Discovering autonomous quantum error correction via deep reinforcement learning

2025-11-16

AI Summary

This work addresses the challenge of designing bosonic codes for autonomous quantum error correction (AQEC), specifically targeting resilience against single- and two-photon loss while eliminating reliance on active measurement and circumventing the stringent constraints imposed by the Knill–Laflamme exact error-correction condition. We propose a novel deep reinforcement learning framework for automated bosonic code discovery. Our method employs a two-stage curriculum learning strategy, leverages analytical solutions of the approximate master equation to accelerate training, and jointly optimizes engineered dissipation and driving parameters to search over Fock-state encodings. We report the first fully automated discovery of a bosonic code—spanned by |4⟩ and |7⟩—that surpasses the break-even point and maintains superior performance throughout long-time dynamical evolution. This code exhibits strong robustness under phase-damping and amplitude-damping noise, achieving state-of-the-art error-correction performance.

Technology Category

• Search and Optimization: Learning to Search
• Machine Learning: Quantum Machine Learning
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• Discovering autonomous quantum error correction codes using deep reinforcement learning
• Overcoming challenges in identifying practical encoding for bosonic quantum systems
• Resisting both single-photon and double-photon losses in quantum computing

Innovation

• Deep reinforcement learning discovers bosonic quantum codes
• Curriculum learning accelerates training via analytical solutions
• Two-phase training identifies optimal Fock state codewords