Fast parallel decoder for optimal geometrically local quantum codes

The rapid advancement of quantum computing has made the development of efficient quantum error correction codes a critical area of research for ensuring the reliability of large-scale quantum computers. Recent work on geometrically local quantum codes [1-5] has shown promising results in achieving both optimal code properties and practical error correction through the use of almost linear-time decoders [5]. However, while these advancements mark a significant step forward, the need for scalable and efficient decoding strategies remains a key challenge. This thesis explores several directions for improving and extending the performance of geometrically local quantum code decoders. Specifically, we investigate the potential of parallel decoders and their integration with existing surface code decoders [6-11] to enhance speed and scalability under random circuit-level noise. Furthermore, we explore the applicability of parallel window decoding techniques [7], both in space and time directions, as a means of optimizing the decoding process. Through these avenues, this work aims to contribute to the development of more efficient, fault-tolerant decoding algorithms that can support the practical implementation of large-scale quantum computers. The findings from this thesis could provide valuable insights into the optimization of geometrically local codes and lead to advancements in quantum error correction methods, with a focus on practical deployment for near-term quantum systems. 

The student will start by conducting a comprehensive literature review. As an initial task, they will apply the parallel window decoding technique to the repetition code and simulate its performance. Building on this foundation, the student will work toward understanding how to extend the technique to the surface code, with the ultimate goal of applying it to optimal geometrically local quantum codes. 

References 
[1] Elia Portnoy. Local quantum codes from subdivided manifolds. arXiv preprint arXiv:2303.06755, 2023.  
[2] Ting-Chun Lin, Adam Wills, and Min-Hsiu Hsieh. Geometrically local quantum and classical codes from subdivision. arXiv preprint arXiv:2309.16104, 2023.  
[3] Dominic J Williamson and Nouédyn Baspin. Layer codes. arXiv preprint arXiv:2309.16503, 2023.  
[4] Xingjian Li, Ting-Chun Lin, and Min-Hsiu Hsieh. Transform arbitrary good quantum ldpc codes into good geometrically local codes in any dimension. arXiv preprint arXiv:2408.01769, 2024. 
[5] Eggerickx, Q., Wills, A., Lin, T. C., De Greve, K., & Hsieh, M. H. (2024). Almost Linear Decoder for Optimal Geometrically Local Quantum Codes. arXiv preprint arXiv:2411.02928. 
[6] Austin G Fowler. Minimum weight perfect matching of fault-tolerant topological quantum error correction in average o(1) parallel time. arXiv preprint arXiv:1307.1740, 2013.  
[7] Luka Skoric, Dan E Browne, Kenton M Barnes, Neil I Gillespie, and Earl T Campbell. Parallel window decoding enables scalable fault tolerant quantum computation. Nature Communications, 14(1):7040, 2023.  
[8] Yue Wu and Lin Zhong. Fusion blossom: Fast mwpm decoders for qec. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 1, pages 928–938. IEEE, 2023.  
[9] Poulami Das, Christopher A Pattison, Srilatha Manne, Douglas M Carmean, Krysta M Svore, Moinuddin Qureshi, and Nicolas Delfosse. Afs: Accurate, fast, and scalable error-decoding for fault-tolerant quantum computers. In 2022 IEEE International Symposium on High-Performance Computer Architecture (HPCA), pages 259–273. IEEE, 2022.  
[10] Xinyu Tan, Fang Zhang, Rui Chao, Yaoyun Shi, and Jianxin Chen. Scalable surface-code decoders with parallelization in time. PRX Quantum, 4(4):040344, 2023.  
[11] Namitha Liyanage, Yue Wu, Alexander Deters, and Lin Zhong. Scalable quantum error correction for surface codes using fpga. In 2023 IEEE International Conference on Quantum Computing and Engineering (QCE), volume 1, pages 916–927. IEEE, 2023.

Type of Project: Thesis

Master's degree: Master of Science; Master of Engineering Science

Master program: Physics; Nanoscience & Nanotechnology

Duration: 10 months

Supervisor: Bart Soree (EE, Nano, Physics)

For more information or application, please contact the supervising scientists Quinten Eggerickx (Quinten.Eggerickx@imec.be) and George Simion (George.Simion@imec.be). 

Only for self-supporting students.