A Quantum Observable for the Graph Isomorphism Problem

Details A Quantum Observable for the Graph Isomorphism Problem A Quantum Observable for the Graph Isomorphism Problem

1999-01-13

arxiv.org/abs/quant-ph/9901029v1

Physics

Quantum Physics

5 pages, no figures

Scientific paper

Suppose we are given two graphs on $n$ vertices. We define an observable in
the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with
certainty if the graphs are isomorphic and ``no'' with probability at least
$1-n!/2^m$ if the graphs are not isomorphic. We do not know if this observable
is efficiently implementable.

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