# A quantum-inspired tensor network method for constrained combinatorial optimization problems

arXiv: https://arxiv.org/abs/2203.15246 · HTML: https://mlsanity.com/paper/2203.15246/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2022.

## Built on by (most cited first, 8 of 8)

- [Tensor networks for interpretable and efficient quantum-inspired machine learning](https://mlsanity.com/paper/2311.11258/) (2023)
- [Generative Learning of Continuous Data by Tensor Networks](https://mlsanity.com/paper/2310.20498/) (2023)
- [Quantum-inspired Techniques in Tensor Networks for Industrial Contexts](https://mlsanity.com/paper/2404.11277/) (2024)
- [Cons-training Tensor Networks: Embedding and Optimization Over Discrete Linear Constraints](https://mlsanity.com/paper/2405.09005/) (2024)
- [Efficient Finite Initialization with Partial Norms for Tensorized Neural Networks and Tensor Networks Algorithms](https://mlsanity.com/paper/2309.06577/) (2023)
- [T'ecnicas Quantum-Inspired en Tensor Networks para Contextos Industriales](https://mlsanity.com/paper/2404.17645/) (2024)
- [A Quantum-Inspired Algorithm for Solving Sudoku Puzzles and the MaxCut Problem](https://mlsanity.com/paper/2510.19835/) (2025)
- [ILP-BO: Integer Linear Programming-Based Black-Box Optimization](https://mlsanity.com/paper/2609.33131/) (2026)

## Abstract (arXiv)

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.