Realistic cost for the model of coherent computing

TL;DR

This paper analyzes the success probability of a coherent computing model for solving Ising spin problems, showing it decreases exponentially for hard instances, thus questioning its practical feasibility.

Contribution

It provides a theoretical analysis demonstrating the exponential decay of success probability in the coherent computing model for certain problem instances.

Findings

Success probability decreases exponentially with problem size.

The model is physically unfeasible for polynomial-cost solutions.

Hard instances significantly impact the success rate.

Abstract

For the model of so-called coherent computing recently proposed by Yamamoto et al. [Y. Yamamoto et al., New Gen. Comput. 30 (2012) 327-355], a theoretical analysis of the success probability is given. Although it was claimed as their prospect that the Ising spin configuration problem would be efficiently solvable in the model, here it is shown that the probability of finding a desired spin configuration decreases exponentially in the number of spins for certain hard instances. The model is thus physically unfeasible for solving the problem within a polynomial cost.