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Transfer Learning in Reinforcement Learning for Quantum Error Correction: Evaluating Scale-Invariant Decoding of Quantum LDPC Codes

Zhang Shuhan, Fan Yang, Tanaka Hiroshi, Dian Zhou, Zeng Xuan

Published Jul 21, 2026• 0 citations
Publisher

Abstract

The realization of fault-tolerant quantum computing relies fundamentally on the efficient and accurate decoding of quantum error-correcting codes. Recently, Deep Reinforcement Learning (DRL) has emerged as a promising approach for decoding complex codes, such as quantum Low-Density Parity-Check (qLDPC) codes, due to its ability to adapt to correlated noise and system specific irregularities. However, the computational cost of training these intelligent agents scales prohibitively with the code distance and the number of physical qubits. In this work, we present an analytical and theoretical framework for transfer learning in DRL-based quantum decoders. We explore the scale-invariant properties of qLDPC codes, specifically focusing on how the structural symmetries in hypergraph product and lifted product codes can be exploited by scalable neural architectures. By formulating the decoding process as a Markov Decision Process (MDP) mapped onto a translationally and structurally invariant graph, we demonstrate that a Deep Q-Network (DQN) trained on a small lattice (e.g., an $[[625, 25]]$ qLDPC code) can be zero-shot transferred or rapidly fine-tuned for a significantly larger lattice (e.g., an $[[900, 50]]$ qLDPC code). We provide rigorous theoretical bounds on the performance degradation under dimensionality mismatch and present comprehensive empirical results. Our experiments show that fine-tuning a pre-trained agent requires orders of magnitude fewer samples than training from scratch, while retaining near-optimal logical error suppression. These findings provide a concrete pathway toward scalable, low-latency machine learning architectures for large-scale fault-tolerant quantum processors.

