Finding Solutions to NP Problems: Philosophical Difference Between Quantum and Evolutionary Search Algorithms

TL;DR

This paper compares quantum and evolutionary search algorithms for solving NP problems, highlighting their fundamental philosophical differences through experiments on SAT, 3SAT, and TSP instances.

Contribution

It provides a detailed analysis of the contrasting philosophies behind quantum and evolutionary search methods for NP problems, supported by empirical case studies.

Findings

Quantum and evolutionary algorithms differ fundamentally in their approach to NP problems.

Experimental results illustrate the distinct search behaviors of the two methods.

The paper clarifies philosophical distinctions despite both being non-deterministic.

Abstract

There is no known polynomial-time algorithm that can solve an NP problem. Evolutionary search has been shown to be a viable method of finding acceptable solutions within a reasonable time period. Recently quantum computers have surfaced as another alternative method. But these two methods use radically different philosophies for solving NP problems even though both search methods are non-deterministic. This paper uses instances of {\bf SAT}, {\bf 3SAT} and {\bf TSP} to describe how these two methods differ in their approach to solving NP problems.