Hypergraph Ramsey Numbers and Adiabatic Quantum Algorithm

TL;DR

This paper extends a quantum algorithm for classical Ramsey numbers to hypergraph Ramsey numbers R(m, n; r), demonstrating how their computation can be formulated as a combinatorial optimization problem solvable via adiabatic quantum evolution.

Contribution

It introduces a method to compute hypergraph Ramsey numbers R(m, n; r) using adiabatic quantum algorithms, generalizing previous approaches for classical Ramsey numbers.

Findings

Mapping hypergraph Ramsey number computation to optimization problems

Proposed quantum algorithm for R(m, n; r)

Potential for quantum speedup in hypergraph Ramsey number calculations

Abstract

Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently presented a quantum algorithm for the computation of the Ramsey numbers R(m, n) using adiabatic quantum evolution. We consider that the two-color Ramsey numbers R(m, n; r) for r-uniform hypergraphs can be computed by using the similar ways in [Phys. Rev. Lett. 108, 010501 (2012)]. In this comment, we show how the computation of R(m, n; r) can be mapped to a combinatorial optimization problem whose solution be found using adiabatic quantum evolution.