{
  "id": "2304.06617",
  "version": "v1",
  "published": "2023-04-13T15:37:39.000Z",
  "updated": "2023-04-13T15:37:39.000Z",
  "title": "Exact and lower bounds for the quantum speed limit in finite dimensional systems",
  "authors": [
    "Mattias T. Johnsson",
    "Lauritz van Luijk",
    "Daniel Burgarth"
  ],
  "comment": "13 pages",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "A fundamental problem in quantum engineering is determining the lowest time required to ensure that all possible unitaries can be generated with the tools available, which is one of a number of possible quantum speed limits. We examine this problem from the perspective of quantum control, where the system of interest is described by a drift Hamiltonian and set of control Hamiltonians. Our approach uses a combination of Lie algebra theory, Lie groups and differential geometry, and formulates the problem in terms of geodesics on a differentiable manifold. We provide explicit lower bounds on the quantum speed limit for the case of an arbitrary drift, requiring only that the control Hamiltonians generate a topologically closed subgroup of the full unitary group, and formulate criteria as to when our expression for the speed limit is exact and not merely a lower bound. These analytic results are then tested and confirmed using a numerical optimization scheme. Finally we extend the analysis to find a lower bound on the quantum speed limit in the common case where the system is described by a drift Hamiltonian and a single control Hamiltonian.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-13T15:37:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum speed limit",
      "finite dimensional systems",
      "drift hamiltonian",
      "explicit lower bounds",
      "single control hamiltonian"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}