发表机构
IMPACT AI, Office of Data Science and Informatics (ODSI)/NASA MSFC; Research Institute for Advanced Computer Science (RIACS), Universities Space Research Association (USRA); The University of Alabama in Huntsville（IMPACT AI，数据科学与信息办公室（ODSI）/NASA马歇尔太空飞行中心; 高级计算机科学研究所（RIACS），大学空间研究协会（USRA）; 阿拉巴马大学亨茨维尔分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结构化量子核AeRot，通过时间感知的编码电路在Lorenz-63混沌预测中超越经典核，将优势定位于不稳定鞍点区域。
AI 中文摘要
量子核承诺提供指数级大的特征空间，但具有表达力的电路会使其Gram矩阵失去信息量，带宽调整会使其坍缩为经典RBF核，而实际共识是量子核在经典数据上毫无增益。我们回答了另一个富有成效的问题，一个架构性问题：编码电路的结构能否携带调优后的经典核所缺乏的归纳偏置。我们引入AeRot，一种量子核，将l2归一化延迟窗口的振幅编码与分组单量子比特旋转层融合，该层将连续的时间块分配给每个量子比特，使电路具有延迟窗口感知能力。在Lorenz-63核岭回归中，通过100个种子的交叉验证带宽，AeRot优于调优的RBF和Matern-5/2核，优势在物理视界≥0.15时间单位时出现，在0.25时间单位（5个量子比特，窗口32）时达到平均R^2的+0.137提升。对窗口尾部的线性稳定性分析将优势定位于不稳定的鞍点接近区域：AeRot在最不稳定的十分位窗口中赢得83%的窗口，胜率随尾部不稳定性单调上升，并在局部稳定性边界处发生符号翻转。困难在于折叠分支的模糊性：接近鞍点的轨迹局部发散，欧几里得核难以分辨轨迹将承诺于哪个叶瓣。结构诊断确认Gram矩阵在结构上与调优的RBF不同，在每个视界上严格具有更高的目标核对齐。增益是架构性的：时间结构化编码对折叠吸引子的有限样本归纳偏置效应，不附带计算分离性声明。据我们所知，这是首次将量子核优势机制性地定位于经典系统的特定动力学区域。
英文摘要
Quantum kernels promise exponentially large feature spaces, but expressive circuits render their Gram matrices uninformative, bandwidth tuning collapses them toward classical RBF, and the practical consensus is that quantum kernels add nothing on classical data. We answer another productive question, an architectural one: whether the structure of an encoding circuit can carry an inductive bias that tuned classical kernels lack. We introduce AeRot, a quantum kernel fusing amplitude encoding of l2-normalized delay windows with a grouped single-qubit rotation layer that assigns contiguous temporal blocks to each qubit, making the circuit delay-window-aware. On Lorenz-63 kernel ridge regression with cross-validated bandwidths over 100 seeds, AeRot outperforms tuned RBF and Matern-5/2, the advantage emerging at physical horizons >= 0.15 tu and reaching +0.137 mean R^2 at 0.25 tu (5 qubits, window 32). Linear-stability analysis of the window tail localises the advantage to the unstable saddle-approach regime: AeRot wins 83% of windows in the most unstable decile, with the win rate rising monotonically with tail instability and a sign flip at the local stability boundary. The difficulty is fold-branch ambiguity: trajectories approaching the saddle are locally diverging, and Euclidean kernels struggle to resolve which lobe the trajectory will commit to. Structural diagnostics confirm Gram matrices structurally distinct from tuned RBF, with strictly higher target-kernel alignment at every horizon. The gain is architectural: a finite-sample inductive-bias effect of temporally structured encoding on a folded attractor, with no computational-separation claim attached. To our knowledge this is the first mechanistic localisation of quantum-kernel advantage to a specific dynamical regime of a classical system.
