发表机构
California State University, Northridge; California Institute of Technology（加州州立大学北岭分校; 加州理工学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
提出任务分辨的Fisher光谱法，通过定义任务得分坐标分析量子储层计算中的信息丢失，连接基准性能与实验可操作的诊断，指导测量和特征选择。
AI 中文摘要
量子储层计算（QRC）利用固定的量子动力学来编码时间序列，并仅训练经典读出层，但仅凭基准容量无法揭示任务信息是否在储层、测量、特征压缩或有限采样中丢失。我们引入了“任务分辨的Fisher光谱法”，其中预测目标在输入历史的平稳分布上定义了正交的得分坐标。沿这些得分对标记历史进行重新加权，生成精确仿射的储层状态和测量结果族。在同一坐标下，我们获得了多体Fisher信息层次结构，将状态量子Fisher信息、完整测量记录的Fisher信息以及通过多体阶$r$保留的矩矩阵联系起来。每个矩矩阵的二次型恰好是最优线性读出的平稳容量，而有限测量扩展则预测从单次记录到理想期望值特征的趋近过程。测量级量仅需平稳标记记录和测量的结果字符串，无需输入模型或量子态层析。在五自旋开放储层中，相互作用将四阶时间信息路由到更高体相关性中，因此即使常规奇偶校验目标仍然可访问，低阶压缩也可能导致数量级的采样开销。对于相关输入和输出，记录定义的任务得分可预测保留容量、所需特征阶数和测量预算依赖性；优化局部测量轴可恢复原本隐藏的任务信息。该框架将基准性能与储层编码、测量选择、经典表示和采样分配的实验可操作诊断联系起来。
英文摘要
Quantum reservoir computing (QRC) uses fixed quantum dynamics to encode a time series and trains only a classical readout, but a benchmark capacity alone does not reveal whether task information is lost in the reservoir, the measurement, feature compression, or finite sampling. We introduce \emph{task-resolved Fisher spectroscopy}, in which prediction targets define orthonormal score coordinates on the stationary distribution of input histories. Reweighting labeled histories along these scores generates an exactly affine family of reservoir states and measurement outcomes. In the same coordinates, we obtain a many-body Fisher-information hierarchy relating the state quantum Fisher information, the Fisher information of the complete measurement record, and moment matrices retained through many-body order $r$. The quadratic form of each moment matrix is exactly the stationary capacity of the optimal linear readout, while a finite-measurement extension predicts the approach from one-shot records to ideal expectation-value features. The measurement-level quantities require only stationary labeled records and measured outcome strings, not an input model or quantum-state tomography. In a five-spin open reservoir, interactions route fourth-order temporal information into higher-body correlations, so low-order compression can incur orders-of-magnitude sampling overhead even when a conventional parity target remains accessible. For correlated inputs and outputs, record-defined task scores predict held-out capacities, the required feature order, and measurement-budget dependence; optimizing the local measurement axis recovers otherwise hidden task information. The framework connects benchmark performance to experimentally actionable diagnoses of reservoir encoding, measurement choice, classical representation, and shot allocation.
Comments18 pages, 11 figures
