Encoding graphs into quantum states: an axiomatic approach

TL;DR

This paper develops an axiomatic framework to encode various classes of multipartite quantum states as graph-based quantum states, generalizing existing models and accommodating directed and weighted graphs.

Contribution

It introduces a novel axiomatic approach that unifies and extends multiple existing graph-based quantum state representations.

Findings

Includes and generalizes graph, stabilizer, and cluster states.

Enables encoding of directed and weighted graphs.

Provides a flexible formalism for diverse quantum states.

Abstract

A fundamental problem in quantum information is to describe efficiently multipartite quantum states. An efficient representation in terms of graphs exists for several families of quantum states (graph, cluster, stabilizer states), motivating us to extend this construction to other classes. We introduce an axiomatic framework for mapping graphs to quantum states of a suitable physical system. Starting from three general axioms we derived a rich structure which includes and generalizes several classes of multipartite entangled state, like graph/stabilizer states, Gaussian cluster states, quantum random networks and projected entangled pair states (PEPS). Due to its flexibility we can extend the present formalism to include directed and weighted graphs.