AI 中文总结
该研究在量子多体系统中验证了有序与混沌边界信息处理最优的假设，发现量子储层在信息 scrambling 起始处的预测精度及记忆容量呈超扩展性增长，确立了信息 scrambling 作为量子储层性能标度律的作用。
AI 中文摘要
信息处理在有序与混沌边界附近实现最优的观点，已成为神经科学、复杂系统和机器学习领域反复出现的原则。本文在量子多体系统中检验该假设，数值模拟了二维伊辛网络，其自旋数 N 最高达 20，作为量子储层用于时间序列预测。利用非时序关联子（OTOCs），当输入强度变化时，我们定位到信息 scrambling 的起始点，该点分隔了信息在整个储层状态中被冻结与被 scrambling 的区域。我们发现，预测精度在 scrambling 起始处达到峰值，同时储层主动占据的计算基态数量也达到峰值。随后我们证明，预测精度随储层大小呈幂律增长，形式为~N^α：在 scrambling 起始处为超扩展性（α>1），而在两侧区域仅为亚线性（α<1）。最后，我们证明 scrambling 增强了储层记忆的非线性成分，同时降低了其线性容量。在起始处，只要集体弛豫通道提供必要的“遗忘”机制，总记忆容量便会超扩展性增长。这些结果巩固了信息 scrambling 在学习系统中的作用，将其从一个工作点转变为量子储层性能的标度律。
英文摘要
The idea that information processing is optimised near the boundary between order and chaos has emerged as a recurring principle across neuroscience, complex systems, and machine learning. Here we test this hypothesis in quantum many-body systems, numerically simulating two-dimensional Ising networks of up to $N=20$ spins, operated as quantum reservoirs for time-series forecasting. Using out-of-time-order correlators (OTOCs), we locate the onset of information scrambling as the input strength is swept, separating regimes where information is frozen and scrambled across the whole reservoir state. We show that prediction precision peaks at the onset of scrambling, along with the number of computational-basis states that the reservoir actively populates. We then show that prediction precision grows as a power law $\sim N^α$ in the reservoir size, superextensively $(α>1)$ at the onset of scrambling and only sublinearly $(α<1)$ in either neighbouring regime. Finally, we show that scrambling enhances the nonlinear components of the reservoir memory while reducing its linear capacity. At the onset, the total memory capacity grows superextensively, provided that the necessary ``forgetting'' mechanism is supplied by a collective relaxation channel. These results consolidate the role of information scrambling in learning systems, turning it from an operating point into a scaling law for the performance of quantum reservoirs.
Comments15 pages, 8 figures
