A review of "Mem-computing NP-complete problems in polynomial time using polynomial resources" (arXiv:1411.4798)

TL;DR

The paper reviews a device claiming to solve NP-complete problems in polynomial time using polynomial resources, but highlights fundamental issues and exponential resource requirements that challenge this claim.

Contribution

It critically analyzes a proposed analog device for NP-complete problems, clarifying its limitations and the reasons it cannot achieve polynomial-time solutions.

Findings

Device properties are insufficient for polynomial-time NP-complete problem solving

Spectral measurement step is not accounted for in runtime analysis

Scaling up requires exponential resources due to spectral measurement

Abstract

The reviewed paper describes an analog device that empirically solves small instances of the NP-complete Subset Sum Problem (SSP). The authors claim that this device can solve the SSP in polynomial time using polynomial space, in principle, and observe no exponential scaling in resource requirements. We point out that (a) the properties ascribed by the authors to their device are insufficient to solve NP-complete problems in poly-time, (b) runtime analysis offered does not cover the spectral measurement step, (c) the overall technique requires exponentially increasing resources when scaled up because of the spectral measurement step.