{
  "id": "1406.7069",
  "version": "v2",
  "published": "2014-06-27T05:47:17.000Z",
  "updated": "2014-12-12T01:08:29.000Z",
  "title": "On model reduction for quantum dynamics: symmetries and invariant subspaces",
  "authors": [
    "Akshat Kumar",
    "Mohan Sarovar"
  ],
  "comment": "26 pages, 2 figures, 3 algorithms. Version 2 is published version and contains new results on stability of invariant subspaces to perturbations",
  "journal": "J. Phys. A: Math. Theor. 48, 015301 (2014)",
  "doi": "10.1088/1751-8113/48/1/015301",
  "categories": [
    "quant-ph",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized quantum Hamiltonians. In particular, we first formulate an algebraic condition that certifies the existence of invariant subspaces for a model defined by a parameterized Hamiltonian and an initial state. Following this we develop and analyze two methods to explicitly construct a reduced-order model, if one exists. In addition to general results characterizing invariant subspaces of arbitrary finite dimensional Hamiltonians, by exploiting properties of the generalized Pauli group we develop practical tools to speed up simulation of dynamics generated by certain spin Hamiltonians. To illustrate the methods developed we apply them to several paradigmatic spin models.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-27T05:47:17.000Z",
      "abstract": "Simulation of quantum dynamics is a grand challenge of computational physics. In this work we investigate methods for reducing the demands of such simulation by identifying reduced-order models for dynamics generated by parameterized quantum Hamiltonians. In particular, we develop methods to characterize, identify and exploit invariant subspaces defined by a Hamiltonian model and initial state. In addition to general results characterizing invariant subspaces of arbitrary finite dimensional Hamiltonians, by exploiting properties of the generalized Pauli group we develop several practical tools to speed up simulation of dynamics generated by certain spin Hamiltonians. To illustrate the methods developed we apply them to several paradigmatic spin models.",
      "comment": "24 pages, 2 figures. Comments welcome",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2014-12-12T01:08:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum dynamics",
      "model reduction",
      "symmetries",
      "arbitrary finite dimensional hamiltonians",
      "general results characterizing invariant subspaces"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "journal": "Journal of Physics A Mathematical General",
      "year": 2015,
      "month": "Jan",
      "volume": 48,
      "number": 1,
      "pages": "015301"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015JPhA...48a5301K"
    }
  }
}