Date of Award
3-2024
Document Type
Thesis
Degree Name
Master of Science
Department
Department of Electrical and Computer Engineering
First Advisor
Laurence D. Merkle, PhD
Abstract
Quantum Error Correction (QEC) enables both industrial and defense applications of quantum computing. Toric codes and other quantum Low-Density Parity-Check (LDPC) codes are promising and well-researched methods of QEC. However, their decoding cost increases exponentially with a computer’s qubit count. Neural Network (NN) decoders have been shown to decode a code’s error syndrome both accurately and fast enough for a real-time error correcting scheme. Recent key developments introduced Convolutional Neural Network (CNN) to implement a translationally equivariant decoder for a toric code. These CNN decoders both outperform NN decoders and require less training data. This research applies a Group Convolutional Neural Network (GCNN) to this task. Specifically, it introduces GCNNs’ lifting and group convolutions to a CNN decoder architecture to achieve both translational and rotational equivariance. While results show that GCNN do not offer further improved decoding results with less exhaustive datasets, this research demonstrates the difficulties arising from highly dimensional data and highly complex decoders.
AFIT Designator
AFIT-ENG-MS-24-M-185
Recommended Citation
Wang, Jim, "Group Convolutional Decoders for Toric Codes" (2024). Theses and Dissertations. 7696.
https://scholar.afit.edu/etd/7696
Comments
A 12-month embargo was observed for posting this work on AFIT Scholar.
Distribution Statement A, Approved for Public Release. PA case number on file.