When do quantum views help? Complementary classical-quantum representations in multi-view fusion

Azadeh Alavi; Fatemeh Kouchmeshki; Hossein Akhoundi; Yongli Re; Abdolrahman Alavi; Muhammad Usman

quant-phOct 15, 2026

When do quantum views help? Complementary classical-quantum representations in multi-view fusion

Authors: Azadeh Alavi, Fatemeh Kouchmeshki, Hossein Akhoundi, Yongli Re, Abdolrahman Alavi, Muhammad Usman

Organizations: RMIT University, GPO Box 2476, Melbourne VIC 3001, Australia. · Pattern Recognition Pty Ltd, Melbourne, Australia. · Faculty of Information Technology, Monash University, 25 Exhibition Walk, Clayton VIC 3800, Australia.

Abstract

Recent studies have reported promising results from quantum machine learning in drug discovery, healthcare, materials science and cybersecurity. Research includes comparisons with classical machine learning algorithms and the development of sequential hybrid pipelines. We propose that fusion can improve prediction when classical and quantum representations capture complementary predictive relationships. Our classical-quantum multi-view framework preserves the full classical input alongside simulated quantum features. Concatenation and attention combine the views; single-view comparisons, replacement and masking controls assess both views' contributions. Controlled angular-polynomial experiments distinguish targets adequately represented by a single view from those that depend on complementary angular and polynomial relationships. For these mixed targets, fusion improves prediction by combining the relevant feature sets, while matched classical representations recover the same benefit, linking the improvement to their complementary predictive content. Controlled classification tests further show that gains depend on alignment between the chosen representation and the target, and on a suitable fusion rule. Benchmark validation shows improved mean predictive performance over classical baselines on Wine, Wisconsin Diagnostic Breast Cancer, three-class Fashion-MNIST and Steel Plates Faults within the evaluated protocols. Classical replacement and masking controls remain competitive, classical baselines lead on Digits and Covertype, and outcomes with missing or corrupted views depend on the available inputs. These findings support evaluating quantum representations for their complementary predictive contribution and matching the representation and fusion strategy to the target relationships.

Figures & tables

Figure 1: Representative hybrid information flows. Panels (a) and (c) summarize classical-to-quantum and classical–quantum–classical arrangements [ 26 ] ; (b) shows quantum feature extraction followed by classical learning [ 16 ] . Panel (d) shows the retained-input fusion arrangement studied here, with retained-input bypass models as prior architectural precedent [ 45 ] . Arrows show forward processing, rather than the training optimizer. Each quantum stage transforms its input into numerical features; Section 2.1 explains the operations involved. The arrangements are schematic and may overlap in a complete model.

Figure 2: Single-qubit geometry and readout. (a) The angles

\vartheta

and

\varphi

locate a pure state on the Bloch sphere; the purple arrow is its Bloch vector. The blue guide marks its vertical coordinate

r_{z}

. (b) This coordinate determines the probabilities of the two

Z

outcomes and their signed mean. Mixed local states lie inside the sphere. The experiments extend this readout principle to multi-qubit local and pairwise observables.

Figure 3: Matched attention-fusion model. (a) Standardization preserves all

d

classical input features; the circuit branch compresses the input to nine coordinates. Three trainable circuit layers produce 18 exact readouts. (b) The classical summary provides each attention query; all 19 tokens provide keys and values. Four head outputs update the summary through projection, residual addition, normalization and a feed-forward block. Only that summary is classified. Blue denotes the retained classical path, purple the circuit branch and teal fusion. Att-C replaces the circuit at its 18-feature interface; Q-mask blocks its tokens from the summary.

1	Fit standardization and nine-component PCA on the fitting set; retain those transformations for monitoring and prediction.
2	Initialize the classical encoder, circuit angles, token embeddings, attention projections and classifier.
3	For each epoch and shuffled fitting minibatch:
4	Retain the full standardized input; obtain circuit angles from the PCA scores using Eq. ( 8 ).
5	Encode the nine qubits, apply the three circuit layers and calculate the 18 local/pair expectation values.
6	Form the classical summary $t_{0}$ and readout tokens $t_{a}$ using Eq. ( 9 ).
7	Pool the joint tokens with the four summary queries in Eq. ( 10 ); apply projection, residual connections, normalization and the feed-forward block.

