{
  "annotation_id": "b264d024-88a3-4828-bdf2-bacf2e03f4b8",
  "date_created": "2026-03-02T18:02:34.317000Z",
  "date_modified": "2026-03-02T18:02:34.317000Z",
  "file_hash": "328d12d5779ac5e2ba1e3fd02c463555d11413fc4eddb57ef46c312f7b474f8d",
  "private": false,
  "record": {
    "abstract": "We present an efficient quantum algorithm for the exact evaluation of either\nthe fully ferromagnetic or anti-ferromagnetic q-state Potts partition function\nZ for a family of graphs related to irreducible cyclic codes. This problem is\nrelated to the evaluation of the Jones and Tutte polynomials. We consider the\nconnection between the weight enumerator polynomial from coding theory and Z\nand exploit the fact that there exists a quantum algorithm for efficiently\nestimating Gauss sums in order to obtain the weight enumerator for a certain\nclass of linear codes. In this way we demonstrate that for a certain class of\nsparse graphs, which we call Irreducible Cyclic Cocycle Code (ICCC_\\epsilon)\ngraphs, quantum computers provide a polynomial speed up in the difference\nbetween the number of edges and vertices of the graph, and an exponential speed\nup in q, over the best classical algorithms known to date.",
    "arxiv_id": "quant-ph/0703023",
    "authors": [
      "Joseph Geraci",
      "Daniel A. Lidar"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00220-008-0438-0",
    "journal_ref": "Comm. Math. Phys. 279, 735 (2008)",
    "title": "On the Exact Evaluation of Certain Instances of the Potts Partition   Function by Quantum Computers",
    "url": "https://arxiv.org/abs/quant-ph/0703023"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "522964e2-c2e0-425d-b944-947bbaf8a661",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}