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Quantum Machine Learning

Asia University · AI and Quantum Research Center

Quantum Machine Learning

Neural Quantum Embedding and Tensor-Network Acceleration

Quantum machine learning explores how quantum representations and computational methods can support learning from data. This page introduces a hybrid quantum–classical approach to biomedical classification, focusing on Neural Quantum Embedding (NQE), Quantum Support Vector Classification (QSVC), and tensor-network simulation.

The page is intended to guide self-learners through the relationship between feature representation and quantum-kernel classification. NQE uses a trainable classical neural network to transform the input before quantum encoding, with the aim of improving class separability and supporting QSVC performance. Our research examines this approach in gene-expression analysis and extends it to medical-image classification.

Alongside predictive performance, the computational cost of evaluating quantum kernels remains an important challenge. Tensor networks address this challenge by representing quantum circuits as connected arrays and evaluating them through optimized contraction. Together, learned embeddings and efficient simulation provide a framework for investigating the accuracy and computational efficiency of quantum-kernel methods in biomedical research.

01 / Representation learning

Neural Quantum Embedding for QSVC

Select the figure to enlarge it.
Figure 1. NQE training workflow illustrated for an mRNA dataset. The fidelity-based objective guides updates to the classical neural network [2].

The predictive performance of QSVC depends on the representation of the input data within the quantum feature space. NQE addresses this dependence by learning a task-specific transformation before quantum encoding.

A trainable classical neural network transforms the input features, which are subsequently encoded by a quantum circuit. A fidelity-based objective uses the overlap between pairs of quantum states to update the neural-network parameters, encouraging similarity among samples from the same class and separation between different classes. [1]

The optimized transformation is then applied before kernel construction and classification. Our studies examine this approach for gene-expression analysis and extend it to medical-image classification. [2] [3] [4]

Select the figure to enlarge it.
Figure 2. Six-qubit ZZ feature map used in the NQE component. Source: medical-image manuscript [4].

02 / Computational acceleration

Tensor-Network Acceleration

Although learned representations can improve classification, repeated quantum-kernel evaluations remain computationally demanding. Tensor networks provide a structured representation of quantum states and gates, allowing the quantities required for kernel construction to be calculated through tensor contraction.

The contraction order determines the size of intermediate tensors and, consequently, the computational and memory requirements. An optimized contraction path can reduce this cost while preserving the mathematical result. Our implementation uses NVIDIA cuTensorNet for GPU-accelerated evaluation. [2] [4]

Select the figure to enlarge it.
Figure 3. Quantum-circuit representation as a tensor network and an example of contraction-path optimization. Both paths produce the same result with different computational costs [4].

In the medical-image framework, NQE-transformed features are encoded using a Basic State Preparation (BSP) feature map. The circuit is represented as a tensor network to evaluate the quantum kernel, which is subsequently used by QSVC for classification. [4]

Select the figure to enlarge it.
Figure 4. BSP feature map used for quantum-kernel evaluation and tensor-network simulation. Rotation angles encode the input features [4].

Together, NQE and tensor-network simulation address complementary aspects of the framework: the quality of the feature representation and the efficiency of quantum-kernel evaluation.

Classification performance remains dependent on the dataset and feature-map design. Tensor-network contraction accelerates simulation; it does not independently guarantee an improvement in predictive accuracy.

References

  1. Hur, T., Araujo, I. F., and Park, D. K. (2024). Neural Quantum Embedding: Pushing the Limits of Quantum Supervised Learning. Physical Review A, 110, 022411.
  2. Astuti, A., Li, T.-Y., See, S., and Ng, K.-L. (2025). Enhancing the Performance and Speed of Quantum Support Vector Classifier via Neural Quantum Embedding and Tensor Network. 2025 Second International Conference on Artificial Intelligence for Medicine, Health and Care (AIxMHC), pp. 50–53.IEEE Xplore · DOI: 10.1109/AIxMHC65380.2025.00018
  3. Astuti, A., Shih, P.-K., Lee, S.-C., Mekala, V. R., Wijaya, E. B., and Ng, K.-L. (2025). Use of hybrid quantum-classical algorithms for enhancing biomarker classification. PLOS ONE, 20(7), e0327928.PLOS ONE · DOI: 10.1371/journal.pone.0327928
  4. Astuti, A., Shih, P.-K., Tsai, J. J. P., and Ng, K.-L. Enhancing High-Dimensional Medical Image Classification via Hybrid Neural Quantum Embedding and Tensor Network Acceleration. Manuscript draft.

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