Algorithm 1: Matched classical–quantum attention fusion

Target	$d$	C	Q	C+Q	Union	RBF
Polynomial	3	0.1030	1.0128	0.1033	0.1038	0.1332
	4	0.1043	1.0132	0.1048	0.1056	0.1544
	5	0.1059	1.0141	0.1059	0.1081	0.1815
Angular	3	0.9330	0.1008	0.1011	0.1036	0.3604
	4	0.9378	0.1015	0.1015	0.1055	0.5827
	5	0.9465	0.1021	0.1021	0.1078	0.7752

Table 1: Controlled regression with 256 training observations, full sine coefficient

\kappa=1

and 20 independent repetitions. Mean expected-loss RMSE; lower is better. C is polynomial, Q is the selected pair-readout view, and C+Q is feature-kernel fusion. Union is the matched classical combination; RBF uses all raw inputs. The noise limit is 0.1. These are the diagnostic models of Section 3.2 . Repetition SDs and 95% intervals are in Section S8.

Procedure	Mean	SD
C	0.386	0.018
Q	0.395	0.014
C+Q	0.256	0.018
$Q_{\rm ind}$	0.503	0.004
C+ $Q_{\rm ind}$	0.397	0.016
C+T	0.387	0.019

Table 2: Same-input constructed target with

w=0.5

. Summed Brier loss over ten data/circuit repetitions. All fitted procedures use logistic classifiers; lower is better. The target includes a readout of Q, while

Q_{\rm ind}

is an independent circuit draw. RP and RF are classical feature alternatives with the same added-feature count.

Model	Additive	Interaction	Fourier
C	0.561 (0.004)	0.695 (0.003)	0.694 (0.001)
Q	0.585 (0.001)	0.694 (0.001)	0.693 (0.001)
C+Q, additive	0.402 (0.010)	0.696 (0.004)	0.693 (0.001)
C+Q, interaction	0.436 (0.005)	0.666 (0.007)	0.693 (0.001)
C+replacement	0.570 (0.006)	0.694 (0.001)	0.580 (0.026)
Trig., all inputs	0.563 (0.003)	0.699 (0.014)	0.504 (0.009)

Table 3: Constructed block-target test log loss: mean (SD) over three independent generated datasets. Lower is better. The final row is the conditional expected Bayes loss, not a fitted model.

Method	Wine	WDBC	Digits
MLP	0.963 (0.031)	0.970 (0.007)	0.953 (0.017)
Concat-CQ	0.966 (0.029)	0.969 (0.008)	0.944 (0.022)
Att-CQ	0.975 (0.021)	0.972 (0.009)	0.950 (0.010)
Att-C	0.977 (0.023)	0.971 (0.007)	0.949 (0.016)
Q-mask	0.978 (0.018)	0.971 (0.007)	0.948 (0.014)

Table 4: Matched neural macro-

F_{1}

under the calibrated 240-epoch protocol: mean (fold SD). Each mean averages two initialization-specific scores after pooling three outer folds. SD describes the six fold scores, not the standard error of the mean. Higher is better.

	Clean		Missing		Noisy
Method	Mean	SD	Mean	SD	Mean	SD
TMC (extended)	0.037	0.001	0.042	0.002	0.041	0.001
Attention C	0.046	0.002	0.133	0.012	0.051	0.002
Attention C+Q	0.049	0.005	0.131	0.023	0.054	0.005
Attention C+Qp	0.047	0.006	0.134	0.017	0.052	0.006

Table 5: Native-view attention on all 2,000 Multiple Features objects. Mean and SD are calculated across three repetitions, each pooling three outer folds. Missing and noisy Brier losses first average the six source-specific conditions within a repetition. All losses are summed Brier; lower is better. TMC uses its extended training sensitivity.

Multiple Features
Input	Method	Brier loss	Accuracy
Complete	TMC	0.032 (0.006)	0.974 (0.008)
	TMC Q	0.032 (0.006)	0.976 (0.007)
Missing	TMC	0.036 (0.007)	0.975 (0.007)
	TMC Q	0.036 (0.007)	0.976 (0.006)
CUB image–text benchmark

Table 6: Evidence-fusion extension: mean (SD) over three grouped holdouts. The Multiple Features missing condition averages six source removals. TCVC † is the observed-only adaptation. Lower summed Brier loss and higher accuracy are preferred.

