A Quantum Observable for the Graph Isomorphism Problem

Mark Ettinger; Peter Hoyer

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arXiv · quant-ph/9901029

A Quantum Observable for the Graph Isomorphism Problem

Mark Ettinger·Peter Hoyer

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Abstract

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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Mark Ettinger, Peter Hoyer. 1999-01-13. A Quantum Observable for the Graph Isomorphism Problem. https://arxiv.org/abs/quant-ph/9901029

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