Kernel-based optimization of measurement operators for quantum reservoir computers

TL;DR

This paper introduces a kernel-based method to optimize measurement operators in quantum reservoir computers, improving their prediction accuracy and efficiency, especially for large qubit systems, with applications demonstrated in image classification and time series prediction.

Contribution

It extends the kernel framework to recurrent QRCs, deriving an exact Hilbert--Schmidt kernel representation for optimal measurements, enhancing training efficiency and adaptability to hardware constraints.

Findings

Optimized measurement operators reduce prediction error.

Method outperforms conventional training for large qubit systems.

Effective in complex tasks like chaotic time series and image classification.

Abstract

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.