{
  "id": "2003.01073",
  "version": "v1",
  "published": "2020-03-02T18:05:14.000Z",
  "updated": "2020-03-02T18:05:14.000Z",
  "title": "Quantum Jamming: Critical Properties of a Quantum Mechanical Perceptron",
  "authors": [
    "Claudia Artiaco",
    "Federico Balducci",
    "Giorgio Parisi",
    "Antonello Scardicchio"
  ],
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "quant-ph"
  ],
  "abstract": "In this paper we analyze the quantum dynamics of the perceptron model, where a particle is constrained on a $(N-1)$-dimensional sphere, subjected to a set of $M=\\alpha N$ randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of hard spheres in Euclidean space in $d\\to\\infty$ dimensions. We find that the quantum critical point at $\\alpha=2$ does not show the mean-field exponents of the classical model, which points to a non-trivial critical quantum theory. We also find that the physics of such a quantum critical point is not confined to the low-temperature region. Our findings have implications for the theory of glasses at ultra-low temperatures and for the study of quantum machine-learning algorithms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-02T18:05:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quantum mechanical perceptron",
      "critical properties",
      "quantum jamming",
      "quantum critical point",
      "non-trivial critical quantum theory"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}