Efficiently encoding classical visual data into quantum states is essential for realizing practical quantum neural networks (QNNs). However, existing encoding schemes often discard spatial and semantic information when adapting high-dimensional images to the limited qubits of Noisy Intermediate-Scale Quantum (NISQ) devices. We propose a Fidelity-Preserving Quantum Encoding (FPQE) framework that performs near lossless data compression and quantum encoding. FPQE employs a convolutional encoder-decoder to learn compact multi-channel representations capable of reconstructing the original data with high fidelity, which are then mapped into quantum states through amplitude encoding. Experimental results show that FPQE performs comparably to conventional methods on simple datasets such as MNIST, while achieving clear improvements on more complex ones, outperforming PCA and pruning based encodings by up to 10.2\% accuracy on Cifar-10. The performance gain grows with data complexity, demonstrating FPQE's ability to preserve high-level structural information across diverse visual domains. By maintaining fidelity during classical to quantum transformation, FPQE establishes a scalable and hardware efficient foundation for high-quality quantum representation learning.Efficiently encoding classical visual data into quantum states is essential for realizing practical quantum neural networks (QNNs). However, existing encoding schemes often discard spatial and semantic information when adapting high-dimensional images to the limited qubits of Noisy Intermediate-Scale Quantum (NISQ) devices. We propose a Fidelity-Preserving Quantum Encoding (FPQE) framework that performs near lossless data compression and quantum encoding. FPQE employs a convolutional encoder-decoder to learn compact multi-channel representations capable of reconstructing the original data with high fidelity, which are then mapped into quantum states through amplitude encoding. Experimental results show that FPQE performs comparably to conventional methods on simple datasets such as MNIST, while achieving clear improvements on more complex ones, outperforming PCA and pruning based encodings by up to 10.2\% accuracy on Cifar-10. The performance gain grows with data complexity, demonstrating FPQE's ability to preserve high-level structural information across diverse visual domains. By maintaining fidelity during classical to quantum transformation, FPQE establishes a scalable and hardware efficient foundation for high-quality quantum representation learning.

quant-pharXiv:2511.15363Nov 20, 20250 citations

Evaluation of the Neural Quantum Theory in Vision

H. Richard Blackwell

The American Journal of PsychologyJul 1, 195311 citations

Quantum Neural Information Processing

Mitja Peruš, Chu Kiong Loo

IGI Global eBooksJan 1, 20110 citations

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

Ziyang Li, Xiaofei Fu, Lingdong Meng +1 more

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.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.

Scientific ReportsSep 1, 20253 citations

Overcoming the Representational Limitations of Amplitude Encoding for Quantum Neural Networks

Vincent Gurgul, David Prinz

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 $d$ features using only $\mathcal{O}(\log_2 d)$ 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.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 $d$ features using only $\mathcal{O}(\log_2 d)$ 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.

quant-pharXiv:2610.41824Nov 2, 2026

Quantum Neural Computation

Vladimir G. Ivancevic, Tijana T. Ivancevic

Springer eBooksJan 1, 201046 citations

d

features using only

\mathcal{O}(\log_2 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.