{
  "id": "2004.01227",
  "version": "v1",
  "published": "2020-04-02T19:08:38.000Z",
  "updated": "2020-04-02T19:08:38.000Z",
  "title": "Supervised Learning with Quantum Measurements",
  "authors": [
    "Fabio A. González",
    "Vladimir Vargas-Calderón",
    "Herbert Vinck-Posada"
  ],
  "categories": [
    "quant-ph",
    "cs.LG"
  ],
  "abstract": "This letter reports a novel method for supervised machine learning based on the mathematical formalism that supports quantum mechanics. The method uses projective quantum measurement as a way of building a prediction function. Specifically, the correlation between input and output variables is represented as the state of a bipartite quantum system. The state is estimated from training samples through an averaging process that produces a density matrix. Prediction of the label for a new sample is made by performing a projective measurement on the bipartite system with an operator, prepared from the new input sample, and applying a partial trace to obtain the state of the subsystem representing the outputs. The method can be seen as a generalization of Bayesian inference classification and as a type of kernel-based learning method. One remarkable characteristic of the method is that it does not require learning any parameters through optimization. We illustrate the method with different 2-D classification benchmark problems and different quantum information encodings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-02T19:08:38.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "supervised learning",
      "supports quantum mechanics",
      "quantum information encodings",
      "classification benchmark problems",
      "bipartite quantum system"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}