Neural representations learned by neural networks encode task-relevant information, but their behavior under communication constraints is still poorly understood. We propose an information-theoretic framework for the comparison of classical compression and quantum-inspired amplitude encoding for the transfer of representations under controlled dimensional constraints. We analyze frozen intermediate features extracted from a pretrained ResNet-50 on the ImageNet-1K validation set at different depths in the network. The classical pipeline performs rate-controlled dimensionality reduction and uniform quantization, while the quantum-inspired pipeline does amplitude encoding and computational-basis probability decoding without variational circuits or trainable quantum parameters. Quality of representation was evaluated using differential entropy and a decoder-based lower bound on mutual information. Classical compression achieves higher decoder-based mutual information lower bounds at moderate and high communication budgets. However, the quantum-inspired pipeline retained a larger fraction of decoder-extractable task-relevant information under severe dimensional compression, with resource-normalized information efficiency providing a complementary perspective to the substantially higher absolute decoder-based mutual information lower bounds of the classical pipeline. Robustness analyses with qubit reduction and physically motivated noise models showed predictable degradation. Ablation and SHAP analyses indicate that task-relevant information is structured within representational subspaces. These findings support quantum-inspired representation transfer as a framework for studying communication-efficient neural representation transfer under low-bandwidth constraints.
Neural representations learned by neural networks encode task-relevant information, but their behavior under communication constraints is still poorly understood. We propose an information-theoretic framework for the comparison of classical compression and quantum-inspired amplitude encoding for the transfer of representations under controlled dimensional constraints. We analyze frozen intermediate features extracted from a pretrained ResNet-50 on the ImageNet-1K validation set at different depths in the network. The classical pipeline performs rate-controlled dimensionality reduction and uniform quantization, while the quantum-inspired pipeline does amplitude encoding and computational-basis probability decoding without variational circuits or trainable quantum parameters. Quality of representation was evaluated using differential entropy and a decoder-based lower bound on mutual information. Classical compression achieves higher decoder-based mutual information lower bounds at moderate and high communication budgets. However, the quantum-inspired pipeline retained a larger fraction of decoder-extractable task-relevant information under severe dimensional compression, with resource-normalized information efficiency providing a complementary perspective to the substantially higher absolute decoder-based mutual information lower bounds of the classical pipeline. Robustness analyses with qubit reduction and physically motivated noise models showed predictable degradation. Ablation and SHAP analyses indicate that task-relevant information is structured within representational subspaces. These findings support quantum-inspired representation transfer as a framework for studying communication-efficient neural representation transfer under low-bandwidth constraints.
Quantum neural networks (QNNs), harnessing superposition and entanglement, have shown potential to surpass classical methods in complex learning tasks but remain limited by hardware constraints and noisy conditions. In this work, we present a novel framework for transferring knowledge from classical convolutional neural networks (CNNs) to QNNs via knowledge distillation, thereby reducing the need for resource intensive quantum training and error mitigation. We conduct extensive experiments using two parameterized quantum circuits (PQCs) with 4 and 8 qubits on MNIST, Fashion MNIST, and CIFAR10 datasets. The approach demonstrates consistent accuracy improvements attributed to distilled knowledge from larger classical networks. Through ablation studies, we systematically compare the effect of state of the art dimensionality reduction techniques fully connected layers, center cropping, principal component analysis, and pooling to compress high-dimensional image data prior to quantum encoding. Our findings reveal that fully connected layers retain the most salient features for QNN inference, thereby surpassing other down sampling approaches. Additionally, we examine state of the art data encoding methods (amplitude, angle, and qubit encoding) and identify amplitude encoding as the optimal strategy, yielding superior accuracy across all tested datasets and qubit configurations. Through computational analyses, we show that our distilled 4-qubit and 8-qubit QNNs achieve competitive performance while utilizing significantly fewer parameters than their classical counterparts. Our results establish a promising paradigm for bridging classical deep learning and emerging quantum computing, paving the way for more powerful, resource conscious models in quantum machine intelligence.
