Finding optimal measurement operators is crucial for the performance of quantum reservoir computers (QRCs), since they employ a fixed quantum feature map. We formulate the training of both stateless (quantum extreme learning machines, QELMs) and stateful (memory dependent) QRCs in the framework of kernel ridge regression. This approach renders an optimal measurement operator that minimizes prediction error for a given reservoir and training dataset. For large qubit numbers, this method is more efficient than the conventional training of QRCs. We discuss efficiency and practical implementation strategies, including Pauli basis decomposition and operator diagonalization, to adapt the optimal observable to hardware constraints. Numerical experiments on image classification and time series prediction tasks demonstrate the effectiveness of this approach, which can also be applied to other quantum ML models.

翻译：寻找最优测量算子对于量子储备计算机（QRCs）的性能至关重要，因为它们采用固定的量子特征映射。我们将无状态（量子极限学习机，QELMs）和有状态（依赖记忆）QRCs的训练问题在核岭回归框架下进行形式化。该方法可得到一个针对给定储备系统和训练数据集最小化预测误差的最优测量算子。对于大量量子比特的情况，此方法比传统的QRC训练更高效。我们讨论了效率与实用实现策略，包括泡利基分解和算子对角化，以使最优可观测量适应硬件约束。在图像分类和时间序列预测任务上的数值实验验证了该方法的有效性，该方法也可应用于其他量子机器学习模型。