https://doi.org/10.1140/epjqt/s40507-025-00446-y
Research
Exploring the FPGA and ASIC design space of belief propagation and ordered statistics decoders for quantum error correction codes
1
Department of Computer Architecture and Automatics, Complutense University of Madrid, Madrid, Spain
2
Instituto de Telecomunicaciones y Aplicaciones Multimedia, Universitat Politecnica de Valencia, Valencia, Spain
Received:
10
April
2025
Accepted:
10
November
2025
Published online:
20
November
2025
Belief propagation (BP) combined with ordered statistics decoding (OSD) provides a good balance between accuracy and complexity for many quantum error correction (QEC) codes, making it nearly universal. However, the complexity of OSD can limit real-time decoding, particularly for superconducting qubits, and the limits of classical hardware decoders have not been fully explored. Therefore, it is important to assess the architecture of OSD for different code families, such as surface codes and bicycle bivariate codes, under realistic assumptions like the detector error model. This paper introduces a BP + OSD parallel architecture implemented on FPGA and ASIC for surface codes (distances 3–21) and bicycle bivariate codes (distances 6–24). Results show that for surface codes up to distance 9, the OSD post-processor fits into a single VCU129 FPGA, achieving a frequency of 200 MHz with a worst-case latency of 134 μs. For bicycle bivariate codes, the limit is distance 12, with a frequency of 244 MHz and a worst-case latency of 84 μs. In ASIC, with 45 nm technology, latency improves by 31%, but area resources grow significantly, making parallel implementation beyond distance 12 impractical on a single chip. The designs were verified using a hardware emulator, ensuring that the decoder’s behavior matches software simulations and revealing interesting results like potential error floors at low logical error rates.
Key words: Quantum error correction / Quantum LDPC codes / BP + OSD / FPGA and ASIC decoders / Hardware emulation
© The Author(s) 2025
Open Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by-nc-nd/4.0/.
