Maximally entangled gapped ground state of lattice fermions

Abstract

Entanglement between the constituents of a quantum system is an essential resource in the implementation of many quantum processes and algorithms. Indeed, universal quantum computation is possible by measuring individual qubits that constitute highly entangled ``cluster states.'' In this work, it is shown that the unique gapped ground state of noninteracting fermions hopping on a specially prepared lattice is equivalent to a cluster state, where the entanglement between qubits results from fermionic indistinguishability and antisymmetry. A deterministic strategy for universal measurement-based quantum computation with this resource is described. Because most matter is composed of fermions, these results suggest that resources for quantum information processing might be generic in nature.