Quantum Elastic Net and the Traveling Salesman Problem

TL;DR

This paper explores how quantum incoherent tunneling can be utilized to develop new algorithms for solving NP-hard problems like the Traveling Salesman Problem, potentially surpassing classical computational methods.

Contribution

It introduces a novel approach using quantum incoherent tunneling to address NP-hard problems, expanding the quantum algorithm toolkit beyond interference-based methods.

Findings

Quantum incoherent tunneling can be harnessed for optimization algorithms.

Potential for quantum algorithms to outperform classical solutions on NP-hard problems.

Proposes a new quantum approach for the Traveling Salesman Problem.

Abstract

Theory of computer calculations strongly depends on the nature of elements the computer is made of. Quantum interference allows to formulate the Shor factorization algorithm turned out to be more effective than any one written for classical computers. Similarly, quantum wave packet reduction allows to devise the Grover search algorithm which outperforms any classical one. In the present paper we argue that the quantum incoherent tunneling can be used for elaboration of new algorithms able to solve some NP-hard problems, such as the Traveling Salesman Problem, considered to be intractable in the classical theory of computer computations.