Method	Wine	WDBC	Covertype	Fashion	Steel
Classical	0.943 (0.079)	0.966 (0.019)	0.811 (0.009)	0.969 (0.007)	0.768 (0.015)
Quantum	0.205 (0.017)	0.405 (0.101)	0.335 (0.036)	0.491 (0.032)	0.381 (0.038)
CQ latent	0.844 (0.047)	0.950 (0.027)	0.771 (0.013)	0.963 (0.012)	0.640 (0.034)
CQ attention	0.967 (0.036)	0.966 (0.016)	0.780 (0.028)	0.963 (0.012)	0.771 (0.012)
CQ early	0.928 (0.033)	0.960 (0.024)	0.806 (0.018)	0.971 (0.008)	0.738 (0.025)
CQ late	0.852 (0.077)	0.954 (0.027)	0.794 (0.020)	0.964 (0.007)	0.717 (0.047)

Table 7: Five-benchmark fusion-stage experiment. Macro-

F_{1}

mean (fold SD) over five folds. Fashion and Steel denote Fashion-MNIST and Steel Plates Faults. Covertype and Fashion use the three-class subsets specified in the text.

Figure 4: Balanced visual summary of the retained benchmark results. (a) Matched calibrated macro- $F_{1}$ means and descriptive fold SDs from Table 4 ; the bars are not confidence intervals. (b) Change from the classical mean for every fusion route in Table 7 , multiplied by 100. Positive values favour fusion. The colour range is clipped at $\pm 5$ , while annotations show the actual differences of the displayed means. Fashion and Steel denote the evaluated Fashion-MNIST subset and Steel Plates Faults. Fold SDs for this panel remain in Table 7 . The panels use different protocols and support separate comparisons.

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On the Complementarity of Quantum and Classical Features: Adaptive Hybrid Quantum-Classical Feature Fusion for Breast Cancer Classification

Yasmin Rodrigues Sobrinho, João Renato Ribeiro Manesco, João Paulo Papa

Department of Computing, São Paulo State University, Ave. Engenheiro Luiz Edmundo Carrijo Coube, 14-01 - Vargem Limpa, Bauru, 17033-360, São Paulo, Brazil

Hybrid Quantum-Classical ML Medical Image Classification

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The integration of quantum machine learning with classical deep learning offers promising avenues for medical image analysis by mapping data into high-dimensional Hilbert spaces. However, unifying these paradigms remains challenging due to optimization asymmetries. We propose a hybrid quantum-classical architecture for breast cancer diagnosis based on a dual-branch feature-extraction pipeline. Our framework unifies complementary representations from classical models and trainable or deterministic (non-trainable) quantum circuits. Three fusion strategies are introduced: Static Hybrid Fusion (SHF) for offline extraction, Dynamic Hybrid Fusion (DHF) for end-to-end co-adaptation, and Temperature-Scaled Hybrid Fusion (TSHF). Inspired by multimodal learning, TSHF uses a learnable scalar to balance branch gradient dynamics and address optimization bottlenecks. We evaluate BreastMNIST, INbreast, and BUS-UCLM, spanning ultrasound and mammography, using ResNet-18 and a shallow CNN, with five independent runs per configuration. Fusion improves over the strongest classical baseline on all three benchmarks. On BreastMNIST, TSHF with ResNet-18 and a non-trainable circuit achieves 88.33% accuracy, 92.09% F1-score, and 92.09% AUC-ROC, versus 84.74% accuracy and 87.08% AUC-ROC for ResNet-18 alone. On INbreast, SHF with the same pairing performs best, at 70.42% accuracy, 72.96% F1-score, and 80.28% AUC-ROC. On BUS-UCLM, SHF with a trainable circuit achieves 78.46% accuracy and 84.66% F1-score, over seven accuracy points above the best standalone branch. Adaptive fusion is not universally beneficial: static fusion performs best on the two smaller datasets, suggesting an additional estimation burden from co-adaptation and learned calibration under limited data. Clinical applicability requires validation beyond the small, low-resolution datasets and simulated quantum circuits considered here.

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