{
  "id": "2010.15281",
  "version": "v1",
  "published": "2020-10-28T23:37:59.000Z",
  "updated": "2020-10-28T23:37:59.000Z",
  "title": "Probing coherence and noise tolerance in discrete-time quantum walks: unveiling self-focusing and breathing dynamics",
  "authors": [
    "A. R. C. Buarque",
    "W. S. Dias"
  ],
  "comment": "4 figures, 6 pages",
  "categories": [
    "quant-ph"
  ],
  "abstract": "The sensitivity of quantum systems to external disturbances is a fundamental problem for the implementation of functional quantum devices, quantum information and computation. Based on remarkable experimental progress in optics and ultra-cold gases, we study the consequences of a short-time (instantaneous) noise while an intensity-dependent phase acquisition is associated with a qubit propagating on $N$-cycle. By employing quantum coherence measures, we report emerging unstable regimes in which hitherto unknown quantum walks arise, such as self-focusing and breathing dynamics. Our results unveil appropriate settings which favor the stable regime, with the asymptotic distribution surviving for weak nonlinearities and disappearing in the thermodynamic limit with $1/N$. The diagram showing the threshold between different regimes reveals the quantum gates close to Pauli-Z as more noise-tolerant. As we move towards the Pauli-X quantum gate, such aptness dramatically decreases and the threshold to self-focusing regime becomes almost unavoidable. Quantum gates close to Hadamard exhibit an unusual aspect, in which an increment of the nonlinear strength can remove the dynamics from self-focusing regime.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-10-28T23:37:59.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete-time quantum walks",
      "breathing dynamics",
      "noise tolerance",
      "probing coherence",
      "quantum gates close"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 6,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}