Organizations: Centre for Quantum Software and Information, University of Technology Sydney, 15 Broadway, Ultimo, Sydney, 2007, NSW, Australia. · Bikash’s Quantum (OPC) Pvt. Ltd., Balindi, Mohanpur, 741246, WB, India. · Universit`a degli Studi di Cagliari, Via Is Mirrions, Cagliari, 09123, Italy.
We propose a geometry-driven quantum-inspired classification framework that integrates Correlation Group Structures (CGR), compact SWAP-test-based overlap estimation, and selective variational quantum decision modelling. Rather than directly approximating class posteriors, the method adopts a geometry-first paradigm in which samples are evaluated relative to class medoids using overlap-derived Euclidean-like and angular similarity channels. CGR organizes features into anchor-centered correlation neighbourhoods, generating nonlinear, correlation-weighted representations that enhance robustness in heterogeneous tabular spaces. These geometric signals are fused through a non-probabilistic margin-based fusion score, serving as a lightweight and data-efficient primary classifier for small-to-moderate datasets. On Heart Disease, Breast Cancer, and Wine Quality datasets, the fusion-score classifier achieves 0.8478, 0.8881, and 0.9556 test accuracy respectively, with macro-F1 scores of 0.8463, 0.8703, and 0.9522, demonstrating competitive and stable performance relative to classical baselines. For large-scale and highly imbalanced regimes, we construct compact Delta-distance contrastive features and train a variational quantum classifier (VQC) as a nonlinear refinement layer. On the Credit Card Fraud dataset (0.17% prevalence), the Delta + VQC pipeline achieves approximately 0.85 minority recall at an alert rate of approximately 1.31%, with ROC-AUC 0.9249 and PR-AUC 0.3251 under full-dataset evaluation. These results highlight the importance of operating-point-aware assessment in rare-event detection and demonstrate that the proposed hybrid geometric-variational framework provides interpretable, scalable, and regime-adaptive classification across heterogeneous data settings.
Figures & tables
Dataset
Metric
Fusion (ours)
LogReg
LinearSVM
RBF_SVM
RandomForest
Heart Disease
Accuracy
0.8478
0.8565
0.8565
0.8870
0.8913
Macro-F1
0.8463
0.8551
0.8551
0.8861
0.8898
Weighted-F1
0.8479
0.8566
0.8566
0.8871
0.8911
ROC-AUC
–
0.9021
0.8997
0.9372
0.9408
PR-AUC
–
0.8976
0.8908
0.9435
0.9437
Breast Cancer
Accuracy
0.8881
0.9860
0.9580
0.9720
0.9790
Table 1: Test-set comparison: Fusion-score (ours) vs. classical baselines across Heart Disease, Breast Cancer, and Wine Quality. Metrics are rows and models are columns. For Fusion, the reported setting is the validation-selected best- k and α⋆ per dataset.
Metric
Ours ( Δ +VQC, τ =0.3)
LogReg_raw
LinearSVM_raw
RF_raw
N evaluated
284,807
284,807
284,807
284,807
Prevalence
0.0017
0.0017
0.0017
0.0017
Alert rate
0.0131
0.0130
0.0133
0.0128
Precision (fraud)
0.1124
0.1188
0.1157
0.1277
Recall (fraud)
0.8496
0.8963
0.8923
0.9492
F1 (fraud)
0.1985
0.2098
0.2049
0.2251
Table 2: Fraud classification on the full dataset (raw-feature baselines) under an alert-rate matched operating point. The proposed model is scored using the fixed VQC threshold τ=0.3 .
Metric
Ours ( Δ +VQC, τ =0.3)
LogReg_SMOTE
LinearSVM_SMOTE
RF_SMOTE
N evaluated
284,807
284,807
284,807
284,807
Prevalence
0.0017
0.0017
0.0017
0.0017
Alert rate
0.0131
0.0130
0.0130
0.0090
Precision (fraud)
0.1124
0.1192
0.1193
0.1835
Recall (fraud)
0.8496
0.8984
0.9004
0.9512
F1 (fraud)
0.1985
0.2105
0.2107
0.3076
Table 3: Fraud classification on the full dataset (raw-feature baselines with SMOTE applied on the training split) under an alert-rate matched operating point. The proposed model is scored using the fixed VQC threshold τ=0.3 .
Metric
Ours ( Δ +VQC, τ =0.3)
LogReg_raw
LinearSVM_raw_cal
RF_raw
N evaluated
284,807
284,807
284,807
284,807
Prevalence
0.0017
0.0017
0.0017
0.0017
Alert rate
0.0131
0.0242
0.0012
0.0016
Precision (fraud)
0.1124
0.0658
0.8663
0.9516
Recall (fraud)
0.8496
0.9228
0.5793
0.8801
F1 (fraud)
0.1985
0.1229
0.6943
0.9145
Table 4: Fraud classification on the full dataset at a fixed classical decision threshold of 0.5 (raw-feature baselines). The proposed model is shown for reference using τ=0.3 .
Metric
Ours ( Δ +VQC, τ =0.3)
LogReg_SMOTE
LinearSVM_SMOTE_cal
RF_SMOTE
N evaluated
284,807
284,807
284,807
284,807
Prevalence
0.0017
0.0017
0.0017
0.0017
Alert rate
0.0131
0.0046
0.0049
0.0017
Precision (fraud)
0.1124
0.3279
0.3059
0.9433
Recall (fraud)
0.8496
0.8659
0.8679
0.9126
F1 (fraud)
0.1985
0.4757
0.4523
0.9277
Table 5: Fraud classification on the full dataset at a fixed classical decision threshold of 0.5 (raw-feature baselines with SMOTE applied on the training split). The proposed model is shown for reference using τ=0.3 .
