Knapsack and Shortest Path Problems Generalizations from a Quantum-Inspired Tensor Network Perspective

Sergio Muñiz Subiñas, Jorge Martínez Martín, Alejandro Mata Ali, Javier Sedano, Ángel Miguel García-Vico

2025

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.

Paper Citation

in Harvard Style

Subiñas S., Martín J., Ali A., Sedano J. and García-Vico Á. (2025). Knapsack and Shortest Path Problems Generalizations from a Quantum-Inspired Tensor Network Perspective. In Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT; ISBN 978-989-758-761-0, SciTePress, pages 81-88. DOI: 10.5220/0013489000004525

in Bibtex Style

@conference{iqsoft25,
author={Sergio Subiñas and Jorge Martín and Alejandro Ali and Javier Sedano and Ángel García-Vico},
title={Knapsack and Shortest Path Problems Generalizations from a Quantum-Inspired Tensor Network Perspective},
booktitle={Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT},
year={2025},
pages={81-88},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0013489000004525},
isbn={978-989-758-761-0},
}

in EndNote Style

TY - CONF

JO - Proceedings of the 1st International Conference on Quantum Software - Volume 1: IQSOFT
TI - Knapsack and Shortest Path Problems Generalizations from a Quantum-Inspired Tensor Network Perspective
SN - 978-989-758-761-0
AU - Subiñas S.
AU - Martín J.
AU - Ali A.
AU - Sedano J.
AU - García-Vico Á.
PY - 2025
SP - 81
EP - 88
DO - 10.5220/0013489000004525
PB - SciTePress