AI 中文总结
研究针对量子储层性能取决于家族选择且现有诊断资源需求大的问题，引入基于序统计表现力得分ORS和有效秩$R_{\mathrm{eff}}$的可扩展框架，验证了ORS得分，其能捕捉储层家族表现力层次，$R_{\mathrm{eff}}$决定表现力转化为预测信息的时机。
AI 中文摘要
量子储层为量子机器学习提供了一条硬件友好的途径，用固定的随机动力学和经典读出取代可训练电路。由于储层未优化，性能完全取决于储层家族的选择，但现有诊断方法所需资源随系统规模呈指数增长。我们引入了一个基于两个互补量的可扩展、硬件无关的框架。第一个是与任务无关的序统计（ORS）表现力得分，它仅将储层集合的最大输出概率与解析哈尔基线进行比较，无需重建完整输出分布，与希尔伯特空间维度无关且可进行封闭形式的去极化噪声校正，可直接用于硬件。第二个是特征矩阵的与任务相关的有效秩$R_{\mathrm{eff}}$，用于衡量有多少与输入相关的信息到达读出。我们针对已建立的复杂性诊断验证了ORS得分，并确认它在模拟噪声和IBM量子硬件上仍具有信息性。在合成和真实的量子极端学习机及量子储层计算基准测试中，ORS捕捉储层家族的内在表现力层次结构，而$R_{\mathrm{eff}}$则决定何时该表现力成为可用的预测信息。
英文摘要
Quantum reservoirs offer a hardware-friendly route to quantum machine learning, replacing trainable circuits with fixed random dynamics and a classical readout. Because the reservoir is not optimized, performance depends entirely on the choice of reservoir family, yet existing diagnostics demand resources that grow exponentially with system size. We introduce a scalable, hardware-agnostic framework built on two complementary quantities. The first is a task-independent order-statistics (ORS) expressivity score, which compares only the largest output probabilities of a reservoir ensemble against an analytical Haar baseline. It never reconstructs the full output distribution, is cost-independent of Hilbert-space dimension, and admits a closed-form depolarizing noise correction, making it directly usable on hardware. The second is the task-dependent effective rank $R_{\mathrm{eff}}$ of the feature matrix, which measures how much input-dependent information reaches the readout. We validate the ORS score against established complexity diagnostics and confirm it remains informative under simulated noise and on IBM quantum hardware. Across synthetic and real quantum extreme learning machine and quantum reservoir computing benchmarks, ORS captures the intrinsic expressivity hierarchy of reservoir families while $R_{\mathrm{eff}}$ determines when that expressivity becomes usable predictive information.
