{
  "annotation_id": "a07c63da-1b8a-4749-b463-8518182534ac",
  "date_created": "2026-03-02T18:02:34.184000Z",
  "date_modified": "2026-03-02T18:02:34.184000Z",
  "file_hash": "f88f65dc394df67f017d0e1131f110ba8ae5a468d1f9b10e77abdbd4d30200fe",
  "private": false,
  "record": {
    "abstract": "We consider the problem whether graph states can be ground states of local\ninteraction Hamiltonians. For Hamiltonians acting on n qubits that involve at\nmost two-body interactions, we show that no n-qubit graph state can be the\nexact, non-degenerate ground state. We determine for any graph state the\nminimal d such that it is the non-degenerate ground state of a d-body\ninteraction Hamiltonian, while we show for d\u0027-body Hamiltonians H with d\u0027\u003cd\nthat the resulting ground state can only be close to the graph state at the\ncost of H having a small energy gap relative to the total energy. When allowing\nfor ancilla particles, we show how to utilize a gadget construction introduced\nin the context of the k-local Hamiltonian problem, to obtain n-qubit graph\nstates as non-degenerate (quasi-)ground states of a two-body Hamiltonian acting\non n\u0027\u003en spins.",
    "arxiv_id": "quant-ph/0612186",
    "authors": [
      "M. Van den Nest",
      "K. Luttmer",
      "W. D\u00fcr",
      "H. J. Briegel"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.77.012301",
    "journal_ref": "Phys. Rev. A 77, 012301 (2008)",
    "title": "Graph states as ground states of many-body spin-1/2 Hamiltonians",
    "url": "https://arxiv.org/abs/quant-ph/0612186"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ccca5e00-edf4-4b0c-8a44-c22bfcf59134",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}