{
  "id": "0806.0385",
  "version": "v3",
  "published": "2008-06-02T20:17:10.000Z",
  "updated": "2009-07-06T14:17:50.000Z",
  "title": "Adiabatic Quantum Computation with a 1D projector Hamiltonian",
  "authors": [
    "Avatar Tulsi"
  ],
  "comment": "revised version",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on the corresponding ground state. The minimum energy gap which governs the time required for a successful evolution is shown to be proportional to the overlap of the ground states of the initial and final Hamiltonians. We show that such evolutions exhibit a rapid crossover as the ground state changes abruptly near the transition point where the energy gap is minimum. Furthermore, a faster evolution can be obtained by performing a partial adiabatic evolution within a narrow interval around the transition point. These results generalize and quantify earlier works.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2009-07-06T14:17:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "03.67.Lx"
    ],
    "keywords": [
      "adiabatic quantum computation",
      "1d projector hamiltonian",
      "transition point",
      "final hamiltonian",
      "minimum energy gap"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevA.80.052328",
      "journal": "Physical Review A",
      "year": 2009,
      "month": "Nov",
      "volume": 80,
      "number": 5,
      "pages": "052328"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009PhRvA..80e2328T"
    }
  }
}