Quantum-Classical Pipeline

• Quantum-Classical Pipeline is a structured workflow that integrates classical data reduction and quantum algorithms for enhanced analysis.
• The pipeline employs methods like PCA for compressing features and quantum kernel estimation through QSVM for improved classification performance.
• This hybrid approach minimizes quantum hardware limitations while delivering scalable, efficient solutions in domains such as neuroimaging and diagnostics.

A quantum-classical pipeline is a structured workflow that integrates classical computing methods and quantum algorithms to achieve scalable, efficient, and practical data processing, analysis, or optimization for real-world tasks. This architecture leverages the strengths of both platforms: classical CPUs/GPUs perform high-throughput preprocessing, feature extraction, or parameter optimization, while quantum processors are employed for computational blocks where quantum feature mapping, entanglement, or kernel estimation can potentially yield enhanced expressivity, separability, or efficiency.

1. Architecture and Foundational Principles

A typical quantum-classical pipeline comprises multiple stages. The classical segments handle data preprocessing, feature engineering, extraction, reduction, and systems integration. Quantum subroutines are inserted for specific tasks where quantum transformations, encodings, or kernel methods may outperform or complement classical models given constraints such as qubit count, coherence time, and gate noise.

For example, in "CompressedMediQ: Hybrid Quantum Machine Learning Pipeline for High-Dimensional Neuroimaging Data" (Chen et al., 2024), the pipeline includes:

• Stage 1: Classical high-performance computing for MRI pre-processing (bias correction, tissue segmentation, spatial normalization via SPM12/DARTEL), yielding modulated, template-aligned probability maps.
• Stage 2: CNN-based spatial feature extraction and dimensionality reduction using principal component analysis (PCA) to compress tens of thousands of features to a compact $\mathbf{x}\in\mathbb R^8$ vector.
• Stage 3: Quantum Support Vector Machine (QSVM) classification, with quantum angle encoding onto three qubits and quantum kernel estimation via SWAP/overlap circuits.

This block-wise segregation is a recurring pattern: classical modules operate on high-dimensional data and provide compressed, informative representations suitable for quantum encoding, thus accommodating limited current quantum resources (NISQ era).

2. Classical Preprocessing and Feature Reduction

Classical preprocessing typically involves normalization, transformation, segmentation, and dimension reduction. Linear algebraic methods such as covariance analysis and principal component analysis (PCA) enable a reduction from large raw feature vectors to a small subset suitable for quantum encoding (often $\ell\ll d$, where $d$ is the original dimension and $\ell$ the reduced quantum input dimension):

$$\Sigma = \frac{1}{n}\sum_{i} (x_i-\mu)(x_i-\mu)^T,\qquad \Sigma = V\Lambda V^T,\qquad x_{\mathrm{reduced}} = V_\ell^T(x-\mu)$$

where $V_\ell$ contains the top $\ell$ eigenvectors.

This denoising and compression stage is critical given limited quantum hardware—NISQ devices generally provide only a few usable qubits, and deep quantum circuits suffer pronounced decoherence. PCA or similar reductions minimize circuit depth and measurement overhead (Chen et al., 2024).

3. Quantum Data Encoding and Feature Mapping

Quantum encoding schemes translate classical feature vectors into quantum states. Common methods include:

• Angle Encoding: Each component $x^{(k)}$ maps to a rotation angle $\theta_k=\pi x^{(k)}$, encoding via qubit-wise $R_y(\theta_k)$ gates onto $\ell$ qubits:

$$U_{\mathrm{enc}}(x) = \bigotimes_{k=1}^\ell R_y(\theta_k),\qquad |\psi(x)\rangle = U_{\mathrm{enc}}(x)|0\rangle^{\otimes \ell}$$

• Amplitude Encoding: Normalizes the input so $\|x\|_2=1$ (requiring $N=\log_2(\ell)$ qubits):

$|\psi(x)\rangle = \sum_{i=1}^{2^N} x_i |i\rangle$

The choice of encoding is dictated by hardware limitations, the feature dimension, and the nature of downstream quantum algorithms (Chen et al., 2024, Li et al., 21 Oct 2025). Angle encoding supports shallow circuits amenable to current devices.

4. Quantum Kernel Methods and Classification

In quantum kernel pipelines, classical features encoded as quantum states enable quantum kernel estimation—key for support vector machines (SVMs) and related classifiers. The pipeline computes pairwise quantum kernels via state overlap:

$$k(x_i,x_j) = |\langle \psi(x_i)|\psi(x_j)\rangle|^2$$

This kernel matrix is input into a classical or quantum SVM dual optimization problem:

$$L(\alpha) = \sum_i \alpha_i - \frac{1}{2} \sum_{i,j} \alpha_i \alpha_j y_i y_j k(x_i, x_j)$$

subject to $0\leq\alpha_i\leq C$ and $\sum_i \alpha_i y_i=0$.

