用量子储层+核方法实现高效时序学习,可解释且有理论保证。
QuaRK: A Quantum Reservoir Kernel for Time Series Learning
- 量子储层通过逐点注入生成特征,用经典阴影测技术高效测量局部可观测量。
- 在合成β-混合数据上实现良好泛化,支持有限样本下的性能预测。
- 适合需要可解释性与理论保障的高维时序建模任务,如金融或生物信号分析。
量子储层计算为时序学习提供了一条有前景的路径,通过丰富的量子动力学建模序列数据,仅需对轻量级经典读出层进行训练。然而,现有研究中兼具高效性与可实施性的量子储层架构及学习保证仍较少。为此,我们提出QuaRK,一个端到端框架,将硬件现实的量子储层特征提取器与基于核的读出方案结合。给定一组采样点序列,储层依次注入这些点,利用经典阴影层析技术高效测量k局部可观测量,生成紧凑特征向量,随后经典核读出层通过显式正则化和快速优化学习目标映射。该流程暴露清晰的计算调控参数——电路宽度、深度及测量预算,同时保留核方法对非线性时间函数的建模灵活性,并可扩展至高维数据。我们进一步为依赖时间数据提供了学习理论意义上的泛化保证,将设计与资源选择与有限样本性能关联,为构建可靠时序学习者提供原则性指导。实验验证了QuaRK的有效性,展示了在合成beta-混合时间序列任务上预测的插值与泛化行为。
原文摘要 · Abstract (English)
Quantum reservoir computing offers a promising route for time series learning by modelling sequential data via rich quantum dynamics while the only training required happens at the level of a lightweight classical readout. However, studies featuring efficient and implementable quantum reservoir architectures along with model learning guarantees remain scarce in the literature. To close this gap, we introduce QuaRK, an end-to-end framework that couples a hardware-realistic quantum reservoir featurizer with a kernel-based readout scheme. Given a sequence of sample points, the reservoir injects the points one after the other to yield a compact feature vector from efficiently measured k-local observables using classical shadow tomography, after which a classical kernel-based readout learns the target mapping with explicit regularization and fast optimization. The resulting pipeline exposes clear computational knobs -- circuit width and depth as well as the measurement budget -- while preserving the flexibility of kernel methods to model nonlinear temporal functionals and being scalable to high-dimensional data. We further provide learning-theoretic generalization guarantees for dependent temporal data, linking design and resource choices to finite-sample performance, thereby offering principled guidance for building reliable temporal learners. Empirical experiments validate QuaRK and illustrate the predicted interpolation and generalization behaviours on synthetic beta-mixing time series tasks.
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