{
  "id": "quant-ph/0106077",
  "version": "v1",
  "published": "2001-06-13T16:24:44.000Z",
  "updated": "2001-06-13T16:24:44.000Z",
  "title": "Simulating Arbitrary Pair-Interactions by a Given Hamiltonian: Graph-Theoretical Bounds on the Time Complexity",
  "authors": [
    "P. Wocjan",
    "D. Janzing",
    "Th. Beth"
  ],
  "comment": "12 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We use an n-spin system with permutation symmetric zz-interaction for simulating arbitrary pair-interaction Hamiltonians. The calculation of the required time overhead is mathematically equivalent to a separability problem of n-qubit density matrices. We derive lower and upper bounds in terms of chromatic index and the spectrum of the interaction graph. The complexity measure defined by such a computational model is related to gate complexity and a continuous complexity measure introduced in a former paper. We use majorization of graph spectra for classifying Hamiltonians with respect to their computational power.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2001-06-13T16:24:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time complexity",
      "graph-theoretical bounds",
      "permutation symmetric zz-interaction",
      "simulating arbitrary pair-interaction hamiltonians",
      "n-qubit density matrices"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2001quant.ph..6077W"
    }
  }
}