Analog Errors in Ising Machines

TL;DR

This paper investigates how analog errors in Ising Machines affect their success probability, deriving a scaling law to maintain performance, supported by experiments and simulations.

Contribution

It provides a theoretical scaling law for error tolerance in Ising Machines, supported by empirical validation, to understand their reliability for solving NP-hard problems.

Findings

Success probability decays exponentially with problem size at fixed error levels

A sufficient error scaling law is derived to maintain fixed success probability

Experimental and simulation results corroborate the theoretical predictions

Abstract

Recent technological breakthroughs have precipitated the availability of specialized devices that promise to solve NP-Hard problems faster than standard computers. These `Ising Machines' are however analog in nature and as such inevitably have implementation errors. We find that their success probability decays exponentially with problem size for a fixed error level, and we derive a sufficient scaling law for the error in order to maintain a fixed success probability. We corroborate our results with experiment and numerical simulations and discuss the practical implications of our findings.