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

• URL: http://arxiv.org/abs/2506.11711v1
• Date: Fri, 13 Jun 2025 12:27:34 GMT
• Title: Knapsack and Shortest Path Problems Generalizations From A Quantum-Inspired Tensor Network Perspective
• Authors: Sergio Muñiz Subiñas, Jorge Martínez Martín, Alejandro Mata Ali, Javier Sedano, Ángel Miguel García-Vico,
• Abstract summary: We present two quantum-inspired algorithms to solve the knapsack and the shortest path problems.<n>The methods provide an exact equation which returns the optimal solution of the problems.
• Score: 40.5694560588179
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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