Complexity of commuting Hamiltonians on a square lattice of qubits

Details Complexity of commuting Hamiltonians on a square lattice of qubits Complexity of commuting Hamiltonians on a square lattice of qubits

2011-05-13

arxiv.org/abs/1105.2843v2

Quantum Inf. Comput. 11, 901 (2011)

Physics

Quantum Physics

16 pages, 12 figures. v2: Minor corrections. Accepted version, Journal-Ref added

Scientific paper

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.

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