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arXiv · 2203.15246

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

Tianyi Hao·Xuxin Huang·Chunjing Jia·Cheng Peng
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Abstract

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.

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Tianyi Hao, Xuxin Huang, Chunjing Jia, Cheng Peng. 2022-03-29. A quantum-inspired tensor network method for constrained combinatorial optimization problems. https://doi.org/10.3389/fphy.2022.906590

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