{
  "id": "2001.03622",
  "version": "v1",
  "published": "2020-01-10T19:00:01.000Z",
  "updated": "2020-01-10T19:00:01.000Z",
  "title": "Quantum embeddings for machine learning",
  "authors": [
    "Seth Lloyd",
    "Maria Schuld",
    "Aroosa Ijaz",
    "Josh Izaac",
    "Nathan Killoran"
  ],
  "comment": "11 pages, 6 figures; tutorial available at https://pennylane.ai/qml/app/tutorial_embeddings_metric_learning.html",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum classifiers are trainable quantum circuits used as machine learning models. The first part of the circuit implements a quantum feature map that encodes classical inputs into quantum states, embedding the data in a high-dimensional Hilbert space; the second part of the circuit executes a quantum measurement interpreted as the output of the model. Usually, the measurement is trained to distinguish quantum-embedded data. We propose to instead train the first part of the circuit---the embedding---with the objective of maximally separating data classes in Hilbert space, a strategy we call quantum metric learning. As a result, the measurement minimizing a linear classification loss is already known and depends on the metric used: for embeddings separating data using the l1 or trace distance, this is the Helstrom measurement, while for the l2 or Hilbert-Schmidt distance, it is a simple overlap measurement. This approach provides a powerful analytic framework for quantum machine learning and eliminates a major component in current models, freeing up more precious resources to best leverage the capabilities of near-term quantum information processors.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-10T19:00:01.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "machine learning",
      "quantum embeddings",
      "first part",
      "near-term quantum information processors",
      "high-dimensional hilbert space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}