Computing Hypergraph Ramsey Numbers by Using Quantum Circuit

TL;DR

This paper introduces a quantum algorithm leveraging quantum counting circuits to compute two-color Ramsey numbers for r-uniform hypergraphs, building on prior work with adiabatic quantum evolution.

Contribution

It presents a novel quantum algorithm specifically designed for hypergraph Ramsey numbers using quantum counting circuits, expanding quantum computational methods in combinatorics.

Findings

Demonstrates the feasibility of quantum counting for hypergraph Ramsey numbers

Provides a new quantum approach that potentially improves computational efficiency

Extends quantum algorithms from simple graphs to r-uniform hypergraphs

Abstract

Gaitan and Clark [Phys. Rev. Lett. 108, 010501 (2012)] have recently shown a quantum algorithm for the computation of the Ramsey numbers using adiabatic quantum evolution. We present a quantum algorithm to compute the two-color Ramsey numbers for r-uniform hypergraphs by using the quantum counting circuit.