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IEEE Conference on Artificial Intelligence (CAI)

Matrix Product States as a framework for efficient simulation of quantum kernel methods for classification

Antonio J. Rivera-Pérez, Noelia Sánchez-Gómez, Jara J. Bermejo-Vega, Carlos Cano

Published May 8, 2026• 0 citations
Publisher

Abstract

Tensor networks and Matrix Product States (MPS) are commonly used to efficiently perform classical simulations of specific quantum circuits with low entanglement. In this work, we propose an approach to use MPS as an efficient framework for quantum kernel simulation for binary classification via SVMs. To this end, classical data are first embedded into higher-dimensional quantum states using shallow ZZ feature maps. We employ ZZ feature maps with low connectivity that limits entanglement, enabling us to assess whether effective classical data encoding can be achieved while retaining efficient classical simulation. This way, quantum kernels are efficiently computed through MPS overlap. We study the computational cost and accuracy as a function of the depth of the feature maps. Experiments on different classical datasets show that low entanglement quantum feature maps can achieve competitive classification performance at the same time as being efficiently simulable on classical computers.

DOI
10.1109/cai68641.2026.11536438

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Tensor networks and Matrix Product States (MPS) are commonly used to efficiently perform classical simulations of specific quantum circuits with low entanglement. In this work, we propose an approach to use MPS as an efficient framework for quantum kernel simulation for binary classification via SVMs. To this end, classical data are first embedded into higher-dimensional quantum states using shallow ZZ feature maps. We employ ZZ feature maps with low connectivity that limits entanglement, enabling us to assess whether effective classical data encoding can be achieved while retaining efficient classical simulation. This way, quantum kernels are efficiently computed through MPS overlap. We study the computational cost and accuracy as a function of the depth of the feature maps. Experiments on different classical datasets show that low entanglement quantum feature maps can achieve competitive classification performance at the same time as being efficiently simulable on classical computers.
Data representation in quantum state space offers an alternative function space for machine learning tasks. However, benchmarking these algorithms at a practical scale has been limited by ineffective simulation methods. We develop a quantum kernel framework using a Matrix Product State (MPS) simulator and employ it to perform a classification task with 165 features and 6400 training data points, well beyond the scale of any prior work. We make use of a circuit ansatz on a linear chain of qubits with increasing interaction distance between qubits. We assess the MPS simulator performance on CPUs and GPUs and, by systematically increasing the qubit interaction distance, we identify a crossover point beyond which the GPU implementation runs faster. We show that quantum kernel model performance improves as the feature dimension and training data increases, which is the first evidence of quantum model performance at scale.
In recent years, interest in expressing the success of neural networks to the quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated systems. Matrix product state (MPS) is the well-designed class of tensor network states, which plays an important role in processing of quantum information. In this paper, we have shown that matrix product state as one-dimensional array of tensors can be used to classify classical and quantum data. We have performed binary classification of classical machine learning dataset Iris encoded in a quantum state. Further, we have investigated the performance by considering different parameters on the ibmqx4 quantum computer and proved that MPS circuits can be used to attain better accuracy. Further, the learning ability of MPS quantum classifier is tested to classify evapotranspiration (EToET_{o}ETo​) for Patiala meteorological station located in Northern Punjab (India), using three years of historical dataset (Agri). Furthermore, we have used different performance metrics of classification to measure its capability. Finally, the results are plotted and degree of correspondence among values of each sample is shown.
Interest in quantum computing has increased significantly. Tensor network theory has become increasingly popular and widely used to simulate strongly entangled correlated systems. Matrix product state (MPS) is a well-designed class of tensor network states that plays an important role in processing quantum information. In this letter, we show that MPS, as a one-dimensional array of tensors, can be used to classify classical and quantum data. We have performed binary classification of the classical machine learning data set Iris encoded in a quantum state. We have also investigated its performance by considering different parameters on the ibmqx4 quantum computer and proved that MPS circuits can be used to attain better accuracy. Furthermore the learning ability of an MPS quantum classifier is tested to classify evapotranspiration (ET[Formula: see text]) for the Patiala meteorological station located in northern Punjab (India), using three years of a historical data set (Agri). We have used different performance metrics of classification to measure its capability. Finally, the results are plotted and the degree of correspondence among values of each sample is shown.
This work presents a quantum machine learning approach for bipartite entanglement detection in 3×3 quantum systems using a support vector machine with quantum kernels. The classifier is trained to distinguish separable from entangled states, which includes both PPT-detectable and PPT-non-detectable instances, based on classical simulations of parameterized quantum feature maps combined with dimensionality reduction via PCA. Our results show that Pauli-based feature map kernels achieve higher classification accuracy than amplitude embedding at the same PCA dimension, reaching up to 78% accuracy for PCA =8, while amplitude embedding requires PCA =32 to attain comparable performance. We also show that increasing the number of Pauli feature map repetitions does not lead to consistent accuracy improvements, despite significantly increasing circuit depth and computational overhead.
Remote sensing applications increasingly rely on multimodal Earth observation data to improve land-cover classification. However, conventional kernel methods may struggle to capture complex nonlinear relationships between modalities such as synthetic aperture radar (SAR) and multispectral optical imagery. In this work, we investigate a quantum kernel learning framework based on data reuploading feature maps for fused Sentinel-1 and Sentinel-2 data. Input features are first reduced using Tucker decomposition and mapped into quantum states via a parameterized multi-layer circuit consisting of non-commuting rotations and entangling operations. The feature map repeatedly encodes classical data across multiple layers with layer-specific scaling, enabling richer representations than shallow embeddings. Pairwise overlaps between quantum states define a kernel matrix used in a classical support vector machine for classification. We benchmark the proposed quantum kernel against classical linear, polynomial, and radial basis function kernels using multiple evaluation metrics, including accuracy, macro F1-score, and Matthews correlation coefficient. Results indicate that deeper quantum feature maps achieve competitive performance but do not consistently outperform well-tuned classical kernels. These findings highlight the importance of feature map design and parameterization in quantum kernel methods.
Quantum kernel methods have emerged as a promising approach for leveraging high-dimensional feature spaces in machine learning, particularly in domains where classical kernel methods face scalability limitations. In this work, we present the first large-scale study of fidelity-quantum-kernel support vector machines for hyperspectral data classification without requiring heavy prior feature selection or dimensionality reduction. By simulating quantum kernels using tensor network contraction techniques and GPU acceleration, we overcome the computational bottlenecks traditionally associated with quantum models, achieving quadratic scaling O(n^2) in the number of qubits. Our approach enables the evaluation of quantum kernels on hyperspectral data with hundreds of spectral bands, aligning quantum feature spaces with real-world remote sensing applications. We provide an in-depth analysis of kernel bandwidth optimization, demonstrating its crucial role in mitigating exponential concentration effects and ensuring the model's ability to generalize. Experimental results on binary classification (Indian Pines and Methane Detection) and multiclass classification (Indian Pines) demonstrate that quantum kernels achieve competitive performance compared to a broad range of state-of-the-art classical baselines. As illustrative cases, on four 50-band splits selected from Indian Pines, the quantum model achieved a 78.0 pm6.2% accuracy for a binary classification task compared to 72.0 pm5.0% for the standard radial basis function (RBF) kernel. For a four-class classification task, the quantum kernel reached 83.3 pm3.1% accuracy, outperforming several state-of-the-art baselines. On five 75-band splits selected from the Methane Detection dataset, the quantum approach yielded 58.5\pm5.0% accuracy versus 55.1\pm2.5% for the classical counterpart...