quant-phOct 13, 2026

Representation Geometry and Inductive Biases in Quantum Classifiers across Classical Visual Benchmarks

Authors: Yu Yamaoka, Weng Ian Chan, Kosuke Mitarai

Organizations: Center for Quantum Information and Quantum Biology, The University of Osaka, 1-2 Machikaneyama, Toyonaka, 560-0043, Osaka, Japan. · SANKEN, The University of Osaka, 1-5 Yamadaoka, Suita, 565-0871, Osaka, Japan. · Graduate School of Engineering Science, The University of Osaka, 1-3 Machikaneyama, Toyonaka, 560-8531, Osaka, Japan.

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Abstract

Quantum Machine Learning (QML) has a theoretical advantage over classical algorithms for specific synthetic data that is computationally hard. However, it remains unclear whether such theoretical advantages play a meaningful role for realistic classical data, such as natural images. Quantum structural properties induced by unitary operations or entanglement introduce inductive biases that differ from those of classical models, potentially leading to distinct learning behavior on real-world data. In a fully quantum learning pipeline, classical real-world data are first encoded into quantum states via a quantum feature mapping, analogous to a classical feature extractor, and a quantum classifier then classifies the resulting states. Quantum feature mappings generate representations that are difficult to realize classically, while also inducing representation-level biases that do not necessarily match the structure of realistic data. To enable a fair comparison at the classifier level, we focus on the classifier and use classical feature extractors that already provide powerful representations for natural images. By controlling the data scale and supervision strength, we analyze how the unitary structure of quantum classifiers affects generalization, and show that their effectiveness depends strongly on the geometry of the input representations. These results indicate that quantum classifiers benefit from classical features that are aligned with quantum feature spaces. Our analysis shows that kernel alignment identifies representations compatible with quantum feature spaces, providing insights into translating classical models into quantum algorithms.

Figures & tables

Figure 1: Quantum classification pipeline using classical features. UentU_{ent} is a fixed entangling unitary applied across the qubits.
Figure 2: Mean test accuracy with 9595 % confidence interval as error bars across different dataset sizes (higher is better).
Figure 4: Test accuracy on cross-dataset and cross-feature comparison.
Figure 5: Relationship between the change in kernel-target alignment ΔKTA\Delta\mathrm{KTA} and the test accuracy difference ΔAcc\Delta\mathrm{Acc} . Each point corresponds to a dataset–backbone pair, with colors indicating datasets and marker shapes indicating backbones. A positive correlation (Pearson r=0.312r=0.312 , Spearman ρ=0.429\rho=0.429 ) indicates that performance differences follow changes in representation alignment.
Figure 6: Test accuracy versus the number of trainable parameters for each dataset using CLIP-extracted image features and a quantum classifier head.
Appendix figures & tables5 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A: Gate structure for encoding and weight matrix
Figure B: Overview of our Q-LLP.
Figure C: Test accuracy as a function of parameter count for classical and quantum classifiers when the quantum feature map does not improve kernel–label alignment ( Δ\Delta KTA <0<0 ). In these settings, the classical representation already provides a favorable feature geometry, and both models exhibit similar scaling behavior with respect to parameter count.
Figure D: Test accuracy (We report mean and standard deviation over random seeds. The setting is fixed to: CIFAR10 ×\times CLIP (Frac =0.1=0.1 ), Flowers102 ×\times CLIP (Frac =1.0=1.0 ), and Food101 ×\times CLIP (Frac =0.1=0.1 ).
Dataset/resourceVersion/subset usedLicense status
CIFAR-104-class subsetsNon-Commercial Use
Fashion-MNIST4-class subsetsMIT
SVHN4-class subsetsNon-Commercial Use
STL-104-class subsetsNon-Commercial Use; images acquired from ImageNet
Oxford-IIIT Pet4-class subsetsCC BY-SA 4.0
Oxford Flowers 1024-class subsetsNon-Commercial Use
Appendix
Table A: Dataset license status summary.
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