Matrix Product State Representations

TL;DR

This paper thoroughly investigates matrix product state (MPS) representations for pure multipartite quantum states, focusing on their canonical forms, symmetry properties, and applications in classical simulations of quantum systems.

Contribution

It introduces new methods for obtaining canonical forms of MPS, analyzes the role of translation symmetry, and extends results on frustration free Hamiltonians and state generation.

Findings

Derived canonical forms for MPS with and without translation symmetry

Provided efficient algorithms for MPS representation and manipulation

Discussed applications in classical simulation of quantum systems

Abstract

This work gives a detailed investigation of matrix product state (MPS) representations for pure multipartite quantum states. We determine the freedom in representations with and without translation symmetry, derive respective canonical forms and provide efficient methods for obtaining them. Results on frustration free Hamiltonians and the generation of MPS are extended, and the use of the MPS-representation for classical simulations of quantum systems is discussed.