Diversity-Aware Ensemble of Quantum-Classical Models via Combinatorial Fusion

Jingyan Xu; Yuanhong Wu; Samuel Yen-Chi Chen; Sean Patten; Christina Schweikert; D. Frank Hsu

quant-phOct 9, 2026

Diversity-Aware Ensemble of Quantum-Classical Models via Combinatorial Fusion

Authors: Jingyan Xu, Yuanhong Wu, Samuel Yen-Chi Chen, Sean Patten, Christina Schweikert, D. Frank Hsu

Organizations: Laboratory of Informatics and Data Mining, Department of Computer and Information Science, Fordham University, New York, NY, USA · Wells Fargo, New York, NY, USA · Division of Computer Science, Mathematics and Science, St. John’s University, Queens, NY, USA

Abstract

Variational quantum circuits (VQCs) are highly sensitive to circuit architecture, yet most quantum machine learning pipelines select a single best design and discard the remaining candidates. This paper addresses whether the structural diversity across quantum circuit search spaces can be used to produce stronger predictions through model fusion. We apply Combinatorial Fusion Analysis (CFA), a model fusion framework that selects and combines multiple scoring systems using rank-score function (RSF) and cognitive diversity (CD), to a pool of 29 architecturally diverse classical models and quantum circuits. Using a diversity-aware model selection method, we identify subsets of maximally diverse models and combine them with both score and rank combination. Experiments on four binary classification benchmarks covering different domains demonstrate that CFA-based hybrid classical-quantum fusion consistently outperform the best individual model on every dataset considered with improvements up to 6.03% in accuracy. When comparing with relevant literatures, the CFA framework further achieves superior performance across all four datasets.

Figures & tables

Dataset	#Obs.	#Feat.	Majority class ratio	Description
Heart disease	270	13	0.556	Heart-related clinical data; predict presence vs absence of heart disease.
Ionosphere	351	34	0.641	Radar returns; predict good vs bad ionospheric signals.
Pima Diabetes	768	8	0.651	Medical measurements; predict diabetes outcome (0/1).
Spambase	4601	57	0.606	Email contents; classify spam vs non-spam.

TABLE I : Summary of the four benchmark datasets used in our paper. The majority-class ratio is the proportion of samples in the most frequent class.

Panel of Figure 2 — Fig. 1 : VQC architecture.

Panel of Figure 3 — Fig. 2 : Representative circuit architectures on $n=4$ qubits, illustrating three design philosophies in the 8-circuit pool. (a) StrongEnt; (b) TTN; (c) IQP. The remaining five circuits (BasicEnt, TwoDesign, Random, QAOA, MPS) follow one of these three philosophies and are described in the text.

Panel of Figure 4 — Fig. 3 : Workflow of combining quantum and classical models using CFA.

Fig. 5 : Diversity rank-score functions for the four datasets.

Panel of Figure 6 — Fig. 4 : Relationship among score function $s_{A}$ , rank function $r_{A}$ , and rank-score function $f_{A}$ .

Panel of Figure 7 — Fig. 6 : Rank-score function graphs on the test sets of the four datasets (quantum models are highlighted in maroon).

Datasets	Best single model		Best combined model
	Model	Performance	Model	Comb. type	Performance	Improvement
Heart disease	TTN	AUC: 0.9106	AdaBoost+ TTN +	ASC/WSCP	AUC: 0.9444	3.38%
			H_RY_cyc + QAOA			3.38%
Ionosphere	GBM or	Acc: 0.9434	H_RZ_std +GBM+	WSCDS	Acc: 0.9811	3.77%
	SVM_RBF		SVM_RBF+AdaBoost			3.77%
Pima diabetes	Adaboost or	Acc: 0.7845	AdaBoost+ StrongEnt	ASC/WSCP	Acc: 0.8448	6.03%

TABLE II : Best single-model and best CFA-based combined-model results on four benchmark datasets. For each dataset, we report the strongest individual model and its performance, together with the best-performing combined model selected by the proposed CFA framework, the corresponding combination type, and the relative improvement over the best single model. Maroon text denotes quantum models.

Dataset	Category	Models
Heart disease	Quantum	TTN, QAOA, H_RY_cyc
Heart disease	Classical	AdaBoost, GBM
Ionosphere	Quantum	H_RZ_std
Ionosphere	Classical	RF, GBM, SVM_RBF, AdaBoost
Pima diabetes	Quantum	StrongEnt, BasicEnt, H_RX_cyc
Pima diabetes	Classical	AdaBoost, SVM_RBF

TABLE III : List of selected models per dataset

Dataset	Paper	Year	Model	Performance
Heart disease	Qi et al. [ 66 ]	2021	Cost-sensitive ensemble (RF+LR+SVM+ELM+KNN, full features)	AUC: 0.8799
	Mukherjee et al. [ 67 ]	2017	SVM	AUC: 0.8985
	Heidari et al. [ 68 ]	2022	Hybrid quantum neural network and random forest (HQRF)	AUC: 0.9164
	Our method (CFA)	2026	AdaBoost+ TTN + H_RY_cyc + QAOA	AUC: 0.9444
Ionosphere	Santucci [ 69 ]	2017	Quantum nearest mean classifier (QNMC)	Acc: 0.8350
	Tychola et al. [ 70 ]	2023	Quantum SVM	Acc: 0.8400

TABLE IV : Benchmark comparison of the proposed method vs. recent reported results on four datasets. For each dataset, three studies are listed with publication year, model, and reported performance. The final row for each dataset shows the proposed classical-quantum combined model and its performance. Maroon text denotes quantum circuits from our framework.

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Beth Israel Deaconess Medical Center & Harvard Medical School Boston, MA, USA · Department of Electrophysics National Yang Ming Chiao Tung University Hsinchu, Taiwan

Quantum Machine Learning Tabular ML Variational Quantum Circuits

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Variational quantum circuits (VQCs) are a leading approach to quantum machine learning on near-term devices, yet it remains unclear which circuit architecture yields the best accuracy-parameter trade-off on classical tabular data. We present a systematic empirical comparison of four VQC families -- multi-layer fully-connected (FC-VQC), residual (ResNet-VQC), hybrid quantum-classical transformer (QT), and fully quantum transformer (FQT) -- across five regression and classification benchmarks. Our key findings are: \textbf{(i)}~FC-VQCs achieve 90-96% of the

R^2

of attention-based VQCs while using 40-50% fewer parameters, and consistently outperform equal-capacity MLPs (mean

R^2{=}0.829

vs.\ MLP

_{720}

0.753

on Boston Housing, 3-seed average); \textbf{(ii)}~~FC-VQC's Type~~4 inter-block connectivity provides partial cross-token mixing that approximates the role of attention -- explicit quantum self-attention yields only marginal gains on most datasets while significantly increasing parameter count; \textbf{(iii)}~~expressibility saturates at circuit depth~~

{\approx}\,3

, explaining why shallow VQCs already cover the Hilbert space effectively; \textbf{(iv)}~LayerNorm on the fully quantum transformer improves classification accuracy, suggesting normalization is important when all operations are quantum; \textbf{(v)}~in our noise study on Boston Housing, FQT degrades gracefully under depolarizing noise while QT collapses. All results are validated across three random seeds. These findings provide practical architectural guidance for deploying VQCs on near-term quantum hardware.

Abstract

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