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arXiv · 1004.0206

k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs

Jamie Smith
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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].

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Jamie Smith. 2010-04-01. k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs. https://arxiv.org/abs/1004.0206

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