arXiv:2506.22335quant-phcs.LG2025-06被引 9

量子储层计算机可精准预测混沌系统,且对噪声有强鲁棒性。

Robust quantum reservoir computers for forecasting chaotic dynamics: generalized synchronization and stability

  • 将量子储层视为耦合动力系统,利用广义同步机制建模。
  • 能学习混沌系统的李雅普诺夫谱、吸引子维数等不变特性。
  • 提出GS=ESP准则,确保模型稳定,适合近中期量子硬件应用。

我们证明了循环量子储层计算机(QRCs)及其无循环架构(RF-QRCs)是学习和预测时间序列中混沌动力学的稳健工具。首先,将量子储层计算机解释为耦合动力系统,其中储层作为响应系统受训练数据驱动,即广义同步(GS)系统。其次,通过推导量子储层更新的雅可比矩阵,证明量子储层能学习混沌动力学及其不变性质,如李雅普诺夫谱、吸引子维度及协变李雅普诺夫向量。第三,借助广义同步理论,提出设计鲁棒量子储层的方法:提出准则 $GS=ESP$——广义同步蕴含回声状态性质(ESP),反之亦然。理论上证明RF-QRCs天然满足此准则。最后,模拟噪声实验表明,噪声引起的耗散反而增强模型鲁棒性。不同维度系统的数值验证支持结论。本工作为在近中期量子硬件上设计用于混沌时间序列预测的鲁棒量子机器开辟了新路径。

原文摘要 · Abstract (English)

We show that recurrent quantum reservoir computers (QRCs) and their recurrence-free architectures (RF-QRCs) are robust tools for learning and forecasting chaotic dynamics from time-series data. First, we formulate and interpret quantum reservoir computers as coupled dynamical systems, where the reservoir acts as a response system driven by training data; in other words, quantum reservoir computers are generalized-synchronization (GS) systems. Second, we show that quantum reservoir computers can learn chaotic dynamics and their invariant properties, such as Lyapunov spectra, attractor dimensions, and geometric properties such as the covariant Lyapunov vectors. This analysis is enabled by deriving the Jacobian of the quantum reservoir update. Third, by leveraging tools from generalized synchronization, we provide a method for designing robust quantum reservoir computers. We propose the criterion $GS=ESP$: GS implies the echo state property (ESP), and vice versa. We analytically show that RF-QRCs, by design, fulfill $GS=ESP$. Finally, we analyze the effect of simulated noise. We find that dissipation from noise enhances the robustness of quantum reservoir computers. Numerical verifications on systems of different dimensions support our conclusions. This work opens opportunities for designing robust quantum machines for chaotic time series forecasting on near-term quantum hardware.

量子计算混沌预测储层计算鲁棒性

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