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arXiv:2605.00038

Lottery BP: Unlocking Quantum Error Decoding at Scale

Yanzhang Zhu, Chen-Yu Peng, Yun Hao Chen, Yeong-Luh Ueng, Di Wu

cs.ARquant-phSubmitted Apr 28, 2026• Announced Apr 29, 2026• 0 citations• Revised Aug 2, 2026 (v3)
v1 · Apr 28, 2026v2 · May 5, 2026v3 · Aug 2, 2026
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Abstract

During a QEC cycle, quantum error decoding stands on the critical path. To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. To move closer to the goal above, this paper contributes in three aspects, including decoder algorithm, decoder architecture, and decoding simulator. First, we propose Lottery BP, a lightweight decoder that introduces guided randomness to break the symmetric deadlock caused by quantum degeneracy during decoding. Lottery BP improves the decoding accuracy over BP by up to 6 orders. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, exemplifying a hierarchical decoder architecture. PolyQec is configurable for surface code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., up to 4 orders of magnitude less for surface codes. Third, we develop Syndrilla, a modular PyTorch-based decoding simulator that enables fair, extensible decoder evaluation with unified accuracy and performance metrics. On GPUs, Syndrilla runs 1 order of magnitude faster than CUDAQX.

Comments
14 pages, 17 figures

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During a QEC cycle, quantum error decoding stands on the critical path. To enable fault tolerance on millions of qubits in real time, scalable decoding is necessary, which motivates this paper. Existing decoding algorithms (decoders), such as clustering, matching, belief propagation (BP), and neural networks, suffer from one or more of inaccuracy, costliness, and incompatibility, upon a broad set of quantum error correction codes, such as surface code and bivariate bicycle code. Therefore, there exists a gap between existing decoders and an ideal decoder that is accurate, fast, general, and scalable simultaneously. To move closer to the goal above, this paper contributes in three aspects, including decoder algorithm, decoder architecture, and decoding simulator. First, we propose Lottery BP, a lightweight decoder that introduces guided randomness to break the symmetric deadlock caused by quantum degeneracy during decoding. Lottery BP improves the decoding accuracy over BP by up to 6 orders. Second, we design a PolyQec architecture that implements Lottery BP as a local decoder and ordered statistics decoding (OSD) as a global decoder, exemplifying a hierarchical decoder architecture. PolyQec is configurable for surface code and X/Z check. Since Lottery BP boosts the local decoding accuracy, PolyQec invokes the costly global OSD decoder less frequently over BP+OSD to enhance the scalability, e.g., up to 4 orders of magnitude less for surface codes. Third, we develop Syndrilla, a modular PyTorch-based decoding simulator that enables fair, extensible decoder evaluation with unified accuracy and performance metrics. On GPUs, Syndrilla runs 1 order of magnitude faster than CUDAQX.
Quantum error correction (QEC) via error decoding is essential towards fault-tolerant quantum computing, but extremely costly to simulate. However, existing simulators are often CPU-based and suffer from severe performance bottlenecks, especially when scaling to extensive simulations with large code distances or low physical error rate. In this work, we introduce Syndrilla, a PyTorch-based across-platform QEC simulation framework. The framework is highly modular, allowing flexible integration and customization of the error model, syndrome model, decoding configuration (algorithm and data format), and logical check type. Experimental results show that Syndrilla achieves10×∼20×10 \times \sim 20 \times10×∼20×speedup over CPU, when running on both AMD and NVIDIA GPUs, and decoding data format does not degrade accuracy, demonstrating the practicality and efficiency of Syndrilla to instigate future QEC research.
Quantum error correction (QEC) for fault-tolerant quantum computing requires a balanced decoding solution that offers high performance, low complexity, and low latency. However, the de facto standard - belief propagation (BP) combined with ordered statistics decoding (OSD) - suffers from excessive iterations in the BP stage and high complexity in the OSD stage. To address these challenges, we propose an evolutionary BP (EBP) decoder optimized via a differential evolution (DE) algorithm. By leveraging the gradient-free nature of DE, we enable end-to-end optimization of the EBP+OSD structure to maximize overall performance. In addition, a multi-objective selection rule is introduced to suppress frequent OSD activation, significantly reducing complexity overhead. Simulation results on surface codes and quantum low-density parity-check (QLDPC) codes demonstrate that EBP+OSD simultaneously achieves both superior decoding performance and substantially lower complexity compared to conventional BP+OSD, particularly in stringent low-latency regimes.
