A repetitive amplitude encoding method for enhancing the mapping ability of quantum neural networks.

With the rapid development of quantum machine learning, quantum neural networks (QNNs) have become a research hotspot. However, the quantum gates used to implement feature mapping in this model are all linear transformations, which directly affects the mapping ability of the model. Therefore, how to enhance the mapping capability of QNN is an important issue that has not yet been effectively addressed. This paper proposes a repetitive amplitude encoding method that encodes the probability amplitudes of multiple qubit blocks by repeatedly using the same set of classical data, effectively improving the mapping capability of QNN. Taking the MNIST dataset as an example, the experimental results comparing the repetitive amplitude encoding method with several existing encoding methods show that, firstly, when the number of classes is fixed, the repetitive amplitude encoding is superior to other methods. Secondly, when the number of hidden layers in QNN is fixed, as the number of classes increases, the performance of repetitive amplitude encoding not only consistently outperforms other methods, but this advantage becomes increasingly apparent. Finally, the repetitive amplitude encoding-based QNN was applied to reservoir lithology identification in the field of oil and gas exploration, IRIS and WINe classification datasets. By comparing with classical neural networks, the proposed method was validated for its adaptability to different classification problems and superior classification performance compared to classical neural networks.