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We consider the problem whether graph states can be ground states of localinteraction Hamiltonians. For Hamiltonians acting on n qubits that involve atmost two-body interactions, we show that no n-qubit graph state can be theexact, non-degenerate ground state. We determine for any graph state theminimal d such that it is the non-degenerate ground state of a d-bodyinteraction Hamiltonian, while we show for d'-body Hamiltonians H with d'<dthat the resulting ground state can only be close to the graph state at thecost of H having a small energy gap relative to the total energy. When allowingfor ancilla particles, we show how to utilize a gadget construction introducedin the context of the k-local Hamiltonian problem, to obtain n-qubit graphstates as non-degenerate (quasi-)ground states of a two-body Hamiltonian actingon n'>n spins.Comment: 10 pages, 1 figur

physical review. a, atomic, molecular, and optical physics/physical review, a, atomic, molecular, and optical physics

Graph states as ground states of many-body spin-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>1</mml:mn><mml:mo>∕</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:math>Hamiltonians

Graph states as ground states of many-body spin-1∕2Hamiltonians