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.
Markus Hellgren (Thu,) studied this question.