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

TL;DR

SeeMPS is a Python library that implements tensor network algorithms using MPS and QTT formalisms, enabling efficient computations in quantum physics and numerical analysis.

Contribution

It provides a comprehensive, finite precision linear algebra package for tensor network operations and algorithms in Python, supporting both physics and numerical applications.

Findings

Efficiently compresses large vector spaces using MPS/TT formalism.

Supports low-level tensor operations and high-level algorithms.

Applicable to quantum physics and multidimensional numerical problems.

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.