Low-latency Quantum Error Correction Enabled by Evolutionary Decoding with 5 Iterations

Quantum computers promise revolutionary computational power, but their susceptibility to errors presents a significant hurdle to realising this potential. Researchers Hee-Youl Kwak from University of Ulsan, Seong-Joon Park from Pohang University of Science and Technology, and Hyunwoo Jung from Korea Advanced Institute of Science and Technology, alongside colleagues, now demonstrate a new decoding method that substantially improves error correction performance while minimising computational demands. Their work introduces an ‘evolutionary’ approach to belief propagation, a standard error-correction technique, and combines it with ordered statistics decoding. This innovative method, termed EBP+OSD, achieves faster and more accurate decoding, particularly when speed is critical, representing a crucial step towards building practical and reliable quantum computers.

Evolutionary Decoding Accelerates Quantum Error Correction

Quantum error correction (QEC) represents a critical challenge in realising practical quantum computation, as qubits are inherently susceptible to noise and decoherence. Traditional decoding algorithms, while effective, often suffer from significant latency, hindering real-time error correction. This work introduces an evolutionary belief propagation plus ordered statistics decoding (BP+OSD) algorithm designed to substantially reduce decoding latency without compromising performance. The proposed method leverages the strengths of both belief propagation and ordered statistics decoding, while incorporating an evolutionary strategy to optimise the decoding process for specific quantum error correcting codes.

The core innovation lies in the adaptive adjustment of decoding parameters using an evolutionary algorithm, inspired by principles of natural selection., This allows the decoder to dynamically refine its performance based on the characteristics of the error patterns encountered during the decoding process. Specifically, the algorithm evolves a population of decoding parameter sets, evaluating their effectiveness through simulations and selecting the best-performing sets for reproduction and mutation. This iterative process leads to a decoder that is highly tuned to the specific noise model and code structure, resulting in improved decoding speed and accuracy. The team demonstrates the effectiveness of the evolutionary BP+OSD algorithm on the surface code, a leading candidate for fault-tolerant quantum computation.

Results show a significant reduction in decoding latency compared to conventional BP and OSD algorithms, while maintaining comparable or superior error correction performance. The algorithm achieves a reduction in decoding time of up to 30% for codes with a distance of 7, and maintains a logical error rate comparable to state-of-the-art decoders. This improvement in latency is crucial for enabling real-time feedback and control in quantum computing systems, paving the way for more robust and reliable quantum computations.,.

Optimized Decoding with Evolutionary Belief Propagation

The research team developed an evolutionary belief propagation (EBP) decoder, enhancing the standard belief propagation algorithm with trainable weights optimised via the differential evolution algorithm. This innovative approach enables end-to-end optimization when combined with ordered statistics decoding (OSD), resulting in improved decoding performance and reduced computational complexity. Experiments focused on surface codes and low-density parity-check codes, demonstrating that the EBP+OSD decoder outperforms BP+OSD, particularly under strict low-latency constraints requiring only five belief propagation iterations. A key methodological advancement lies in the edge-indexed sharing scheme, which strategically reduces the number of weights needed for decoding., This scheme defines a specific weight set based on the degree of connections within the code, allowing for reuse of weights across different surface codes and significantly reducing optimization time.

For instance, the team demonstrated that a single optimized weight set for a surface code with a distance of 7 could be effectively applied to other codes, streamlining the process. This weight sharing method maintains a constant number of weights regardless of code distance, contrasting with traditional methods where the number of weights increases quadratically. To further refine the optimization process, the researchers introduced a selection criterion within the differential evolution algorithm. This criterion prioritizes weight sets that achieve a lower fraction of falsely resolved parity predictions, even if the improvement in layer error rate is minimal, contributing to a more efficient convergence., The results demonstrate that the EBP+OSD decoder consistently improves the decoding threshold for both surface and QLDPC codes.

Specifically, the team achieved a threshold increase from 15.5% for surface codes and substantial improvements in pseudo-threshold for QLDPC codes, indicating enhanced error correction capabilities. Comparative analysis against existing decoders, including MWPM, FFNN, CNN, and AMBP, confirms that the EBP+OSD decoder achieves state-of-the-art performance, even with a limited number of iterations. Furthermore, the research team quantified a 35%, 63% reduction in total computational complexity using EBP+OSD, demonstrating a significant advancement in decoding efficiency.,.

Evolutionary Decoding Boosts Quantum Error Correction

Scientists have developed an evolutionary belief propagation (EBP) decoder for quantum error correction, achieving improved performance and reduced computational complexity compared to existing methods. This work addresses the challenge of maintaining data integrity in quantum computers, which are susceptible to errors due to the nature of quantum mechanics. The team incorporated trainable weights into the standard belief propagation algorithm and optimized these weights using a differential evolution algorithm, enabling end-to-end optimization when combined with ordered statistics decoding (OSD)., Experiments conducted on both surface codes and quantum low-density parity-check (QLDPC) codes demonstrate that the EBP+OSD decoder outperforms conventional BP+OSD decoders. Specifically, the research focused on codes including the rotated surface code [[d2, 1, d]] and QLDPC codes [[72, 12, 6]], [[90, 8, 10]], and [[144, 12, 12]].

The EBP+OSD decoder achieves this improvement while substantially reducing the activation of the computationally intensive OSD stage, leading to lower overall complexity. A key achievement is the ability to attain these results with only 5 iterations of the belief propagation algorithm, a significant reduction compared to previous approaches requiring 32 iterations (BP+OSD) or even 150 iterations (BP with memory). Measurements confirm that the EBP+OSD decoder delivers enhanced performance under strict low-latency constraints, crucial for real-time quantum computation. The optimization process also incorporates a weight sharing technique, improving efficiency and allowing for weight reuse across similar code classes. This research represents a significant step towards practical quantum error correction, offering a favorable balance between decoding performance and computational complexity under limited-latency conditions.,.

Evolutionary Decoding Boosts Quantum Error Correction

Researchers have introduced an evolutionary belief propagation (EBP) decoder that significantly enhances both the performance and efficiency of quantum error correction. The approach extends standard belief propagation by incorporating trainable weights, which are optimised using a differential evolution algorithm. This enables end-to-end optimisation when the decoder is combined with ordered statistics decoding.

Experimental results show that the EBP decoder delivers superior decoding performance with substantially lower computational complexity compared to existing methods, particularly under strict low-latency constraints. Specifically, the method achieves a threshold gain of 0.9% for surface codes and 2.9% for low-density parity-check codes, while reducing computational complexity by up to 57% and 62%, respectively. These gains arise from both a decrease in the average number of decoding iterations and a reduced activation probability of the ordered statistics decoding stage.

This work represents the first application of evolutionary optimisation to belief propagation decoding and offers a promising pathway toward practical, low-latency decoders for quantum error correction.