Quantum Hypergraph States

TL;DR

This paper introduces quantum hypergraph states, a new class of multiqubit states based on hypergraphs, with a generalized stabilizer formalism, and explores their properties and relevance to quantum algorithms.

Contribution

It generalizes graph states to hypergraph states, develops a stabilizer formalism for them, and links these states to quantum algorithms like Deutsch-Jozsa and Grover.

Findings

Hypergraph states generalize graph states.

A stabilizer formalism for hypergraph states is established.

Connections to quantum algorithms are demonstrated.

Abstract

We introduce a class of multiqubit quantum states which generalizes graph states. These states correspond to an underlying mathematical hypergraph, i.e. a graph where edges connecting more than two vertices are considered. We derive a generalised stabilizer formalism to describe this class of states. We introduce the notion of k-uniformity and show that this gives rise to classes of states which are inequivalent under the action of the local Pauli group. Finally we disclose a one-to-one correspondence with states employed in quantum algorithms, such as Deutsch-Jozsa's and Grover's.