HQCNN: Hybrid Quantum Convolutional Neural Network

• HQCNN is a hybrid quantum-classical model that couples classical CNN layers with parameterized quantum circuits for enhanced and efficient feature extraction.
• It comprises diverse architectural patterns, including CNN-to-QNN pipelines, quantum preprocessing combined with CNNs, and canonical QCNN cores adapted to NISQ hardware constraints.
• Empirical evaluations in image and medical diagnostics demonstrate competitive accuracies and improved robustness, highlighting HQCNN's potential despite current qubit and noise limitations.

Hybrid Quantum Convolutional Neural Network (HQCNN) designates a class of hybrid quantum-classical models in which convolutional feature extraction, convolution-inspired hierarchical processing, or both are coupled to parameterized quantum circuits (PQCs) and classical readout layers. In the current literature, the label covers several related but non-identical constructions: a classical CNN whose latent features are passed to a QNN layer, a hybrid pipeline with classical downsampling and a quantum convolution/pooling core, and quanvolutional or random-circuit preprocessing whose outputs are consumed by a conventional CNN (Shi et al., 2023, Zaman et al., 2024, Houssein et al., 2021). This suggests HQCNN is best understood as an architectural family rather than a single canonical network.

1. Conceptual scope and nomenclature

The most restrictive usage of HQCNN corresponds to a quantum convolutional neural network embedded in a hybrid pipeline. In that formulation, the structure is typically: input encoding, quantum convolution, quantum pooling, measurement, and classical output mapping. A comparative study of hybrid quantum-classical image classifiers describes QCNN in exactly these terms, while also emphasizing that NISQ limitations require classical convolution and pooling before the quantum circuit and a classical fully connected layer afterward (Zaman et al., 2024).

A broader usage appears in papers that call a hybrid model “QCNN” or “HQCNN” even when the quantum component is not a canonical hierarchical quantum convolution/pooling stack. The Iris classifier labeled QCNN is explicitly described as closer to a variational quantum classifier or circuit-centric hybrid model than to the canonical QCNN architecture of Cong et al. (Tomal et al., 2024). Likewise, a breast histopathology study uses the term for three models in which a classical CNN ends in a scalar feature and a lightweight PQC performs the final binary decision (Guha et al., 2024).

A third usage treats HQCNN as a general hybrid design principle rather than a fixed topology. The parallel proportional fusion of spiking and quantum branches is presented as relevant to HQCNN because it challenges the assumption that hybrid quantum-classical models must be serial, even though the implemented model is not convolutional and uses an SNN rather than a CNN (Xu et al., 2024).

Family	Characteristic pipeline	Representative papers
CNN-to-QNN hybrids	classical CNN extractor $\rightarrow$ quantum layer/classifier $\rightarrow$ classical output	(Shi et al., 2023, Guha et al., 2024, Shahjalal et al., 16 Sep 2025)
Hybrid QCNN cores	classical downsizing $\rightarrow$ quantum convolution/pooling $\rightarrow$ measurement $\rightarrow$ classical FC	(Zaman et al., 2024, Ahmed et al., 6 May 2025, Kim et al., 25 Feb 2026)
Quantum preprocessing + classical CNN	quantum patch transform or random circuit feature map $\rightarrow$ classical CNN	(Houssein et al., 2021, Ng et al., 2024)

2. Architectural patterns

A common serial pattern is the classical CNN backbone followed by a quantum layer. In multi-class image classification, one studied pipeline is

$$\text{image} \rightarrow \text{CNN feature extractor} \rightarrow \text{QNN layer} \rightarrow \text{FC layer} \rightarrow \text{prediction},$$

with the QNN acting either as a quantum hidden layer or as a quantum classifier layer. The same study contrasts this design with a PCA-reduced, angle-encoded QNN and argues that the CNN front end is preferable because it learns features end-to-end, captures local patterns and textures, preserves multi-scale structure, includes nonlinear activations, and provides better feature representations for the QNN than global PCA reduction (Shi et al., 2023).

Another major pattern is quanvolutional or quantum-convolutional preprocessing. In the COVID-19 chest X-ray system, the first classical convolution is replaced by a quantum convolution layer built from random quantum circuits on $2 \times 2$ patches. The quantum layer outputs 4 channels, after which a nine-layer classical CNN performs deeper feature learning and final classification; the reported total parameter count is 120,394 (Houssein et al., 2021). A color-space study follows a similar quantum-front-end strategy, using a fixed $2 \times 2$ quantum kernel that scans each channel, measures Pauli-$Z$ expectations, and passes the resulting feature map to a classical head (Ng et al., 2024).

