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Compound Error Modeling and Synthesis in Deep Reinforcement Learning for Quantum Error Correction

Liu Ming, Tanaka Hiroshi, Wang Jian

Published Jul 21, 2026• 0 citations
Publisher

Abstract

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 $24\%$ 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.

DOI
10.5281/zenodo.21469703

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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.
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 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 advent of promising quantum error correction (QEC) codes with efficient resource utilization and high-performance fault-tolerant quantum memories signifies a critical step towards realizing practical quantum computation. While surface codes have been a dominant approach, their limitations have spurred the development of more advanced QEC architectures. These advanced codes often present increased complexity, demanding innovative decoding methodologies. This work investigates the application of reinforcement learning (RL) techniques, including hybrid and multi-agent approaches, to enhance the decoding of various advanced QEC architectures. By leveraging the ability of RL to learn optimal strategies from noisy syndrome measurements, we explore the potential for achieving improved logical error rates and scalability compared to traditional decoding methods. Our approach examines the adaptation of reinforcement learning to exploit the structural properties of these modern QEC models. We also explore the benefits of combining different RL algorithms to address the multifaceted nature of the decoding problem, considering factors such as code degeneracy and real-world noise characteristics. With our proposed method, we are able to demonstrate that an autonomously trained agent can derive decoding schemes for the complex decoding requirement of advanced QEC architectures.
The practical realization of fault-tolerant quantum computing critically hinges on the capacity of quantum error correction (QEC) schemes to robustly mitigate physical noise. Among the foremost candidates, the surface code is distinguished by its high threshold and local stabilizer checks. In recent years, neural network-based decoders, particularly those leveraging deep reinforcement learning (RL) and convolutional architectures, have demonstrated competitive performance against algorithmic staples such as Minimum Weight Perfect Matching (MWPM) and Union-Find. However, the vast majority of these learned decoders are trained and evaluated under idealized phenomenological or circuit-level depolarizing noise models. Real-world quantum processors exhibit complex, compound noise profiles encompassing crosstalk, leakage, non-Markovian temporal drift, and spatially correlated errors. In this work, we empirically evaluate the robustness of state-of-the-art neural decoders against highly structured compound noise models. We introduce a comprehensive stress-testing methodology tailored to quantify the degradation of the logical error rate when decoders are subjected to out-of-distribution noise characteristics. Our empirical results reveal that while neural decoders can overfit to their training noise profile, strategically designed training curricula and architecture regularizations enable significant resilience. We provide extensive numerical benchmarks validating that learned decoders can maintain near-optimal pseudothresholds across a broad spectrum of shifting noise conditions, highlighting their readiness for real-world superconducting qubit deployments.
The practical realization of fault-tolerant quantum computing critically hinges on the capacity of quantum error correction (QEC) schemes to robustly mitigate physical noise. Among the foremost candidates, the surface code is distinguished by its high threshold and local stabilizer checks. In recent years, neural network-based decoders, particularly those leveraging deep reinforcement learning (RL) and convolutional architectures, have demonstrated competitive performance against algorithmic staples such as Minimum Weight Perfect Matching (MWPM) and Union-Find. However, the vast majority of these learned decoders are trained and evaluated under idealized phenomenological or circuit-level depolarizing noise models. Real-world quantum processors exhibit complex, compound noise profiles encompassing crosstalk, leakage, non-Markovian temporal drift, and spatially correlated errors. In this work, we empirically evaluate the robustness of state-of-the-art neural decoders against highly structured compound noise models. We introduce a comprehensive stress-testing methodology tailored to quantify the degradation of the logical error rate when decoders are subjected to out-of-distribution noise characteristics. Our empirical results reveal that while neural decoders can overfit to their training noise profile, strategically designed training curricula and architecture regularizations enable significant resilience. We provide extensive numerical benchmarks validating that learned decoders can maintain near-optimal pseudothresholds across a broad spectrum of shifting noise conditions, highlighting their readiness for real-world superconducting qubit deployments.
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.