Multi-class classification employs one-vs-rest or one-vs-one QSVMs, yielding robust predictions even in challenging clinical contexts ("CompressedMediQ" shows 96.1% quantum accuracy vs. 78.8% classical SVM for dementia staging; early-stage quantum precision attained 98–99%) (Chen et al., 2024).

5. Scalability and NISQ Considerations

Quantum-classical pipelines in the NISQ regime maintain shallow quantum circuits, small qubit counts ($N\leq3$–$8$), and minimal entangling gate depth (Chen et al., 2024, Slabbert et al., 2024). Classical precompression ensures input fits the quantum encoding bandwidth, and limits measurement complexity. Noise mitigation (post-selection, symmetry checks) is typically deferred for future versions but recognized as necessary.

Key factors:

• Circuit depth $O(\ell)$: Avoids barren plateaus; only single-qubit rotations and overlap tests.
• Dimensionality reduction: PCA as a classical compression front-end (e.g., $\ell=8$ chosen for quantum stages).
• Measurement overhead: Overlap/SWAP circuits enable kernel estimation with minimal ancilla requirements.
• Error mitigation: Not explicitly integrated yet; hybrid loop architectures are adopted to stabilize learning.

6. Empirical Performance and Application Domains

Quantum-classical pipelines are deployed in a variety of data-rich and computation-intensive fields:

• Neuroimaging: Dementia staging on ADNI/NIFD T1-MRI volumes. Quantum pipelines correct classical classifier misclassifications and enable finer diagnostic granularity (Chen et al., 2024).
• Healthcare diagnostics: Bone fracture X-ray analysis via hybrid PCA/quantum feature fusion reduces feature extraction time 82% with no loss in accuracy (Tomar et al., 19 May 2025).
• Image analysis: Convolutional autoencoder for reduced representation feeding quantum SVM yields near-perfect accuracy for MNIST, competent performance for CIFAR-10 (Slabbert et al., 2024).
• Cybersecurity: Quantum-enhanced feature spaces provide improved attack recall in small-sample regimes for intrusion detection (Sciammarelli et al., 5 Jan 2026).

A key result is that quantum kernels exhibit superior separability, negligible early-stage misclassification, and robust precision—even in high-dimensional, multi-class, or scarce-data settings. PCA and other classical reductions are not merely bottlenecks but essential elements enabling quantum advantages under current hardware constraints.

7. Future Directions and Pipeline Design Trends

Quantum-classical pipelines are continually evolving, with documented future directions including:

• Hardware scaling: Exploiting hardware-efficient ansätze, error mitigation, block-wise quantum encodings for scale-up to $16$–$32$ qubits.
• Pipeline modularity: Clean software architecture with robust interfaces, versioning, and extensibility allows drop-in quantum and classical components (notably in platform-agnostic systems such as EmuPlat (Ye et al., 16 Sep 2025)).
• Insertion point studies: Systematic investigation of quantum layer placement—input, intermediate, output—for neural/feature pipelines (Illésová, 16 Jul 2025).
• Model applications: Expansion to larger datasets, non-imaging domains, and signal processing, leveraging the hybrid loop for classical–quantum parameter optimization.
• Error mitigation and co-design: Classical post-processing refines quantum outputs; automated review gates and value/risk assessments align quantum deployments with production realities (Rohe et al., 2024).

The pipeline model is not monolithic but highly adaptive, integrating classical and quantum strengths for practical, scalable data analysis and learning in environments constrained by quantum hardware expressivity and noise characteristics.

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References:

• "CompressedMediQ: Hybrid Quantum Machine Learning Pipeline for High-Dimensional Neuroimaging Data" (Chen et al., 2024)
• "Leveraging Quantum Layers in Classical Neural Networks" (Illésová, 16 Jul 2025)
• "Hybrid Quantum-Classical Feature Extraction approach for Image Classification using Autoencoders and Quantum SVMs" (Slabbert et al., 2024)
• "A Hybrid Quantum Classical Pipeline for X Ray Based Fracture Diagnosis" (Tomar et al., 19 May 2025)
• "Quantum AI for Cybersecurity: A hybrid Quantum-Classical models for attack path analysis" (Sciammarelli et al., 5 Jan 2026)
• "EmuPlat: A Framework-Agnostic Platform for Quantum Hardware Emulation with Validated Transpiler-to-Pulse Pipeline" (Ye et al., 16 Sep 2025)
• "From Problem to Solution: A general Pipeline to Solve Optimisation Problems on Quantum Hardware" (Rohe et al., 2024)