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

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

2006-12-21

arxiv.org/abs/quant-ph/0612186v1

Phys. Rev. A 77, 012301 (2008)

Physics

Quantum Physics

10 pages, 1 figure

Scientific paper

10.1103/PhysRevA.77.012301

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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