AI 中文总结
研究量子循环神经网络中贫瘠高原问题，核心方法是通过跨时间步参数共享强制时间平移对称性，主要贡献是证明此方法能抑制贫瘠高原，改变梯度缩放比例，增强学习能力，解决表达能力与可训练性的矛盾。
AI 中文摘要
贫瘠高原（梯度指数消失）是训练可扩展量子神经网络的基本障碍。量子循环神经网络（QRNNs）作为处理序列数据的自然架构是否会出现贫瘠高原仍是紧迫问题。本文表明，QRNNs可训练的关键因素不是循环电路拓扑本身，而是通过跨时间步的参数共享来强制时间平移对称性。证明了无参数共享时，QRNNs会出现贫瘠高原，梯度方差随序列长度指数衰减。跨时间步施加参数共享从根本上改变了这种缩放比例，将其转变为多项式依赖，从而抑制了贫瘠高原。数值模拟证实了这些分析预测。通过严格展示时间平移对称性如何抑制QRNNs中的贫瘠高原并增强学习能力，我们的工作将任务对齐对称性确立为解决量子神经网络中表达能力 - 可训练性紧张关系的建设性方法。
英文摘要
Barren plateaus -- the exponential vanishing of gradients -- are a fundamental obstacle to training scalable quantum neural networks. Whether they arise in quantum recurrent neural networks (QRNNs), a natural architecture for sequential data, remains a pressing question. Here we show that the decisive ingredient for trainability in QRNNs is not the recurrent circuit topology per se, but enforcing time-translation symmetry through parameter sharing across time steps. We prove that, without parameter sharing, QRNNs suffer from barren plateaus, with gradient variance decaying exponentially with sequence length. Imposing parameter sharing across time steps fundamentally alters this scaling, transforming it into a polynomial dependence and thereby suppressing the barren plateau. Numerical simulations corroborate these analytical predictions. By rigorously showing how time-translation symmetry suppresses barren plateaus and enhances learning capability in QRNNs, our work establishes task-aligned symmetry as a constructive resolution to the expressivity-trainability tension in quantum neural networks.
Comments8 pages, 4 figures, supplementary information included