Medical-imaging HQCNNs often use a compact classical compressor before a small quantum classifier. One breast cancer framework studies three variants, M1–M3, all of which use a classical CNN feature extractor followed by a simple PQC measured in the $\rightarrow$0-basis (Guha et al., 2024). A later MedMNIST-v2 architecture makes this pattern substantially richer by coupling a five-layer classical convolutional backbone to a 4-qubit variational circuit with angle embedding, trainable $\rightarrow$1 gates, superpositional entanglement, a Quantum Attention-Fourier layer, and dense classical readout (Shahjalal et al., 16 Sep 2025).

A separate line of work preserves the hierarchical QCNN idea more literally. A distributed medical HQCNN uses MobileNetV2 for low-parameter feature compression, angle encoding, a QCNN back-end, and a classical fully connected classifier. Its distinctive contribution is quantum circuit splitting: the original 8-qubit QCNN is reconstructed using only 5 qubits by decomposing the circuit into smaller subcircuits and recombining them (Li et al., 7 Jan 2025). A noise-adaptive hybrid QCNN keeps the hierarchical convolution/pooling backbone but measures qubits that would otherwise be discarded during pooling and feeds those intermediate outcomes to a small classical neural network (Kim et al., 25 Feb 2026).

Hybrid fusion has also become a design axis. QShield adds a quantum processing branch to a CNN backbone and fuses classical and quantum predictions through a dynamic weighting MLP that computes a sample-dependent coefficient $\rightarrow$2 (Azimi et al., 13 Apr 2026). In a different domain, HQCNN for pilot assignment in cell-free massive MIMO uses a pre-processing layer, a QCNN block, and a post-processing layer, with the same PQC reused across all convolutional layers (Nguyen et al., 9 Jul 2025).

3. Quantum representation, convolution, pooling, and readout

A representative HQCNN/QNN pipeline initializes $\rightarrow$3, applies an encoding map $\rightarrow$4, evolves the state with a PQC $\rightarrow$5, and measures in the $\rightarrow$6 basis. One reported readout is

$\rightarrow$7

The same source distinguishes amplitude encoding,

$\rightarrow$8

from angle encoding,

$\rightarrow$9

noting that amplitude encoding is qubit-efficient but costly in state preparation, whereas angle encoding is hardware-friendly but usually requires one qubit per feature and thus motivates dimensionality reduction (Shi et al., 2023).

Single-qubit ansätze vary widely. An optimized multi-class HQNN proposes

$\rightarrow$0

arguing that this increases expressiveness and produces a broader distribution on the Bloch sphere (Shi et al., 2023). At the opposite end of the spectrum, the breast cancer ensemble models use a minimal circuit described only by a Hadamard gate followed by $\rightarrow$1, with $\rightarrow$2-basis measurement (Guha et al., 2024).

Entanglement topology is a central degree of freedom. Early image-classification designs used cyclic entanglement in which each qubit entangles with its next neighbor (Shi et al., 2023). QShield systematizes this choice by defining four variants: no entanglement, linear nearest-neighbor CNOT chains, star entanglement with qubit 0 as a hub, and full all-to-all pairwise CNOT entanglement (Azimi et al., 13 Apr 2026). The MedMNIST-v2 HQCNN uses cyclic CNOT entanglement together with Hadamard and Pauli-$\rightarrow$3 modulation, while its QAF block adds Toffoli gates, controlled-phase operations with exponentially decaying phases, and final Hadamard transforms before joint $\rightarrow$4- and $\rightarrow$5-basis measurement (Shahjalal et al., 16 Sep 2025).

Quantum convolution and pooling are likewise heterogeneous. In the color-space HQCNN, the first quanvolutional stage uses IsingYY and IsingZZ operators, cross-channel CNOT entanglement, controlled rotations in an optimized operator $\rightarrow$6, and two pooling layers built from controlled-phase gates (Ng et al., 2024). By contrast, the noise-adaptive HQCNN deliberately uses a simple QCNN backbone: each convolution block has two single-qubit $\rightarrow$7 gates and one CNOT, and each pooling block has one controlled-$\rightarrow$8 and one controlled-$\rightarrow$9. Its novelty is not the backbone itself, but the retention of depth-stratified information through measurements on qubits discarded at each pooling stage. The multi-basis HQCNN-EM measures

$\rightarrow$0

for each discarded qubit, whereas HQCNN-EZ measures only $\rightarrow$1 (Kim et al., 25 Feb 2026).

4. Training regimes, classical-quantum interfaces, and resource constraints

Most HQCNNs are trained end-to-end in standard deep-learning frameworks, but the objectives differ by task. For image multi-classification, one study uses cross-entropy loss, Adam, learning rate $\rightarrow$2, and 50 epochs (Shi et al., 2023). The color-space HQCNN is trained with cross-entropy loss, AdamW, a ReduceLROnPlateau scheduler, initial learning rate $\rightarrow$3, minimum learning rate $\rightarrow$4, and 20 epochs (Ng et al., 2024). The distributed medical HQCNN uses cross-entropy, Adadelta, learning rate $\rightarrow$5, and batch size 16 (Li et al., 7 Jan 2025). The noise-adaptive HQCNN uses binary cross-entropy for MNIST 0-vs-1 classification and trains the quantum and classical parameters jointly (Kim et al., 25 Feb 2026).

