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arXiv · 1103.1345

Ramsey numbers and adiabatic quantum computing

Frank Gaitan·Lane Clark
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Abstract

The graph-theoretic Ramsey numbers are notoriously difficult to calculate. In fact, for the two-color Ramsey numbers $R(m,n)$ with $m,n\geq 3$, only nine are currently known. We present a quantum algorithm for the computation of the Ramsey numbers $R(m,n)$. We show how the computation of $R(m,n)$ can be mapped to a combinatorial optimization problem whose solution can be found using adiabatic quantum evolution. We numerically simulate this adiabatic quantum algorithm and show that it correctly determines the Ramsey numbers R(3,3) and R(2,s) for $5\leq s\leq 7$. We then discuss the algorithm's experimental implementation, and close by showing that Ramsey number computation belongs to the quantum complexity class QMA.

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Frank Gaitan, Lane Clark. 2012-01-08. Ramsey numbers and adiabatic quantum computing. https://doi.org/10.1103/physrevlett.108.010501

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