A central question in hybrid quantum–classical learning is whether variational quantum circuits (VQCs) preserve task-relevant information more efficiently than classical nonlinearities of equal output dimension. We study this question for drug–target interaction prediction in Alzheimer’s disease drug-repurposing workflows using a Hybrid Quantum–Classical Graph Neural Network (HQGNN). The model compresses 512-dimensional GNN embeddings into a four-qubit VQC (128 × compression) before a classical prediction head. On the DAVIS kinase benchmark, HQGNN achieves concordance index (CI) =0.527 and root mean squared error (RMSE) =0.850 , outperforming a dimension-matched classical bottleneck baseline (CI =0.500 ; random ranking). Under the same compression, the quantum layer recovers 51% of the ranking signal lost by compression relative to the full classical model and yields a 5.4% relative CI gain over the classical bottleneck. This effect is obtained with 24 trainable quantum parameters (representational yield Δ CI/parameter ≈1.13×10−3 ). Under depolarizing noise, RMSE degradation remains below 3.3% at realistic noisy intermediate-scale quantum (NISQ) levels ( p≤0.01 ). Because the present benchmark is evaluated on a single transductive split, these results are interpreted as controlled proof-of-concept evidence of representational efficiency rather than definitive deployment-level generalization.
Abstract In the era of noisy intermediate-scale quantum (NISQ) computing, the stable integration of high-dimensional classical states into quantum neural networks is a critical challenge for quantum reinforcement learning. Existing encoding schemes either rely heavily on classical neural networks, which can overshadow the training contributions of the quantum component, or use standard quantum input methods such as amplitude encoding, which suffer from limited trainability, noise sensitivity, and high implementation costs. To address this challenge, this paper repurposes uniformly controlled rotations (UCR) from static state preparation and static data encoding into a state-encoding interface for quantum neural networks, elevating the process of integrating classical states into quantum neural networks to an independent method-ological layer. Across Gymnasium continuous-control tasks, our UCR encoding achieves the best peak return, final return, and evaluation-curve AUC compared to representative angle encoding and amplitude encoding, with the AUC improving by +5.9 to +53.5 return units over angle encoding. While our UCR encoding is not the method with the fewest gates, it eliminates the classical neural networks on which angle encoding relies during dimensionality reduction, provides a fixed, sample-independent topology, and supports explicit resource accounting. On BipedalWalker-v3, UCR encoding reduces the actor parameter count of angle encoding from 1003 to 229 and increases the final return from 220.4 to 264.9, which is higher than the final return of amplitude encoding. A systematic evaluation of gate-level noise shows that the absolute performance advantage of UCR encoding in complex continuous control tasks persists in the low-noise regime, but this advantage window narrows as the input dimension and quantum circuit depth increase. For high-dimensional classical state inputs, UCR encoding achieves a more stable performance–resource trade-off than typical quantum encoding methods. Motivated by the problem of inputting classical states into quantum neural networks, our approach may be further explored in broader machine learning scenarios and higher-dimensional applications.
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 O(log2d) 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.
Large language and sentence-embedding models provide rich semantic representations, but their high dimensionality poses a challenge for near-term quantum machine learning (QML), where quantum circuits can process only a limited number of input features. We investigate a hybrid quantum-classical pipeline that transforms high-dimensional sentence embeddings into compact representations for variational quantum classification. The workflow combines a pretrained sentence-embedding model, dimensionality reduction, angle encoding, a variational quantum circuit (VQC), and a classical decision layer. We systematically compare principal component analysis (PCA), neighborhood components analysis (NCA), and linear discriminant analysis (LDA), covering both unsupervised and supervised dimensionality reduction. Using the TREC question-classification dataset, we study the relationship between representation dimensionality, information retention, qubit count, and classification performance. Preliminary PCA experiments reveal a strong information bottleneck: reducing 768-dimensional embeddings to 3, 4, 5, and 8 dimensions retains about 8.2%, 10.2%, 11.9%, and 16.4% of the variance, with corresponding classification accuracies of 50.3%, 51.2%, 57.9%, and 63.4%. In contrast, supervised reduction is substantially more efficient. LDA reaches 85.3% accuracy and NCA reaches 83.1% using only 5 dimensions, under a leakage-free cross-validation protocol, compared with 85.1% for a full 384-dimensional classical baseline. These results indicate that supervised dimensionality reduction can preserve task-relevant information far more effectively than variance-based compression, making compact representations a promising route toward practical hybrid quantum-classical NLP models.
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.