Analog Errors in Ising Machines

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.