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arXiv:2511.12482 · Physical Review A

Discovering autonomous quantum error correction via deep reinforcement learning

Yue Yin, Tailong Xiao, Xiaoyang Deng, Ming He, Jianping Fan, Guihua Zeng

quant-phcs.LGSubmitted Nov 16, 2025• Announced Nov 18, 2025• 0 citations• Revised Jun 2, 2026 (v2)
v1 · Nov 16, 2025v2 · Jun 2, 2026
arXivHTMLPDF

Abstract

Quantum error correction is essential for fault-tolerant quantum computing. However, standard methods relying on active measurements may introduce additional errors. Autonomous quantum error correction (AQEC) circumvents this by utilizing engineered dissipation and drives in bosonic systems, but identifying practical encoding remains challenging due to stringent Knill-Laflamme conditions. In this work, we utilize curriculum learning enabled deep reinforcement learning to discover Bosonic codes under approximate AQEC framework to resist both single-photon and double-photon losses. We present an analytical solution of solving the master equation under approximation conditions, which can significantly accelerate the training process of reinforcement learning. The agent first identifies an encoded subspace surpassing the breakeven point through rapid exploration within a constrained evolutionary time-frame, then strategically fine-tunes its policy to sustain this performance advantage over extended temporal horizons. We find that the two-phase trained agent can discover the optimal set of codewords, i.e., the Fock states $\ket{4}$ and $\ket{7}$ considering the effect of both single-photon and double-photon loss. We identify that the discovered code surpasses the breakeven threshold over a longer evolution time and achieve the state-of-art performance. We also analyze the robustness of the code against the phase damping and amplitude damping noise. Our work highlights the potential of curriculum learning enabled deep reinforcement learning in discovering the optimal quantum error correct code especially in early fault-tolerant quantum systems.

Journal reference
Phys. Rev. A 112, 062618 (2025)
DOI
10.1103/rgy3-z928

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Quantum error correction is essential for fault-tolerant quantum computing. However, standard methods relying on active measurements may introduce additional errors. Autonomous quantum error correction (AQEC) circumvents this by utilizing engineered dissipation and drives in bosonic systems, but identifying practical encoding remains challenging due to stringent Knill-Laflamme conditions. In this work, we utilize curriculum learning enabled deep reinforcement learning to discover Bosonic codes under approximate AQEC framework to resist both single-photon and double-photon losses. We present an analytical solution of solving the master equation under approximation conditions, which can significantly accelerate the training process of reinforcement learning. The agent first identifies an encoded subspace surpassing the breakeven point through rapid exploration within a constrained evolutionary time-frame, then strategically fine-tunes its policy to sustain this performance advantage over extended temporal horizons. We find that the two-phase trained agent can discover the optimal set of codewords, i.e., the Fock states ∣4⟩\ket{4}∣4⟩ and ∣7⟩\ket{7}∣7⟩ considering the effect of both single-photon and double-photon loss. We identify that the discovered code surpasses the breakeven threshold over a longer evolution time and achieve the state-of-art performance. We also analyze the robustness of the code against the phase damping and amplitude damping noise. Our work highlights the potential of curriculum learning enabled deep reinforcement learning in discovering the optimal quantum error correct code especially in early fault-tolerant quantum systems.
Autonomous quantum error correction (AQEC) protects logical qubits by engineered dissipation and thus circumvents the necessity of frequent, error-prone measurement-feedback loops. Bosonic code spaces, where single-photon loss represents the dominant source of error, are promising candidates for AQEC due to their flexibility and controllability. While existing proposals have demonstrated the in-principle feasibility of AQEC with bosonic code spaces, these schemes are typically based on the exact implementation of the Knill-Laflamme conditions and thus require the realization of Hamiltonian distances d≥2. Implementing such Hamiltonian distances requires multiple nonlinear interactions and control fields, rendering these schemes experimentally challenging. Here, we propose a bosonic code for approximate AQEC by relaxing the Knill-Laflamme conditions. Using reinforcement learning (RL), we identify the optimal bosonic set of code words (denoted here by RL code), which, surprisingly, is composed of the Fock states |2⟩ and |4⟩. As we show, the RL code, despite its approximate nature, successfully suppresses single-photon loss, reducing it to an effective dephasing process that well surpasses the break-even threshold. It may thus provide a valuable building block toward full error protection. The error-correcting Hamiltonian, which includes ancilla systems that emulate the engineered dissipation, is entirely based on the Hamiltonian distance d=1, significantly reducing model complexity. Single-qubit gates are implemented in the RL code with a maximum distance d_{g}=2.
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.
With a particular emphasis on fixing fault defects caused by bitflip and depolarizing noise, this study explores the use of RL methods within the framework of quantum error correction. This work investigates the flexibility and independence of RL-trained agents in reducing bitflip mistakes by methodically looking at error rates and qubit lifetimes. Furthermore, we study how the top-performing agents are affected by depolarizing noise and present a strategic "Decoded Surface Code" method for fixing mistakes. The results show how RL works in handling different types of errors on its own, revealing subtle dynamics in the quantum system. Quantum error correction is a rapidly developing area, and this study adds to it by shedding light on how reinforcement learning could improve quantum computing's fault tolerance. The study's findings provide a basis for future research into more robust quantum computing systems and have ramifications for the creation of autonomous error-correcting algorithms.
Abstract In the ongoing race towards experimental implementations of quantum error correction (QEC), finding ways to automatically discover codes and encoding strategies tailored to the qubit hardware platform is emerging as a critical problem. Reinforcement learning (RL) has been identified as a promising approach, but so far it has been severely restricted in terms of scalability. In this work, we significantly expand the power of RL approaches to QEC code discovery. Explicitly, we train an RL agent that automatically discovers both QEC codes and their encoding circuits for a given gate set, qubit connectivity and error model, from scratch. This is enabled by a reward based on the Knill-Laflamme conditions and a vectorized Clifford simulator, showing its effectiveness with up to 25 physical qubits and distance 5 codes, while presenting a roadmap to scale this approach to 100 qubits and distance 10 codes in the near future. We also introduce the concept of a noise-aware meta-agent, which learns to produce encoding strategies simultaneously for a range of noise models, thus leveraging transfer of insights between different situations. Our approach opens the door towards hardware-adapted accelerated discovery of QEC approaches across the full spectrum of quantum hardware platforms of interest.
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 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.