Joint Code and Decoder Design for Low-Latency Fault-Tolerant Quantum LDPC Codes

• Applicant: Professor Dr.-Ing. Laurent Schmalen
• Subject Area: Communication Technology and Networks, High-Frequency Technology and Photonic Systems, Signal Processing and Machine Learning for Information Technology ; Hardware Systems and Architectures for Information Technology and Artificial Intelligence, Quantum Engineering Systems
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 567557088

Quantum computing has emerged as a powerful paradigm capable of addressing problems that are exceedingly difficult for classical computers, as exemplified by Shor’s and Grover’s algorithms. However, the fragility of quantum states under noise and the constraints imposed by fundamental quantum principles pose significant challenges to practical implementation. Quantum error correction (QEC) offers a pathway to overcome these hurdles by correcting errors without directly observing the quantum states. Notably, stabilizer-based approaches, such as Calderbank–Shor–Steane (CSS) codes, link quantum error correction with well-established concepts from classical coding theory, ubiquitous in communication systems. The goalof this project is to improve the state-of-the-art of QEC using novel methods inspired by classical coding theory communications. We can formulate three main objectives of the proposal. The first objective of the proposal is to improve the decoder of existing quantum codes. We aim to propose a universal low-latency high-performance decoder for general quantum low-density parity-check (QLDPC) codes by investigating degeneracy-aware neural belief propagation decoding. In particular, we focus on minimizing the decoding latency of the decoder as it is crucial that the decoding is performed constantly in a streaming manner to combat decoherence. To this end, we ensemble decoding schemes from short-block-length communications to improve decoding performance and reduce decoding latency by leveraging multiple parallel decoders. In the second part of the project, we will consider a joint code and decoder design, i.e., we will investigate codes that are equipped with a near-optimum decoder tailored to the specific code. From a code design perspective, we intend to propose novel construction methods for QLDPC codes with appealing properties for decoding. We intend to construct codes with good classical properties such as large minimum distance, a small number of low-weight codewords, optimized Tanner graph structure in terms of short cycles, trapping sets, and absorbing sets. Additionally, we focus on fault-tolerance by focusing on codes with small row and column weights. Hence, we investigate how to optimize the structure of the Tanner graph upon code construction to enable a feasible implementation of the proposed code in realistic QEC systems. Third, we use the insight gained from the previous objectives to design a fault-tolerant QEC scheme. Hereby, we investigate more realistic scenarios and error models involving errors caused by, e.g., syndrome extraction or imperfect gates. In particular, we analyze error correction schemes that protect the syndrome against errors.

• DFG Programme: Research Grants