Determine Ramsey numbers on a quantum computer

TL;DR

This paper introduces a quantum algorithm for calculating Ramsey numbers that offers a quadratic speedup over classical methods by leveraging quantum decision processes and energy level detection.

Contribution

The paper presents a novel quantum algorithm for Ramsey numbers that avoids degeneracy issues and improves computational efficiency compared to classical algorithms.

Findings

Quadratic speedup over classical algorithms

Avoids degeneracy problems in quantum adiabatic evolution

Maps Ramsey number computation to a quantum decision problem

Abstract

We present a quantum algorithm for computing the Ramsey numbers whose computational complexity grows super-exponentially with the number of vertices of a graph on a classical computer. The problem is mapped to a decision problem on a quantum computer, a probe qubit is coupled to a register that represents the problem and detects the energy levels of the problem Hamiltonian. The decision problem is solved by determining whether the probe qubit exhibits resonance dynamics. The algorithm shows a quadratic speedup over its classical counterparts, and the degenerate ground state problem in the adiabatic quantum evolution algorithm for this problem is avoided.