{
  "id": "2104.03295",
  "version": "v1",
  "published": "2021-04-07T17:53:50.000Z",
  "updated": "2021-04-07T17:53:50.000Z",
  "title": "Experimental Quantum Learning of a Spectral Decomposition",
  "authors": [
    "Michael R. Geller",
    "Zoë Holmes",
    "Patrick J. Coles",
    "Andrew Sornborger"
  ],
  "categories": [
    "quant-ph"
  ],
  "abstract": "Currently available quantum hardware allows for small scale implementations of quantum machine learning algorithms. Such experiments aid the search for applications of quantum computers by benchmarking the near-term feasibility of candidate algorithms. Here we demonstrate the quantum learning of a two-qubit unitary by a sequence of three parameterized quantum circuits containing a total of 21 variational parameters. Moreover, we variationally diagonalize the unitary to learn its spectral decomposition, i.e., its eigenvalues and eigenvectors. We illustrate how this can be used as a subroutine to compress the depth of dynamical quantum simulations. One can view our implementation as a demonstration of entanglement-enhanced machine learning, as only a single (entangled) training data pair is required to learn a 4x4 unitary matrix.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-04-07T17:53:50.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "experimental quantum learning",
      "spectral decomposition",
      "4x4 unitary matrix",
      "quantum machine learning algorithms",
      "small scale implementations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}