{
  "annotation_id": "215f3288-5133-4b51-a3d3-2ad0f95a9c9a",
  "date_created": "2026-03-02T18:02:34.654000Z",
  "date_modified": "2026-03-02T18:02:34.654000Z",
  "file_hash": "98f1da3335225deb1ad33b511e6ce9985d7d785e92be302d2b45a082495cbfb3",
  "private": false,
  "record": {
    "abstract": "A discrete-time quantum walk on a graph is the repeated application of a\nunitary evolution operator to a Hilbert space corresponding to the graph. If\nthis unitary evolution operator has an associated group of symmetries, then for\ncertain initial states the walk will be confined to a subspace of the original\nHilbert space. Symmetries of the original graph, given by its automorphism\ngroup, can be inherited by the evolution operator. We show that a quantum walk\nconfined to the subspace corresponding to this symmetry group can be seen as a\ndifferent quantum walk on a smaller quotient graph. We give an explicit\nconstruction of the quotient graph for any subgroup of the automorphism group\nand illustrate it with examples. The automorphisms of the quotient graph which\nare inherited from the original graph are the original automorphism group\nmodulo the subgroup used to construct it. We then analyze the behavior of\nhitting times on quotient graphs. Hitting time is the average time it takes a\nwalk to reach a given final vertex from a given initial vertex. It has been\nshown in earlier work [Phys. Rev. A {\\bf 74}, 042334 (2006)] that the hitting\ntime can be infinite. We give a condition which determines whether the quotient\ngraph has infinite hitting times given that they exist in the original graph.\nWe apply this condition for the examples discussed and determine which quotient\ngraphs have infinite hitting times. All known examples of quantum walks with\nfast hitting times correspond to systems with quotient graphs much smaller than\nthe original graph; we conjecture that the existence of a small quotient graph\nwith finite hitting times is necessary for a walk to exhibit a quantum\nspeed-up.",
    "arxiv_id": "quant-ph/0701173",
    "authors": [
      "Hari Krovi",
      "Todd A. Brun"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1103/PhysRevA.75.062332",
    "journal_ref": "Physical Review A 75, 062332 (2007)",
    "title": "Quantum walks on quotient graphs",
    "url": "https://arxiv.org/abs/quant-ph/0701173"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4f5066d9-9f2d-4613-800a-9f410afdc3b5",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}