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.

翻译：我们提出一种利用Rademacher复杂度界定若干类量子储层泛化误差的方法。针对两类特定量子储层，我们给出了参数依赖的显式界。通过分析泛化界随量子比特数增加的标度规律，我们将结果应用于具有多项式读出函数的储层类别，发现风险界在训练样本数增加时收敛。界中关于量子储层参数与读出参数的显式依赖关系可用于在一定程度控制泛化误差。需要指出的是，这些界随量子比特数$n$呈指数标度。Rademacher复杂度的上界可推广至满足量子动力学与读出函数若干假设的其他储层类别。