{
  "id": "2111.05311",
  "version": "v1",
  "published": "2021-11-09T18:28:46.000Z",
  "updated": "2021-11-09T18:28:46.000Z",
  "title": "Mode connectivity in the loss landscape of parameterized quantum circuits",
  "authors": [
    "Kathleen E. Hamilton",
    "Emily Lynn",
    "Raphael C. Pooser"
  ],
  "comment": "14 pages, related to work presented at QTML 2020",
  "categories": [
    "quant-ph",
    "cs.LG"
  ],
  "abstract": "Variational training of parameterized quantum circuits (PQCs) underpins many workflows employed on near-term noisy intermediate scale quantum (NISQ) devices. It is a hybrid quantum-classical approach that minimizes an associated cost function in order to train a parameterized ansatz. In this paper we adapt the qualitative loss landscape characterization for neural networks introduced in \\cite{goodfellow2014qualitatively,li2017visualizing} and tests for connectivity used in \\cite{draxler2018essentially} to study the loss landscape features in PQC training. We present results for PQCs trained on a simple regression task, using the bilayer circuit ansatz, which consists of alternating layers of parameterized rotation gates and entangling gates. Multiple circuits are trained with $3$ different batch gradient optimizers: stochastic gradient descent, the quantum natural gradient, and Adam. We identify large features in the landscape that can lead to faster convergence in training workflows.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-11-09T18:28:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "parameterized quantum circuits",
      "mode connectivity",
      "near-term noisy intermediate scale quantum",
      "bilayer circuit ansatz",
      "loss landscape characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}