用雷德马克复杂度为量子储池模型提供泛化误差上界，可指导参数设计。
Quantum Reservoir Computing and Risk Bounds
- 基于雷德马克复杂度推导两类量子储池的泛化误差上界。
- 在多项式读出函数下，风险上界随训练样本数收敛。
- 上界随量子比特数指数增长，适用于满足条件的其他储池类。
我们提出一种利用雷德马克复杂度来界定多种量子储池泛化误差的方法。针对两类特定的量子储池，给出了依赖于参数的具体上界。分析了泛化上界随量子比特数量增加的缩放关系。对具有多项式读出函数的类别应用该结果时，发现风险上界随训练样本数增加而收敛。我们的上界中对量子储池和读出参数的显式依赖，可用于在一定程度上调控泛化误差。值得注意的是，这些上界随量子比特数 n 呈指数增长。雷德马克复杂度的上界可推广至满足若干关于量子动力学与读出函数假设的其他储池类别。
原文摘要 · Abstract (English)
We propose a way to bound the generalisation errors of several classes of quantum reservoirs using the Rademacher complexity. We give specific, parameter-dependent bounds for two particular quantum reservoir classes. We analyse how the generalisation bounds scale with growing numbers of qubits. Applying our results to classes with polynomial readout functions, we find that the risk bounds converge in the number of training samples. The explicit dependence on the quantum reservoir and readout parameters in our bounds can be used to control the generalisation error to a certain extent. It should be noted that the bounds scale exponentially with the number of qubits n. The upper bounds on the Rademacher complexity can be applied to other reservoir classes that fulfill a few hypotheses on the quantum dynamics and the readout function.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。