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arXiv:2608.24307

An HPC Approach to Accelerate Tensor Decompositions

Markus Hellgren, Erna Begović Kovač, Hans O. Karlsson, Roman Iakymchuk

Published Aug 25, 2026• 0 citations
arXivHTMLPDF

Abstract

Quantum systems grow in complexity so rapidly that even modest models become difficult to simulate, creating a strong need for methods that can handle high-dimensional data, also known as tensors. In this work, we investigate a novel Jacobi-type tensor algorithm for tensor decomposition and develop a CUDA-based algorithm that supports tensors of arbitrary order on a single GPU. We test the implementation on NVIDIA H100 GPUs and show that the algorithm converges correctly for diagonalizable tensors up to nine dimensions, with runtime scaling in a predictable way as tensor order grows. Finally, our general algorithm outperforms the original MATLAB reference by more than two orders of magnitude.

DOI
10.48550/arxiv.2608.24307

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Quantum systems grow in complexity so rapidly that even modest models become difficult to simulate, creating a strong need for methods that can handle high-dimensional data, also known as tensors. In this work, we investigate a novel Jacobi-type tensor algorithm for tensor decomposition and develop a CUDA-based algorithm that supports tensors of arbitrary order on a single GPU. We test the implementation on NVIDIA H100 GPUs and show that the algorithm converges correctly for diagonalizable tensors up to nine dimensions, with runtime scaling in a predictable way as tensor order grows. Finally, our general algorithm outperforms the original MATLAB reference by more than two orders of magnitude.
Quantum systems grow in complexity so rapidly that even modest models become difficult to simulate, creating a strong need for methods that can handle high-dimensional data. In this work, we investigate a Jacobi-type tensor algorithm in this context and develop a CUDA implementation that supports tensors of arbitrary order on a single GPU. We test the implementation on NVIDIA H100 hardware and show that the algorithm converges correctly for diagonalizable tensors up to nine dimensions, with runtime increasing in a predictable way as tensor order grows.We also apply the method to Heisenberg spin chains and show that it can operate on tensors corresponding to systems of up to N=15 spins, that is, tensors with up to 30 dimensions, which correspond to Hamiltonian matrices of dimension 2N by 2N (for N=15, this is 32768 by 32768). In addition, we demonstrate that the implementation can be used to approximate eigenvalues of the corresponding Hamiltonian matrices. These results confirm that the method scales to high-dimensional problems and is applicable to spectral analysis in quantum physics settings.
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Abstract We present an efficient tensor-network-based approach for simulating large-scale quantum circuits exemplified by quantum support vector machines (QSVMs). Experimentally, leveraging the cuTensorNet library on multiple GPUs, our method effectively reduces the exponential runtime growth to near-quadratic scaling with respect to the number of qubits in practical scenarios. Traditional state-vector simulations become computationally infeasible beyond approximately 50 qubits; in contrast, our simulator successfully handles QSVMs with up to 784 qubits, executing simulations within seconds on a single high-performance GPU. Furthermore, utilizing the message passing interface for multi-GPU environments, our method demonstrates strong linear scalability, effectively decreasing computation time as dataset sizes increase. We validate our framework using the MNIST and Fashion MNIST datasets, achieving successful multiclass classification and highlighting the potential of QSVMs for high-dimensional data analysis. By integrating tensor-network techniques with advanced high-performance computing resources, this work demonstrates both the feasibility and scalability of simulating large-qubit quantum machine learning models, providing a valuable validation tool within the emerging Quantum-HPC ecosystem.
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