Machine Learning Assisted Quantum Error Correction Using Scalable Neural Network Decoders
Typ
Examensarbete för masterexamen
Master's Thesis
Master's Thesis
Program
Physics (MPPHS), MSc
Publicerad
2023
Författare
Havstöm, Pontus
Heuts, Olivia
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
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.
Beskrivning
Ämne/nyckelord
quantum computing, quantum error correction, topological stabilizer codes, surface codes, neural network decoders, convolutional neural networks, graph neural networks.