DOI
10.5281/zenodo.21469523

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The realization of fault-tolerant quantum computing relies fundamentally on the efficient and accurate decoding of quantum error-correcting codes. Recently, Deep Reinforcement Learning (DRL) has emerged as a promising approach for decoding complex codes, such as quantum Low-Density Parity-Check (qLDPC) codes, due to its ability to adapt to correlated noise and system specific irregularities. However, the computational cost of training these intelligent agents scales prohibitively with the code distance and the number of physical qubits. In this work, we present an analytical and theoretical framework for transfer learning in DRL-based quantum decoders. We explore the scale-invariant properties of qLDPC codes, specifically focusing on how the structural symmetries in hypergraph product and lifted product codes can be exploited by scalable neural architectures. By formulating the decoding process as a Markov Decision Process (MDP) mapped onto a translationally and structurally invariant graph, we demonstrate that a Deep Q-Network (DQN) trained on a small lattice (e.g., an [[625,25]][[625, 25]][[625,25]] qLDPC code) can be zero-shot transferred or rapidly fine-tuned for a significantly larger lattice (e.g., an [[900,50]][[900, 50]][[900,50]] qLDPC code). We provide rigorous theoretical bounds on the performance degradation under dimensionality mismatch and present comprehensive empirical results. Our experiments show that fine-tuning a pre-trained agent requires orders of magnitude fewer samples than training from scratch, while retaining near-optimal logical error suppression. These findings provide a concrete pathway toward scalable, low-latency machine learning architectures for large-scale fault-tolerant quantum processors.
The realization of fault-tolerant quantum computing relies fundamentally on the efficient and accurate decoding of quantum error-correcting codes. Recently, Deep Reinforcement Learning (DRL) has emerged as a promising approach for decoding complex codes, such as quantum Low-Density Parity-Check (qLDPC) codes, due to its ability to adapt to correlated noise and system specific irregularities. However, the computational cost of training these intelligent agents scales prohibitively with the code distance and the number of physical qubits. In this work, we present an analytical and theoretical framework for transfer learning in DRL-based quantum decoders. We explore the scale-invariant properties of qLDPC codes, specifically focusing on how the structural symmetries in hypergraph product and lifted product codes can be exploited by scalable neural architectures. By formulating the decoding process as a Markov Decision Process (MDP) mapped onto a translationally and structurally invariant graph, we demonstrate that a Deep Q-Network (DQN) trained on a small lattice (e.g., an [[625,25]][[625, 25]][[625,25]] qLDPC code) can be zero-shot transferred or rapidly fine-tuned for a significantly larger lattice (e.g., an [[900,50]][[900, 50]][[900,50]] qLDPC code). We provide rigorous theoretical bounds on the performance degradation under dimensionality mismatch and present comprehensive empirical results. Our experiments show that fine-tuning a pre-trained agent requires orders of magnitude fewer samples than training from scratch, while retaining near-optimal logical error suppression. These findings provide a concrete pathway toward scalable, low-latency machine learning architectures for large-scale fault-tolerant quantum processors.
Quantum error correction (QEC) is indispensable for the realization of fault-tolerant quantum computers. Surface codes are a leading QEC architecture due to their high error thresholds and planar design. The core challenge lies in the decoding process: inferring latent physical errors from syndrome measurements and applying appropriate corrections. Although there are classical decoders, their performance can degrade with complex noise or be computationally demanding. This paper investigates an advanced Deep Reinforcement Learning (DRL) approach, employing a Dueling Double Deep Q-Network (DQN), to decode X-type Pauli errors on ad=3\mathbf{d}=\mathbf{3}d=3rotated surface code. The DRL agent leverages syndrome history to discern temporal error correlations and utilizes a multi-round correction strategy, enabling iterative refinement of corrective actions within an environment that simulates both physical qubit errors and syndrome measurement noise. After 30,000 training episodes with a 5 % physical error rate and 1 % measurement noise, the agent achieved a 0.00 % logical error rate in the extended test, an average episode reward of 0.38, and successfully cleared syndromes in 63 % of the test cases, demonstrating robust learning of a safe decoding policy. The persistent challenge of high training loss, despite good policy performance, is discussed, offering insights into value function approximation in complex QEC environments.
The practical realization of fault-tolerant quantum computing depends critically on the efficiency and adaptability of quantum error correction (QEC) decoders. Recent advancements have highlighted deep reinforcement learning (DRL) as a promising approach for decoding topological codes. However, training these agents typically assumes simplified, uniform noise models, which fail to capture the complex, compounding errors characteristic of near-term quantum hardware. In this paper, we rigorously formulate the synthesis of compound error models—encompassing thermal relaxation, spatial cross-talk, and non-Markovian memory effects—within the framework of deep reinforcement learning for surface code decoding. We propose a methodological framework for simulating these mismatch environments during training to foster robust policy generalization. Extensive simulations demonstrate that DRL agents trained on our synthesized compound error models achieve up to a 24%24\%24% reduction in logical error rates under realistic noise conditions compared to agents trained on standard depolarizing noise. This work provides a rigorous foundation for synthesizing accurate quantum noise environments for reinforcement learning applications.
Decoding is an essential component of quantum error correction (QEC), translating stabilizer measurement outcomes into corrective actions that suppress logical errors and preserve logical quantum information. Building fault-tolerant architectures requires increasing the code distance, which in turn places growing demands on decoding accuracy, scalability, and practical deployability. While a wide range of decoding algorithms have been proposed and demonstrated, achieving reliable, scalable, and real-time decoding remains a significant challenge. Machine-learning (ML) approaches are particularly well suited to this setting, as quantum error decoding is fundamentally a problem of processing large volumes of classical data with complex spatiotemporal correlations. This chapter surveys ML-based methods for quantum error decoding, with a focus on topological codes and an emphasis on architectural principles, practical performance, and real-time considerations. We first frame decoding as a learning problem and outline key paradigms, including discriminative, generative, and reinforcement-learning formulations. We then introduce the neural network building blocks that underpin most contemporary neural decoders and discuss how these components can be integrated to balance expressivity, scalability, and latency. Building on this architectural perspective, we review recent progress and benchmarks in neural decoding for memory experiments, and discuss real-time decoding, open challenges, and future directions toward scalable fault-tolerant quantum computing.
The practical realization of fault-tolerant quantum computing depends critically on the efficiency and adaptability of quantum error correction (QEC) decoders. Recent advancements have highlighted deep reinforcement learning (DRL) as a promising approach for decoding topological codes. However, training these agents typically assumes simplified, uniform noise models, which fail to capture the complex, compounding errors characteristic of near-term quantum hardware. In this paper, we rigorously formulate the synthesis of compound error models—encompassing thermal relaxation, spatial cross-talk, and non-Markovian memory effects—within the framework of deep reinforcement learning for surface code decoding. We propose a methodological framework for simulating these mismatch environments during training to foster robust policy generalization. Extensive simulations demonstrate that DRL agents trained on our synthesized compound error models achieve up to a 24%24\%24% reduction in logical error rates under realistic noise conditions compared to agents trained on standard depolarizing noise. This work provides a rigorous foundation for synthesizing accurate quantum noise environments for reinforcement learning applications.
Quantum error correction (QEC) is essential for scalable quantum computing. However, it requires classical decoders that are fast and accurate enough to keep pace with quantum hardware. While quantum low-density parity-check codes have recently emerged as a promising route to efficient fault tolerance, current decoding algorithms do not allow one to realize the full potential of these codes in practical settings. Here, we introduce a convolutional neural network decoder that exploits the geometric structure of QEC codes, and use it to probe a novel "waterfall" regime of error suppression, demonstrating that the logical error rates required for large-scale fault-tolerant algorithms are attainable with modest code sizes at current physical error rates, and with latencies within the real-time budgets of several leading hardware platforms. For example, for the [144,12,12][144, 12, 12][144,12,12] Gross code, the decoder achieves logical error rates up to ∼17\sim 17∼17x below existing decoders - reaching logical error rates ∼10−10\sim 10^{-10}∼10−10 at physical error p=0.1%p=0.1\%p=0.1% - with 3-5 orders of magnitude higher throughput. This decoder also produces well-calibrated confidence estimates that can significantly reduce the time overhead of repeat-until-success protocols. Taken together, these results suggest that the space-time costs associated with fault-tolerant quantum computation may be significantly lower than previously anticipated.