{
  "id": "2303.15665",
  "version": "v1",
  "published": "2023-03-28T01:17:08.000Z",
  "updated": "2023-03-28T01:17:08.000Z",
  "title": "Feature Map for Quantum Data: Probabilistic Manipulation",
  "authors": [
    "Hyeokjea Kwon",
    "Hojun Lee",
    "Joonwoo Bae"
  ],
  "comment": "5 pages, 4 figures, 1 table",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The kernel trick in supervised learning signifies transformations of an inner product by a feature map, which then restructures training data in a larger Hilbert space according to an endowed inner product. A quantum feature map corresponds to an instance with a Hilbert space of quantum states by fueling quantum resources to ML algorithms. In this work, we point out that the quantum state space is specific such that a measurement postulate characterizes an inner product and that manipulation of quantum states prepared from classical data cannot enhance the distinguishability of data points. We present a feature map for quantum data as a probabilistic manipulation of quantum states to improve supervised learning algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-03-28T01:17:08.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum data",
      "probabilistic manipulation",
      "inner product",
      "quantum feature map corresponds",
      "quantum state space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}