As quantum computing moves toward fault-tolerant architectures, quantum error correction (QEC) decoder performance is increasingly critical for scalability. Understanding the impact of transitioning from floating-point software to finite-precision hardware is essential, as hardware decoder performance affects code distance, qubit requirements, and connectivity between quantum and classical control units. This paper introduces a hardware emulator to evaluate QEC decoders using real hardware instead of software models. The emulator can explore 10 13 different error patterns in 20 days with a single FPGA device running at 150 MHz, guaranteeing the decoder's performance at logical rates of 10 − 12 , the requirement for most quantum algorithms. In contrast, an optimized C++ software on an Intel Core i9 with 128 GB RAM would take over a year to achieve similar results. The emulator also enables the storage of uncorrectable error patterns that generate logical errors, allowing for offline analysis and the design of new decoders. Using results from the emulator, we propose a method that combines several belief propagation (BP) decoders with different quantization levels, which we define as a diversity-based decoder. Individually, these decoders may show subpar error correction, but together they outperform the floating-point version of BP for quantum low-density parity-check (QLDPC) codes like hypergraph or lifted product. Preliminary results with circuit-level noise and bivariate bicycle codes suggest that hardware insights can also improve software. Our diversity-based proposal achieves a similar logical error rate as the well-known approach, BP with ordered statistics (BP+OSD) decoding, with average speed improvements ranging from 30% to 80%, and 10% to 120% in worst-case scenarios, while reducing post-processing algorithm activation from 47% to 96.93%, maintaining the same accuracy.
Quantum error correction (QEC) is critical for scalable fault-tolerant quantum computing. Topological codes, such as the toric code, offer hardware-efficient architectures but their Tanner graphs contain many girth-4 cycles that degrade the performance of belief-propagation (BP) decoding. For this reason, BP decoding is typically followed by a more complex second stage decoder such as minimum-weight perfect matching. These combined decoders achieve a remarkable performance, albeit at the cost of increased complexity. In this paper we propose two key improvements for the decoding of toric code. The first one is replacing the BP decoder by a neural BP decoder, giving rise to the neural belief-matching decoder which substantially decreases the average decoding complexity. The main drawback of this approach is the high cost associated with the training of the neural BP decoder. To address this issue, we impose a convolutional architecture on the neural BP decoder, enabling weight sharing across the spatially homogeneous structure of the code's factor graph. This design allows a model trained on a modest-size topological code to be directly transferred to much larger instances, preserving decoding quality while dramatically lowering the training burden. Our numerical experiments on toric-code lattices of various sizes demonstrate that this technique does not result in a noticeable loss in performance.
Fault-tolerant quantum computing will require error rates far below those achievable with physical qubits. Quantum error correction (QEC) bridges this gap, but depends on decoders being simultaneously fast, accurate, and scalable. This combination of requirements remains unmet by a machine-learning decoder, nor by any decoder for promising resource-efficient codes such as the color code. Here we introduce AlphaQubit 2, a neural-network decoder that achieves near-optimal logical error rates for both surface and color codes at scale under realistic noise. For the color code, it is orders of magnitude faster than other high-accuracy decoders. We demonstrate real-time decoding faster than 1μs per cycle on commercial accelerators: for the surface code to distance 11, with better accuracy than leading real-time decoders; and the first real-time decoding of the color code to distance 9. These results support the practical application of a wider class of promising QEC codes, and establish a credible path towards high-accuracy, real-time neural decoding at the scales required for fault-tolerant quantum computation.
Quantum error correction (QEC) is critical for scalable and reliable quantum computing, but existing solutions, such as surface codes, incur significant qubit overhead. Quantum low-density parity check (qLDPC) codes have recently emerged as a promising alternative, requiring fewer qubits. However, the lack of efficient decoders remains a major barrier to their practical implementation. In this work, we introduce SymBreak, a novel decoder for qLDPC codes that adaptively modifies the decoding graph to improve the performance of state-of-the-art belief propagation (BP) decoders. Our key contribution is identifying quantum degeneracy as a root cause of the convergence issues often encountered in BP decoding of quantum LDPC codes. We propose a solution that mitigates this issue at the decoding graph level, achieving both fast and accurate decoding. Our results demonstrate that SymBreak outperforms BP and BP+OSD-a more complex variant of BP-with a 16.17×16.17\times16.17× reduction in logical error rate compared to BP and 3.23×3.23\times3.23× compared to BP+OSD across various qLDPC code families. With only an 18.9718.9718.97% time overhead compared to BP, SymBreak provides significantly faster decoding times than BP+OSD, representing a major advancement in efficient and accurate decoding for qLDPC-based QEC architectures.