Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective

TL;DR

This paper introduces quantum-inspired tensor network algorithms for solving knapsack and shortest path problems, providing exact solutions and demonstrating improved efficiency through symmetry use and intermediate calculation reuse.

Contribution

The paper presents novel tensor network algorithms inspired by quantum computing to solve combinatorial optimization problems with exact solutions and enhanced computational efficiency.

Findings

Algorithms solve knapsack and shortest path problems exactly.

Use of symmetries reduces computational complexity.

Performance surpasses some classical algorithms.

Abstract

In this paper, we present two tensor network quantum-inspired algorithms to solve the knapsack and the shortest path problems, and enables to solve some of its variations. These methods provide an exact equation which returns the optimal solution of the problems. As in other tensor network algorithms for combinatorial optimization problems, the method is based on imaginary time evolution and the implementation of restrictions in the tensor network. In addition, we introduce the use of symmetries and the reutilization of intermediate calculations, reducing the computational complexity for both problems. To show the efficiency of our implementations, we carry out some performance experiments and compare the results with those obtained by other classical algorithms.