通过核方法优化量子储层计算的测量算符，提升预测精度与效率
Kernel-based optimization of measurement operators for quantum reservoir computers
- 基于核岭回归框架，推导出历史空间上的最优读出算符表达式
- 在图像分类与时间序列任务中显著降低预测误差，尤其适用于高比特系统
- 适合需要高效训练量子机器学习模型的研究者，兼容硬件限制
寻找最优测量算符对量子储层计算机（QRCs）的性能至关重要，因其采用固定量子特征映射。本文将无状态（量子极限学习机，QELMs）和有状态（依赖记忆）的QRCs统一置于核岭回归框架下，首次推导出历史空间上最优读出可观测量的精确希尔伯特-施密特核表示。该方法可针对给定储层和训练数据集，生成最小化预测误差的最优测量算符。对于大数量子比特情形，其效率优于传统训练方式。文中讨论了实现效率与实际策略，包括泡利基分解和算符对角化，以适配硬件约束。数值实验验证了该方法在图像分类及混沌、强非马尔可夫时间序列预测任务中的有效性。该方法亦可推广至其他量子机器学习模型。
原文摘要 · Abstract (English)
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. We thus extend the kernel viewpoint of supervised quantum models to recurrent QRCs by deriving an exact Hilbert--Schmidt kernel representation of the optimal readout observable on history space. 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. To demonstrate the effectiveness of this approach, we present numerical experiments on image classification and time series prediction tasks, including chaotic and strongly non-Markovian systems. The developed method can also be applied to other quantum machine learning models.
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。