Improved belief propagation is sufficient for real-time decoding of quantum memory (2506.01779v1)

Abstract: We introduce a new heuristic decoder, Relay-BP, targeting real-time quantum circuit decoding for large-scale quantum computers. Relay-BP achieves high accuracy across circuit-noise decoding problems: significantly outperforming BP+OSD+CS-10 for bivariate-bicycle codes and comparable to min-weight-matching for surface codes. As a lightweight message-passing decoder, Relay-BP is inherently parallel, enabling rapid low-footprint decoding with FPGA or ASIC real-time implementations, similar to standard BP. A core aspect of our decoder is its enhancement of the standard BP algorithm by incorporating disordered memory strengths. This dampens oscillations and breaks symmetries that trap traditional BP algorithms. By dynamically adjusting memory strengths in a relay approach, Relay-BP can consecutively encounter multiple valid corrections to improve decoding accuracy. We observe that a problem-dependent distribution of memory strengths that includes negative values is indispensable for good performance.

• The paper introduces Relay-BP, a modified belief propagation algorithm that dynamically adjusts disordered memory strengths to break symmetric trapping sets and boost decoding accuracy.
• It demonstrates superior performance over conventional decoders by significantly reducing logical error rates in qLDPC code scenarios while ensuring real-time operation on FPGA/ASIC platforms.
• The paper highlights the critical role of negative memory strengths and relay ensembling in advancing practical fault-tolerant quantum error correction.

Improved Belief Propagation for Real-Time Quantum Memory Decoding

This paper investigates a novel heuristic decoder termed Relay-BP for decoding errors in quantum circuits, targeting real-time applications on large-scale quantum computers. The authors propose Relay-BP as an enhanced Belief Propagation (BP) technique, aimed at addressing the challenges associated with decoding Quantum Low-Density Parity Check (qLDPC) codes under circuit-level noise. Relay-BP is posited as a compelling alternative to existing decoders, balancing flexibility, accuracy, compactness, and speed—key requirements for fault-tolerant quantum computing.

Core Contributions and Methodology

Relay-BP modifies the conventional BP algorithm by incorporating disordered memory strengths, which effectively breaks the symmetric trapping sets that often hinder convergence. This method is notable for its ability to dynamically adjust these memory strengths, facilitating multiple valid corrections that improve decoding accuracy. The paper positions Relay-BP against existing decoders used for bivariate-bicycle codes and surface codes, demonstrating superior performance in terms of logical error rates.

The authors detail the implementation architecture, designed to be inherently parallel, allowing for efficient deployment on FPGA or ASIC platforms. This parallelism maintains the real-time decoding capabilities while managing low footprint requirements, akin to standard BP implementations. Crucially, Relay-BP showcases adaptability across various qLDPC decoding scenarios, illustrating its computational efficiency alongside maintaining low logical error rates.

Experimental Results and Comparative Analysis

The paper's numerical experiments affirm Relay-BP’s proficiency against established decoding protocols like BP+OSD+CS-10 and min-weight-matching algorithms. The paper presents comprehensive heatmaps and benchmarks, revealing Relay-BP's ability to achieve substantial reductions in logical error rates for quantum memory applications—a significant improvement over existing methodologies, particularly in bivariate-bicycle code scenarios.

Notably, the paper explores the implications of utilizing negative memory strengths, asserting their indispensability for effective decoding—a bold claim that deviates from traditional BP approaches. Relay-BP’s relay ensembling technique further contributes to the rapidity and accuracy by alternating between diverse memory strengths.

Implications and Future Directions

The practical implications of Relay-BP are grounded in its integration into FPGA technologies, offering the potential for real-time quantum error correction which stands as critical in scalable quantum computing. The theoretical aspects, especially those refining BP techniques through disordered memory strengths, contribute valuable insights to the broader field of quantum error correction.

Speculating on future developments, Relay-BP lays the groundwork for advancements in message-passing algorithms, potentially influencing quantum computing architectures that prioritize fault-tolerance and efficiency. Further research could explore the nuanced role of negative memory strengths and optimization techniques for memory strength selection across diverse quantum codes.

Conclusion

In summary, Relay-BP enhances the conventional belief propagation paradigm, addressing key challenges in real-time decoding of quantum circuits. Its innovative approach facilitates significant reductions in logical error rates, marking a promising advancement toward the realization of fault-tolerant quantum computers. This paper contributes a substantial leap in both practical and theoretical domains, underscoring Relay-BP’s potential role in shaping future quantum computing technologies.