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

Paula García-Molina, Juan José Rodríguez-Aldavero, Jorge Gidi, Juan José García-Ripoll (Jan 26 2026).

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.

Arxiv: https://arxiv.org/abs/2601.16734