Quantum gradients are usually handled either by simulator-compatible backpropagation or by parameter-shift differentiation. The histopathology ensemble, the MedMNIST-v2 HQCNN, and the pilot-assignment HQCNN all explicitly use the parameter-shift rule for quantum parameters (Guha et al., 2024, Shahjalal et al., 16 Sep 2025, Nguyen et al., 9 Jul 2025). QShield is optimized in a classical deep-learning workflow but encodes intermediate CNN features into quantum rotation angles after batch-wise normalization and dimensionality matching to a $\rightarrow$6-parameter budget, using projection up, variance-based feature selection, or PCA when required (Azimi et al., 13 Apr 2026).

Because current qubit budgets are small, the classical-quantum interface is typically dominated by compression. Comparative QCNN benchmarking states explicitly that classical convolution and pooling are used before the quantum circuit to reduce large image inputs to the required qubit count (Zaman et al., 2024). The PCA-versus-CNN multi-class study shows the same pressure from another angle: PCA plus angle encoding is a direct route to few-qubit models, but a CNN front end produces more useful compact features for the quantum layer (Shi et al., 2023). Circuit splitting goes further by reconstructing an 8-qubit QCNN on 5-qubit hardware, reducing spatial complexity while preserving the hybrid pipeline (Li et al., 7 Jan 2025).

Parameter efficiency has motivated additional design choices. The pilot-assignment HQCNN reuses the same PQC across all convolutional layers, reducing the approximate quantum parameter count from $\rightarrow$7 in an earlier QCNN design to $\rightarrow$8, where $\rightarrow$9 is the initial qubit count (Nguyen et al., 9 Jul 2025). QShield’s fusion stage is also deliberately compact: a depth-3 MLP with hidden width 128 receives seven summary features derived from the classical and quantum output distributions and predicts a sample-dependent fusion coefficient $\rightarrow$0 (Azimi et al., 13 Apr 2026).

5. Empirical results across domains

Reported HQCNN performance is highly task-dependent, and direct numerical comparison across papers is limited by different datasets, class counts, preprocessing pipelines, and simulator settings. Even so, several recurring empirical patterns are visible.

A central negative result is that naïve low-qubit multi-class image pipelines degrade sharply. In the PCA-plus-angle-encoded QNN setting, binary MNIST/FashionMNIST-style tasks remained near $\rightarrow$1 accuracy, but the same model collapsed on 8-class tasks, with accuracies $\rightarrow$2 and $\rightarrow$3 for PCA dimensions 8 and 10. The authors attribute this to barren plateau or vanishing-gradient behavior. Their improved CNN-based hybrid avoided severe multi-class training failure and achieved around 85% on MNIST and 78.2% on FashionMNIST, with about 5% improvement over a conventional PQC-based QNN baseline (Shi et al., 2023).

Color-space studies show that representation choice interacts strongly with HQCNN behavior. On the ten-class MNIST task, the best HQCNN accuracy was 94.3% in Lab, while the best CNN accuracy was 92.8% in RGB; the HQCNN average accuracy exceeded the CNN across RGB, Lab, YCrCb, and HSV (Ng et al., 2024).

In medical imaging, the reported performance range is broad but often competitive. The COVID-19 chest X-ray HQCNN achieved 98.4% accuracy and 99.3% sensitivity on COVID-19 versus normal, 99% accuracy and 99.7% sensitivity on COVID-19 versus pneumonia, and 88.6% accuracy with 88.8% F1-measure on the three-class setting (Houssein et al., 2021). On BreakHis histopathology images, the best individual hybrid model reached 85.59% accuracy, while probability averaging of M2 and M3 reached 86.72%, with precision 86.54%, recall 82.49%, and F1-score 84.04% (Guha et al., 2024). The distributed HQCNN with MobileNetV2 and circuit splitting reported 91.14% accuracy on HAM10000, 94.54% on ISIC2017, and 89.58% accuracy with 94.87% AUC on the MedMNIST pneumonia subset (Li et al., 7 Jan 2025). On six MedMNIST-v2 datasets, the 4-qubit HQCNN with QAF reported 93.40% ACC and 99.59% AUC on PathMNIST multi-class, 99.91% ACC and 100.00% AUC on PathMNIST binary, 97.99% ACC and 99.95% AUC on OrganAMNIST multi-class, and 87.18% ACC on BreastMNIST (Shahjalal et al., 16 Sep 2025).

