Experimental determination of Ramsey numbers

TL;DR

This paper reports an experimental implementation of a quantum algorithm to determine Ramsey numbers, successfully computing several small cases and demonstrating the largest such adiabatic quantum computation to date.

Contribution

It presents the first experimental realization of an adiabatic quantum algorithm for calculating Ramsey numbers, including the largest implementation to date.

Findings

Successfully determined R(3,3) and R(m,2) for 4≤m≤8

Used 84 qubits for R(8,2) computation, including 28 computational qubits

Achieved the largest experimental adiabatic quantum evolution to date

Abstract

Ramsey theory is a highly active research area in mathematics that studies the emergence of order in large disordered structures. Ramsey numbers mark the threshold at which order first appears and are extremely difficult to calculate due to their explosive rate of growth. Recently, an algorithm that can be implemented using adiabatic quantum evolution has been proposed that calculates the two-color Ramsey numbers $R(m,n)$. Here we present results of an experimental implementation of this algorithm and show that it correctly determines the Ramsey numbers R(3,3) and $R(m,2)$ for $4\leq m\leq 8$. The R(8,2) computation used 84 qubits of which 28 were computational qubits. This computation is the largest experimental implementation of a scientifically meaningful adiabatic evolution algorithm that has been done to date.