We consider the computational complexity of Hamiltonians which are sums of
commuting terms acting on plaquettes in a square lattice of qubits, and we show
that deciding whether the ground state minimizes the energy of each local term
individually is in the complexity class NP. That is, if the ground states has
this property, this can be proven using a classical certificate which can be
efficiently verified on a classical computer. Different to previous results on
commuting Hamiltonians, our certificate proves the existence of such a state
without giving instructions on how to prepare it.Comment: 16 pages, 12 figures. v2: Minor corrections. Accepted version,
Journal-Ref adde