Effective quantum feature maps in quantum extreme reservoir computation from the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>X</mml:mi><mml:mi>Y</mml:mi></mml:mrow></mml:math> model

It is well known in quantum machine learning that the form of the feature map has a significant effect on the operation and performance of those tasks being undertaken. It is essential to investigate how to generate an effective feature map within the limitations of the number of qubits and quantum gates to apply in noisy intermediate-scale quantum devices. In this paper, we explore how the qubit connectivity impacts the performance of quantum extreme reservoir computation (QERC) for image classification using the Hamiltonian. We find that networks of qubits with simple connectivity generate an effective feature map, whereas a network with high connectivity does not since the Hamiltonian on it yields a unitary map with a periodic property. The existence of the periodicity can be fully determined by the underlying connectivity and the overall symmetry of the Hamiltonian. However, the symmetries in the Hamiltonians can contribute to a better generalization for QERC. We further find that it is possible to design QERC to give this high generalization property while maintaining high accuracy. Our work suggests that Hamiltonian dynamics with simple connectivity or symmetry can be exploited as a computational resource in quantum machine learning.