{
  "id": "2207.04319",
  "version": "v1",
  "published": "2022-07-09T18:35:47.000Z",
  "updated": "2022-07-09T18:35:47.000Z",
  "title": "Discrete-time Quantum Walks in Qudit Systems",
  "authors": [
    "Amit Saha",
    "Debasri Saha",
    "Amlan Chakrabarti"
  ],
  "comment": "24 pages, 28 figures. arXiv admin note: text overlap with arXiv:2006.09712",
  "categories": [
    "quant-ph"
  ],
  "abstract": "Quantum walks contribute significantly for developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$ and show its equivalence for circuit realization in an arbitrary finite-dimensional quantum logic for utilizing the advantage of larger state space, which helps to reduce the run-time of the quantum walks as compared to the conventional binary quantum systems. We provide efficient quantum circuits for the implementation of discrete-time quantum walks (DTQW) in one-dimensional position space in any finite-dimensional quantum system using an appropriate logical mapping of the position space on which a walker evolves onto the multi-qudit states. With example circuits for various qudit state spaces, we also explore scalability in terms of $n$-qudit $d$-ary quantum systems. Further, the extension of one-dimensional DTQW to $d$-dimensional DTQW using $2d$-dimensional coin space on $d$-dimensional lattice has been studied, where $d>=2$. Thereafter, the circuit design for the implementation of scalable $d$-dimensional DTQW in $d$-ary quantum systems has been portrayed. Lastly, we exhibit the circuit design for the implementation of DTQW using different coins on various search-spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-09T18:35:47.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "discrete-time quantum walks",
      "qudit systems",
      "kind one-dimensional quantum walk",
      "circuit design",
      "dimensional dtqw"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}