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

M. Van den Nest·K. Luttmer·W. Dür·H. J. Briegel
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Abstract

We consider the problem whether graph states can be ground states of local interaction Hamiltonians. For Hamiltonians acting on n qubits that involve at most two-body interactions, we show that no n-qubit graph state can be the exact, non-degenerate ground state. We determine for any graph state the minimal d such that it is the non-degenerate ground state of a d-body interaction Hamiltonian, while we show for d'-body Hamiltonians H with d' n spins.

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M. Van den Nest, K. Luttmer, W. Dür, H. J. Briegel. 2006-12-21. Graph states as ground states of many-body spin-1/2 Hamiltonians. https://doi.org/10.1103/physreva.77.012301

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