{
  "annotation_id": "ea9754f6-6c5f-4508-aa38-c4cfc3ea7c50",
  "date_created": "2026-02-17T05:53:19.774000Z",
  "date_modified": "2026-02-17T05:53:19.774000Z",
  "file_hash": "b8358b8402bb8af18ce4eb2f75b2335bc14f24a36695175695b1836014887415",
  "private": false,
  "record": {
    "abstract": "For any positive integer $g \\ge 2$, we derive general conditions for the existence of a $2g$-cycle in the Tanner graph of two-dimensional ($2$-D) classical quasi-cyclic (QC) low-density parity-check (LDPC) codes. Based on these conditions, we construct a family of $2$-D classical QC-LDPC codes with girth greater than $4$ by stacking $p \\times p \\times p$ tensors, where $p$ is an odd prime. Furthermore, for composite values of $p$, we propose two additional families of $2$-D classical LDPC codes obtained via similar tensor stacking. In this case, one family achieves girth greater than $4$, while the other attains girth greater than $6$. All the proposed $2$-D classical QC-LDPC codes exhibit an erasure correction capability of at least $p \\times p$. Based on the constructed classical $2$-D QC-LDPC codes, we derive two families of $2$-D entanglement-assisted (EA) quantum low-density parity-check (QLDPC) codes. The first family of $2$-D EA-QLDPC codes is obtained from a pair of binary $2$-D classical LDPC codes and is designed such that the unassisted part of the Tanner graph of the resulting EA-QLDPC code is free of cycles of length four, while requiring only a single ebit to be shared across the quantum transceiver. The second family is constructed from a single $2$-D classical LDPC code whose Tanner graph is free from $4$-cycles. Moreover, the constructed EA-QLDPC codes inherit an erasure correction capability of $p \\times p$, as the underlying classical codes possess the same erasure correction property.",
    "arxiv_id": "2601.08927",
    "authors": [
      "Pavan Kumar",
      "Shayan Srinivasa Garani"
    ],
    "categories": [
      "cs.IT",
      "math.IT"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "Two-dimensional Entanglement-assisted Quantum Quasi-cyclic Low-density Parity-check Codes",
    "url": "https://arxiv.org/abs/2601.08927",
    "version": "v2"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "113d9812-58b8-4e9d-8a5c-8b6d7a1e4973",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}