Quantum hypergraph states

Abstract

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