{
  "id": "1409.3812",
  "version": "v1",
  "published": "2014-09-12T18:26:31.000Z",
  "updated": "2014-09-12T18:26:31.000Z",
  "title": "A quantum algorithm to efficiently sample the work distribution and to estimate the free energy of quantum systems",
  "authors": [
    "Augusto J. Roncaglia",
    "Federico Cerisola",
    "Juan Pablo Paz"
  ],
  "comment": "4 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "We present a new method to measure work and to efficiently sample its probability distribution with fixed precision. The method can be used to estimate free energies on a quantum computer. It is based on three facts: (i) The probability to detect work $w$ in the state $\\rho$ is $P(w)={\\rm tr}[\\rho \\,W(w)]$, where $W(w)$ are positive operators satisfying $\\int dw \\,W(w)=I$. As $W(w)$ define a POVM (positive operator valued measure), work measurement always reduces to a projective measurement performed at a single time on an enlarged system. (ii) Work can be estimated using a variant of the \"phase estimation algorithm\" which is such that work $w$ is detected as the outcome of the single time measurement with probability $P(w)$. (iii) The efficient sampling of $P(w)$ can be combined with fluctuation theorems to estimate differences between the free energy of quantum states.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-09-12T18:26:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "03.67.Ac"
    ],
    "keywords": [
      "free energy",
      "efficiently sample",
      "quantum algorithm",
      "work distribution",
      "quantum systems"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "doi": "10.1103/PhysRevLett.113.250601",
      "journal": "Physical Review Letters",
      "year": 2014,
      "month": "Dec",
      "volume": 113,
      "number": 25,
      "pages": 250601
    },
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014PhRvL.113y0601R"
    }
  }
}