{
  "annotation_id": "33b723e6-5d03-4582-bf47-32a524a79cbd",
  "date_created": "2026-03-02T18:02:06.929000Z",
  "date_modified": "2026-03-02T18:02:06.929000Z",
  "file_hash": "cc26284b4466d8672624ddb6b52dd74d225c5a3fc923740f59de0b41caf73179",
  "private": false,
  "record": {
    "abstract": "Notions of a Gaussian state and a Gaussian linear map are generalized to the\ncase of anticommuting (Grassmann) variables. Conditions under which a Gaussian\nmap is trace preserving and (or) completely positive are formulated. For any\nGaussian map an explicit formula relating correlation matrices of input and\noutput states is presented. This formalism allows to develop the Lagrangian\nrepresentation for fermionic linear optics (FLO). It covers both unitary\noperations and the single-mode projectors associated with FLO measurements.\nUsing the Lagrangian representation we reduce a classical simulation of FLO to\na computation of Gaussian integrals over Grassmann variables. Explicit formulas\ndescribing evolution of a quantum state under FLO operations are put forward.",
    "arxiv_id": "quant-ph/0404180",
    "authors": [
      "Sergey Bravyi"
    ],
    "categories": [
      "quant-ph"
    ],
    "journal_ref": "Quantum Inf. and Comp., Vol. 5, No. 3 (2005) pp.216-238",
    "title": "Lagrangian representation for fermionic linear optics",
    "url": "https://arxiv.org/abs/quant-ph/0404180"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0e8a51c2-0846-49b1-868f-8adfd91a62a0",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}