{
  "annotation_id": "ed239ac4-904e-407b-bcc9-ff6d8b64c5c6",
  "date_created": "2026-03-02T18:02:23.739000Z",
  "date_modified": "2026-03-02T18:02:23.739000Z",
  "file_hash": "fd4bad87cf712af8f262559180d53cd004dcbeb7c00e19cff4f31a83fc79e5d3",
  "private": false,
  "record": {
    "abstract": "An algorithm and its first implementation in C# are presented for assembling\narbitrary quantum circuits on the base of Hadamard and Toffoli gates and for\nconstructing multivariate polynomial systems over the finite field Z_2 arising\nwhen applying the Feynman\u0027s sum-over-paths approach to quantum circuits. The\nmatrix elements determined by a circuit can be computed by counting the number\nof common roots in Z_2 for the polynomial system associated with the circuit.\nTo determine the number of solutions in Z_2 for the output polynomial system,\none can use the Groebner bases method and the relevant algorithms for computing\nGroebner bases.",
    "arxiv_id": "quant-ph/0512064",
    "authors": [
      "Vladimir P. Gerdt",
      "Vasily M. Severyanov"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1117/12.683121",
    "title": "An Algorithm for Constructing Polynomial Systems Whose Solution Space   Characterizes Quantum Circuits",
    "url": "https://arxiv.org/abs/quant-ph/0512064"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "571efd3c-944c-4bf3-8da0-6920aaaa3620",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}