{
  "id": "1908.11857",
  "version": "v1",
  "published": "2019-08-30T17:36:50.000Z",
  "updated": "2019-08-30T17:36:50.000Z",
  "title": "$O(N^3)$ Measurement Cost for Variational Quantum Eigensolver on Molecular Hamiltonians",
  "authors": [
    "Pranav Gokhale",
    "Frederic T. Chong"
  ],
  "comment": "5 pages, 3 figures",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Variational Quantum Eigensolver (VQE) is a promising algorithm for near-term quantum machines. It can be used to estimate the ground state energy of a molecule by performing separate measurements of $O(N^4)$ terms. Several recent papers observed that this scaling may be reducible to $O(N^3)$ by partitioning the terms into linear-sized commuting families that can be measured simultaneously. We confirm these empirical observations by studying the MIN-COMMUTING-PARTITION problem at the level of the fermionic Hamiltonian and its encoding into qubits. Moreover, we provide a fast, pre-computable procedure for creating linearly-sized commuting partitions by solving a round-robin scheduling problem via flow networks.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-30T17:36:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "variational quantum eigensolver",
      "measurement cost",
      "molecular hamiltonians",
      "near-term quantum machines",
      "ground state energy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}