, as the sensitive nature of quantum technology causes unavoidable errors on qubits. Topological stabilizer codes, such as the surface code and its variations, are promising candidates for near term implementations of quan tum error correcting codes. In surface codes, multiple physical qubits are encoded to represent a single logical qubit with a higher tolerance for errors than the indi vidual physical qubits. Errors on data qubits cannot be measured directly, and have to be corrected based on incomplete observations of the system from ancilla qubit measurement syndromes. Classical algorithms called decoders are used to determine correction operators based on the syndromes, which is a non-trivial and computa tionally expensive task. In practice, the error decoding must be fast, and as such it is of interest to develop decoders that rapidly determine correction operations while still remaining sufficiently accurate. Decoders based on neural networks have been shown to yield high decoding accuracy for small distance surface codes, while also having fast decoding time once trained. Many such decoders are however not necessarily scalable and have been designed for a specific code size. In this thesis, we develop two types of neural network based decoders using the deep learning architectures Graph Neural Networks (GNN) and Convolutional Neural Networks (CNN), both of which in principle allow for decoding arbitrarily large codes. We apply the decoders to the rotated surface code under depolarizing noise with perfect syndrome measurements, and evaluate their performance based on their accuracy, computational speed and scalability to large code distances. We show that the the decoders perform on par with the commonly used Minimum Weight Perfect Matching (MWPM) decoder at small codes and low physical error rates, with the CNN decoder outperforming the MWPM decoder for code distance d = 7. We also find that using a sparse graph representation of syndromes yields a favorable computational complexity for the GNN decoder on large-distance codes.
quantum computing, quantum error correction, topological stabilizer codes, surface codes, neural network decoders, convolutional neural networks, graph neural networks.
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