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k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs · Around

2010

k-Boson Quantum Walks Do Not Distinguish Arbitrary Graphs

Smith, Jamie

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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].

Built on

A reduction of a graph to canonical form and an algebra arising during this construction
B. Weisfeiler and A. Lehman · 1968
Earlier work this paper cites.
Coherent configurations i
D. Higman · 1970
Earlier work this paper cites.
On a new high dimensional weisfeiler-lehman algorithm
S Evdokimov, M Karpinski, and I Ponomarenko · 1999
Earlier work this paper cites.

Similar

On highly closed cellular algebras and highly closed isomorphisms
Sergei Evdokimov and Ilia Ponomarenko · 1999
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Cited alongside, same era.

Then

On the relationship between continuous- and discrete-time quantum walk
Andrew M Childs · 2008
Later among the works it cites.
Non-isomorphic graphs with cospectral symmetric powers
A Barghi and I Ponomarenko · 2009
Later among the works it cites.
Two-particle quantum walks applied to the graph isomorphism problem
John King Gamble, Mark Friesen, Dong Zhou, Robert Joynt, and S. N Coppersmith · 2010
Closest in time.

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