# Mathematical open problems in Projected Entangled Pair States

## TL;DR

This paper discusses open mathematical problems related to Projected Entangled Pair States (PEPS), which are used to efficiently represent ground states in quantum many-body systems, aiming to inspire further research in the field.

## Contribution

It introduces and explores key mathematical questions about PEPS, providing a foundation for future theoretical advances in quantum many-body physics.

## Key findings

- Identifies fundamental mathematical questions about PEPS
- Highlights the importance of PEPS in quantum physics
- Provides a basis for future research in the mathematical properties of PEPS

## Abstract

Projected Entangled Pair States (PEPS) are used in practice as an efficient parametrization of the set of ground states of quantum many body systems. The aim of this paper is to present, for a broad mathematical audience, some mathematical questions about PEPS.