{
  "annotation_id": "67db0c03-1340-4ee1-8d84-81cd708a26ca",
  "date_created": "2026-02-17T05:53:20.349000Z",
  "date_modified": "2026-02-17T05:53:20.349000Z",
  "file_hash": "9508879e231af76e68046106e226b0e6ef7fb89b384c165e57d80ed85e9e5818",
  "private": false,
  "record": {
    "abstract": "We extend Nielsen\u0027s formulation of quantum circuit complexity to include intrinsically non-invertible operations. Such gates arise from fusion with topological defect operators and remove a basic limitation of symmetry-based circuits: the inability to change superselection sectors, or in two-dimensional CFTs, conformal families. We realise fusion operations as completely positive, trace-preserving quantum channels acting between sectors, with consistency ensured by the fusion and associator data of an underlying unitary modular tensor category. In contrast to standard Nielsen circuits, non-invertible circuits lead to an optimisation problem that is no longer governed by geodesics on a continuous group manifold but instead reduces to a discrete shortest-path problem on the fusion graph of superselection sectors. We illustrate the framework in representative rational conformal field theories. Finally, we interpret fusion-induced transitions as discrete changes in boundary stress-tensor data, corresponding to shock-like defects in AdS$_3$ gravity.",
    "arxiv_id": "2601.09534",
    "authors": [
      "Saskia Demulder"
    ],
    "categories": [
      "hep-th"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Non-invertible Nielsen circuits and 3d Ising gravity",
    "url": "https://arxiv.org/abs/2601.09534",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "e2d1749c-3a9d-4eed-8196-f2ceb89f4213",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}