English

k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs

Quantum Physics 2010-04-02 v1

Abstract

In this paper, we define k-equivalence, a relation on graphs that relies on their associated cellular algebras. We show that a k-Boson quantum walk cannot distinguish pairs of graphs that are k- equivalent. The existence of pairs of k-equivalent graphs has been shown by Ponomarenko et al. [2, 6]. This gives a negative answer to a question posed by Gamble et al. [7].

Cite

@article{arxiv.1004.0206,
  title  = {k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs},
  author = {Jamie Smith},
  journal= {arXiv preprint arXiv:1004.0206},
  year   = {2010}
}

Comments

5 pages

R2 v1 2026-06-21T15:05:39.123Z