{
  "id": "1711.04006",
  "version": "v1",
  "published": "2017-11-10T20:53:43.000Z",
  "updated": "2017-11-10T20:53:43.000Z",
  "title": "Faster Quantum Algorithm to simulate Fermionic Quantum Field Theory",
  "authors": [
    "Ali Hamed Moosavian",
    "Stephen Jordan"
  ],
  "comment": "18 pages",
  "categories": [
    "quant-ph",
    "hep-th"
  ],
  "abstract": "In quantum algorithms discovered so far for simulating scattering processes in quantum field theories, state preparation is the slowest step. We present a new algorithm for preparing particle states to use in simulation of Fermionic Quantum Field Theory (QFT) on a quantum computer, which is based on the matrix product state ansatz. We apply this to the massive Gross-Neveu model in one spatial dimension to illustrate the algorithm, but we believe the same algorithm with slight modifications can be used to simulate any one-dimensional massive Fermionic QFT. In the case where the number of particle species is one, our algorithm can prepare particle states using $O\\left( \\epsilon^{-3.23\\ldots}\\right)$ gates, which is much faster than previous known results, namely $O\\left(\\epsilon^{-8-o\\left(1\\right)}\\right)$. Furthermore, unlike previous methods which were based on adiabatic state preparation, the method given here should be able to simulate quantum phases unconnected to the free theory.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-10T20:53:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "simulate fermionic quantum field theory",
      "faster quantum algorithm",
      "particle states",
      "matrix product state ansatz",
      "adiabatic state preparation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 18,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}