Robustness-oriented HQCNNs target a different metric regime. QShield reports clean accuracy competitive with classical CNNs—up to 99.06% on MNIST and 79.59% on CIFAR-10 for HQCNN variants—while reducing attack success rates under attacks including FGSM, PGD, APGD, C&W, DeepFool, One-Pixel, and Square Attack. Reported reductions versus the CNN baseline include up to 89.12% under C&W on MNIST, up to 89.72% under Square on OrganAMNIST, and up to 95.71% under Square on CIFAR-10, with linear and full entanglement often performing best (Azimi et al., 13 Apr 2026).

Noise-adaptive hybrid QCNNs show especially large gains under realistic hardware-calibrated noise. For 8-qubit MNIST 0-vs-1 classification under AerSimulator with IBM_Yonsei noise, the standard QCNN achieved BCE $\rightarrow$4 and accuracy $\rightarrow$5, whereas HQCNN-EZ achieved $\rightarrow$6 and $\rightarrow$7, and HQCNN-EM achieved $\rightarrow$8 and $\rightarrow$9. At 10 qubits, the same comparison was $\rightarrow$0 for QCNN, $\rightarrow$1 for HQCNN-EZ, and $\rightarrow$2 for HQCNN-EM (Kim et al., 25 Feb 2026).

Outside vision, HQCNN-style architectures have been applied to combinatorial wireless optimization. In cell-free massive MIMO pilot assignment, the shared-PQC HQCNN converged in about 7 epochs in supervised learning, compared with more than 20 epochs for classical DNN/CNN baselines and an earlier QCNN. In small systems it achieved around 98% of the global optimum, including 18.08 Mbps versus 18.43 Mbps for exhaustive search at $\rightarrow$3 (Nguyen et al., 9 Jul 2025).

6. Limitations, misconceptions, and research directions

Several persistent limitations recur across the literature. The most explicit is that improved HQCNNs do not automatically surpass strong classical baselines. The multi-class image study concludes that even its improved hybrid model still does not outperform strong classical CNNs and remains constrained by qubit limits, encoding cost, barren plateaus, and hardware noise (Shi et al., 2023). The color-space paper reports clear gains on some tasks, especially MNIST, but also describes CIFAR-10 and parts of EuroSAT as mixed rather than uniformly favorable (Ng et al., 2024).

A common misconception is that the term HQCNN implies a standardized quantum analogue of CNNs. The literature does not support that interpretation. Some reported “QCNNs” are canonical hierarchical convolution/pooling architectures, while others are effectively CNN-plus-PQC or VQC-plus-MLP models (Tomal et al., 2024). This suggests that architectural inspection is necessary before comparing reported results across papers.

A second misconception is that hybridization itself establishes quantum advantage. The parallel PPF-QSNN work explicitly states that its “quantum advantage” claim is suggestive rather than formal (Xu et al., 2024). Similar caution follows from simulator dependence in multiple medical HQCNN studies and from the fact that many results are obtained on small datasets, reduced label spaces, or hardware-emulated noise rather than on deployed quantum processors (Li et al., 7 Jan 2025, Shahjalal et al., 16 Sep 2025).

Noise remains a decisive issue. A comprehensive noise analysis shows that QCNN and QuanNN respond very differently to phase flip, bit flip, phase damping, amplitude damping, and depolarizing channels. The strongest general pattern is that phase-only noise can be manageable or occasionally beneficial, while depolarizing and amplitude damping are broadly harmful; the same study notes that QCNN sometimes outperforms its noise-free counterpart under high-probability bit flip, phase flip, and phase damping, but not uniformly across datasets and channels (Ahmed et al., 6 May 2025). QShield and the depth-stratified HQCNN both respond to this problem architecturally rather than only by circuit simplification: one uses entanglement-aware hybrid fusion under explicit mixed noise channels, and the other turns discarded qubits into classical side information (Azimi et al., 13 Apr 2026, Kim et al., 25 Feb 2026).

Current research directions are correspondingly pragmatic. Reported proposals include stronger but still shallow PQCs, full rather than cyclic entanglement where beneficial, parameter sharing across quantum convolution layers, depth-stratified intermediate measurements, quantum circuit splitting, and richer classical-quantum fusion mechanisms (Shi et al., 2023, Nguyen et al., 9 Jul 2025, Kim et al., 25 Feb 2026, Li et al., 7 Jan 2025). Related work also extends the hybrid convolutional idea beyond static images: the Hybrid Quantum Temporal Convolutional Network applies classical temporal windowing and a shared QCNN core to time series, achieving competitive or superior results with substantially fewer parameters on multivariate tasks (Park et al., 27 Feb 2026).

Taken together, the literature portrays HQCNN not as a settled architecture but as an active design space centered on one recurrent compromise: classical modules handle compression, optimization stability, and output calibration, while quantum modules are used for compact nonlinear mixing, entanglement-driven correlation modeling, or hierarchical feature extraction under severe hardware constraints.