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arXiv · 2601.16734

SeeMPS: A Python-based Matrix Product State and Tensor Train Library

Paula García-Molina·Juan José Rodríguez-Aldavero·Jorge Gidi·Juan José García-Ripoll
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Abstract

We introduce SeeMPS, a Python library dedicated to implementing tensor network algorithms based on the well-known Matrix Product States (MPS) and Quantized Tensor Train (QTT) formalisms. SeeMPS is implemented as a complete finite precision linear algebra package where exponentially large vector spaces are compressed using the MPS/TT formalism. It enables both low-level operations, such as vector addition, linear transformations, and Hadamard products, as well as high-level algorithms, including the approximation of linear equations, eigenvalue computations, and exponentially efficient Fourier transforms. This library can be used for traditional quantum many-body physics applications and also for quantum-inspired numerical analysis problems, such as solving PDEs, interpolating and integrating multidimensional functions, sampling multivariate probability distributions, etc.

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Paula García-Molina, Juan José Rodríguez-Aldavero, Jorge Gidi, Juan José García-Ripoll. 2026-01-23. SeeMPS: A Python-based Matrix Product State and Tensor Train Library. https://arxiv.org/abs/2601.16734

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