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Scientific Reports

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

Ziyang Li, Xiaofei Fu, Lingdong Meng, Ruishan Du

Published Sep 1, 2025• 3 citations
Publisher

Abstract

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.

DOI
10.1038/s41598-025-17651-5

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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.
Quantum neural networks (QNNs) integrate the advantages of quantum information with the formidable capabilities of classical neural networks, exhibiting notable potential in image classification tasks. However, the performance of current QNNs in processing multi-class image classification tasks still leaves room for improvement. In this paper, we propose three QNN architectures to enhance the accuracy of multi-class image classification by utilizing techniques of overparameterization, dense pooling, and local feature extraction. These networks are capable of mapping conventional data to the amplitudes of quantum states via amplitude encoding, eschewing the need for traditional dimensionality reduction techniques. Following processing with parameterized quantum circuits (PQCs), we conduct quantum measurements to extract feature information. We validate the proposed architectures using the MNIST dataset for eight-class image classification problems. The experimental results unequivocally demonstrate that the three techniques we employed significantly enhance the accuracy of QNNs in multi-class image classification tasks.
As quantum computers continue to become more capable, the possibilities of their applications increase. For example, quantum techniques are being integrated with classical neural networks to perform machine learning. In order to be used in this way, or for any other widespread use like quantum chemistry simulations or cryptographic applications, classical data must be converted into quantum states through quantum encoding. There are three fundamental encoding methods: basis, amplitude, and rotation, as well as several proposed combinations. This study explores the encoding methods, specifically in the context of hybrid quantum-classical machine learning. Using the QuClassi quantum neural network architecture to perform binary classification of the `3' and `6' digits from the MNIST datasets, this study obtains several metrics such as accuracy, entropy, loss, and resistance to noise, while considering resource usage and computational complexity to compare the three main encoding methods.
The rapid advancement of quantum computing technology has enabled new approaches to developing sophisticated machine learning models. In this paper, we present a multi-class Quantum Convolutional Neural Network (QCNN) architecture enhanced with strongly entangling circuits. The research targets the improvement of model's representation advantage and efficiency in solving classifications. The proposed method combines amplitude encoding with quantum convolutional and pooling layers or QCNN, augmented by strongly entangling layers to capture the data patterns. Experimental results show that our QCNN achieves higher classification accuracy with fewer parameters compared to traditional quantum models on the MNIST dataset. It highlights the potential of our method in complex multi-class classification.
Quantum Neural Networks (QNNs) offer a framework for learning functions from classical data, but their expressive power depends critically on how inputs are encoded into quantum states. Angle encoding can require resources that scale with the number of features, whereas amplitude encoding represents ddd features using only O(log⁡2d)\mathcal{O}(\log_2 d)O(log2​d) qubits. This compactness comes at a representational cost: normalization makes conventional amplitude encoding invariant to nonzero real rescaling of the input, up to an unobservable global phase. We show that this invariance induces an exact, architecture-independent restriction on the resulting hypothesis class. No downstream quantum circuit can distinguish inputs differing by nonzero real scaling. We develop a general condition under which deterministic preprocessing can remove this ambiguity and show that nonlinearity alone is insufficient. Based on this analysis, we introduce a fixed nonlinear feature map that provably distinguishes all real inputs under subsequent amplitude encoding, without adding trainable parameters and while retaining logarithmic qubit scaling. We evaluate the resulting QNN on three canonical classification benchmarks and a nonlinear synthetic dataset against conventional amplitude and angle encoding, as well as a classical neural network. Across these tasks, the proposed encoding consistently improves classification accuracy over both quantum encoding baselines by 21$-$44 %. Our results establish normalization-induced scale invariance as a concrete representational bottleneck of amplitude encoding and demonstrate that it can be removed while preserving a compact quantum representation, marking a step toward quantum models capable of capturing arbitrary relationships in classical data.
Abstract Quantum neural networks have emerged as a promising approach to solving complex problems across various domains, especially when integrated with classical methods. Several hybrid quantum-classical architectures have been developed to leverage the potential of quantum advantages for image classification tasks. The design of the quantum layer plays an important role in exploiting quantum properties such as superposition and entanglement. In this research, we propose hybrid quantum neural networks with multiple quantum layers, utilizing sequential circuits for enhanced feature representation through structured depth, and non-sequential circuits to reduce complexity and improve performance. Our experimental results demonstrate that stacking multiple layers in the quantum circuit enhances performance significantly. Furthermore, the results indicate that the optimal range of 6–10 qubits achieves the best trade-off between accuracy and computational efficiency. The results also show that amplitude embedding consistently outperformed angle embedding for image classification tasks. Notably, our proposed hybrid sequential model with amplitude embedding outperforms traditional convolutional neural networks on MNIST and Fashion-MNIST datasets, while requiring fewer parameters. These findings provide valuable insights for advancing quantum machine learning in real-world applications.
The classical-quantum transfer learning (CQTL) method is introduced to address the challenge of training large-scale, high-resolution image data on a limited number of qubits (ranging from tens to hundreds) in the current Noisy Intermediate-Scale quantum (NISQ) era. existing CQTL frameworks have been demonstrate quantum advantages with a small number of parameters (around 50), but the performance of quantum neural networks is sensitive to the number of parameters. Currently, there is a lack of exploration into larger-scale quantum circuits with more parameters. This paper proposes an amplitude-encoding-based classical-quantum transfer learning (AE-CQTL) framework, accompanied by an effective learning algorithm. The AE-CQTL framework multiplies the parameters of quantum circuits by using multi-layer ansatz. Based on the AE-CQTL framework, we designed and implemented two CQTL neural network models: Transfer learning Quantum Neural Network (TLQNN) and Transfer Learning Quantum Convolutional Neural Network (TLQCNN). Both models significantly expand the parameter capacity of quantum circuits, elevating the parameter scale from a few dozen to over one hundred parameters. In cross-experiments with three benchmark datasets (MNIST, Fashion-MNIST and CIFAR10) and three source models (ResNet18, ResNet50 and DenseNet121), TLQNN and TLQCNN have exceeded the benchmark classical classifier in multiple performance metrics, including accuracy, convergence, stability, and generalization capability. Our work contributes to advancing the application of classical-quantum transfer learning on larger-scale quantum devices in future.