{
  "annotation_id": "f64e5ce7-751d-4ef9-a4fb-01a0e688d45c",
  "date_created": "2026-03-02T18:02:37.232000Z",
  "date_modified": "2026-03-02T18:02:37.232000Z",
  "file_hash": "21e145a8f55d075d34e20cc5719d2de192b9bacbc40d843173afaa50b907a8e7",
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  "record": {
    "abstract": "We address the problems of constructing quantum convolutional codes (QCCs)\nand of encoding them. The first construction is a CSS-type construction which\nallows us to find QCCs of rate 2/4. The second construction yields a quantum\nconvolutional code by applying a product code construction to an arbitrary\nclassical convolutional code and an arbitrary quantum block code. We show that\nthe resulting codes have highly structured and efficient encoders. Furthermore,\nwe show that the resulting quantum circuits have finite depth, independent of\nthe lengths of the input stream, and show that this depth is polynomial in the\ndegree and frame size of the code.",
    "arxiv_id": "quant-ph/0703182",
    "authors": [
      "Markus Grassl",
      "Martin Roetteler"
    ],
    "categories": [
      "quant-ph",
      "cs.IT",
      "math.IT"
    ],
    "doi": "10.1109/ISIT.2007.4557325",
    "journal_ref": "Proceedings 2007 IEEE International Symposium on Information\n  Theory (ISIT 2007), Nice, France, June 2007, pp. 816-820",
    "title": "Constructions of Quantum Convolutional Codes",
    "url": "https://arxiv.org/abs/quant-ph/0703182"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4de22739-a832-4b29-b25f-d8a8fb1e09f7",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}