Dataset
N
d
#classes
Class counts
Split (train/val/test)
best- k
α⋆
Val Acc
Val F1 macro
Heart Disease
918
11
2
(0:410, 1:508)
516/172/230
3
1.00
0.8198
0.8184
Breast Cancer (Wisconsin)
569
30
2
(B:357, M:212)
319/107/143
3
0.90
0.9159
0.9052
Wine Quality (3-class)
178
13
3
(1:59, 2:71, 3:48)
99/34/45
4
0.85
0.9412
0.9428
Table 6: Dataset characteristics and Fusion-score performance (best- k selected by coordinate descent; α tuned via α -sweep on validation).
Dataset
Test Acc
Test F1 macro
Heart Disease
0.8478
0.8463
Breast Cancer (Wisconsin)
0.8881
0.8703
Wine Quality (3-class)
0.9556
0.9522
Table 7: Test-set Fusion-score performance at the selected best- k and α⋆ .
Dataset
Split
Confusion matrix
Heart Disease
Val
[63171478]
Heart Disease
Test
[861817109]
Breast Cancer (Wisconsin)
Val
[679031]
Breast Cancer (Wisconsin)
Test
[9016037]
Wine Quality (3-class)
Val
10001130019
Wine Quality (3-class)
Test
150001820010
Table 8: Fusion-score confusion matrices (rows=true, cols=pred) for the selected best- k per dataset.
In this paper, a learning framework is introduced which incorporates principles of probabilistic inference, variational optimization, and geometry-preserving operations inspired by quantum transformations. The central innovation of this quantum-inspired variational convolution (QiVC) lies in its quantum-inspired rotated ensemble (QiRE) mechanism. QiRE performs differentiable low-dimensional subspace rotations of convolutional weights. By drawing a mathematical analogy from unitary evolution, this approach enables structured uncertainty modeling that respects the intrinsic geometry of the parameter space. To demonstrate its practical potential, the concept is instantiated in a QiVC-based convolutional network (QiVC-Net) and evaluated in the context of biosignal classification, focusing on phonocardiogram (PCG) recordings. The proposed QiVC-Net integrates an architecture in which the QiVC layer does not introduce additional parameters, instead performing an ensemble rotation of the convolutional weights through a structured mechanism ensuring robustness without added highly computational burden. Experiments on two benchmark datasets, PhysioNet CinC 2016 and PhysioNet CirCor DigiScope 2022, show that QiVC-Net achieves state-of-the-art performance, reaching accuracies of 97.84% and 97.89%, respectively. These findings highlight the versatility of the QiVC framework and its promise for advancing uncertainty-aware modeling in real-world biomedical signal analysis. The implementation of the QiVConv layer is available in GitHub for public use.
Amin Golnari, Jamileh Yousefi, Reza Moheimani +1
College of Engineering and Computer Science VinUniversity Hanoi, Vietnam · Shannon School of Business Cape Breton University Sydney, NS, Canada · Faculty of Computer Science Chemnitz University of Technology Chemnitz, Germany +2
We investigate variational quantum classifiers (VQCs) for land-cover classification from multispectral satellite imagery, adopting a feature-map perspective in which the quantum circuit defines a nonlinear data embedding while the readout determines how this representation is exploited. Using the EuroSAT-MS dataset, we perform a systematic one-vs-one evaluation across all class pairs under a controlled experimental protocol, comparing classical baselines (logistic regression, SVMs, neural networks) with VQCs employing both linear readout and quantum-kernel SVM strategies. Our results show that, while VQCs with linear readout do not outperform strong classical baselines such as RBF-SVM, the same trained quantum feature map can significantly improve performance when reused within a kernel-based decision framework. A qubit-count sweep further reveals saturation effects consistent with the mismatch between exponential Hilbert space dimension and linear parameter scaling. Overall, our findings highlight that the effectiveness of quantum models depends critically on the interplay between representation and readout, and that meaningful gains may arise from combining learned quantum feature maps with classical decision mechanisms rather than seeking direct replacement of classical models.
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece · Eulambia Advanced Technologies Ltd, Agiou Ioannou 24, Ag. Paraskevi, 15342, Greece
Quantum kernel methods are a promising branch of quantum machine learning, but their per- formance across data types and encoding choices remains incompletely understood. To address this gap, we developed an algorithmic framework for variational quantum kernels utilizing resource- efficient ansätze for complex classification tasks and introduced a parameter scaling technique to accelerate convergence. We conducted a comprehensive benchmark of this framework on eight chal- lenging, real-world and high-dimensional datasets covering tabular, image, time series, and graph data. Our results show that the proposed quantum kernel demonstrated competitive classification accuracy compared to standard classical kernels in classical simulation, such as the radial basis function (RBF) kernel. This work demonstrates that properly designed quantum kernels can func- tion as versatile, high-performance tools, laying a foundation for quantum-enhanced applications in machine learning. Further research is needed to fully assess the practical performance of quantum methods.
Jiang Yuhan, Matthew Otten
Department of Physics, University of Wisconsin–Madison, Madison, WI 53706, USA · Department of Chemistry, University of Wisconsin–Madison, Madison, WI 53706, USA