Goemans-Williamson MAXCUT approximation algorithm on Loihi

Abstract

Approximation algorithms for computationally complex problems are of significant importance in computing as they provide computational guarantees of obtaining practically useful results for otherwise computationally intractable problems. The demonstration of implementing formal approximation algorithms on spiking neuromorphic hardware is a critical step in establishing that neuromorphic computing can offer cost-effective solutions to significant optimization problems while retaining important computational guarantees on the quality of solutions. Here, we demonstrate that the Loihi platform is capable of effectively implementing the Goemans-Williamson (GW) approximation algorithm for MAXCUT, an NP-hard problem that has applications ranging from VLSI design to network analysis. We show that a Loihi implementation of the approximation step of the GW algorithm obtains equivalent maximum cuts of graphs as conventional algorithms, and we describe how different aspects of architecture precision impacts the algorithm performance.