发表机构
Fudan University; Shanghai Qi Zhi Institute; The Chinese University of Hong Kong; Shanghai Research Center for Quantum Sciences; Hefei National Laboratory（复旦大学; 上海人工智能实验室; 香港中文大学; 上海量子科学研究中心; 合肥国家实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究通过显式量子储层模型，分析混沌区记忆快速衰减与可积点非线性处理受限，为混沌边缘优势提供理论解释并指导量子储层设计。
AI 中文摘要
数值研究表明，量子储层计算在混沌边缘附近表现最优，这一行为通常归因于记忆保持与非线性信息处理之间的平衡。本文构建了一个显式量子储层模型，并严格分析了其混沌区域与可积点。在混沌区域，我们证明高斯酉系综统计导致快速记忆丧失：学习性能随时序任务所需的存储时间呈指数衰减。这种衰减限制了混沌储层学习长程时间依赖的能力。在可积点，由自由费米子模型描述，我们证明振幅编码和费米子两点关联的线性读出无法学习一类耦合当前与过去输入的代表性非线性任务。引入相互作用可缓解这一障碍。通过识别混沌区域中记忆保持的独特限制和可积点上非线性处理的限制，我们的分析为观察到的混沌边缘优势提供了理论基础，并指导用于时间学习的量子储层设计。
英文摘要
Numerical studies suggest that quantum reservoir computing performs optimally near the edge of chaos, a behavior commonly attributed to a balance between memory retention and nonlinear information processing. Here we develop an explicit quantum reservoir model and rigorously analyze its chaotic regime and integrable point. In the chaotic regime, we show that Gaussian-unitary-ensemble statistics lead to rapid memory loss: learning performance decays exponentially with the storage time required by a temporal task. This decay limits the ability of chaotic reservoirs to learn long-range temporal dependencies. At the integrable point, described by a free-fermion model, we prove that amplitude encoding and a linear readout of fermionic two-point correlations cannot learn a representative class of nonlinear tasks coupling present and past inputs. Introducing interactions alleviates this obstruction. By identifying distinct limitations on memory retention in the chaotic regime and nonlinear processing at the integrable point, our analysis provides a theoretical basis for the observed edge-of-chaos advantage and guides the design of quantum reservoirs for temporal learning.
Comments6 pages, 2 figures, plus Supplemental Material (17 pages, 2 figures)
