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

M. Van den Nest, K. Luttmer, W. Dür, H. J. Briegel
2008 Physical Review A. Atomic, Molecular, and Optical Physics  
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.
doi:10.1103/physreva.77.012301 fatcat:tn56rhktizbgbcpqniec5mzgx4