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

• URL: http://arxiv.org/abs/2203.15246v2
• Date: Mon, 5 Sep 2022 19:55:33 GMT
• Title: A quantum-inspired tensor network method for constrained combinatorial optimization problems
• Authors: Tianyi Hao and Xuxin Huang and Chunjing Jia and Cheng Peng
• Abstract summary: We propose a quantum-inspired tensor-network-based algorithm for general locally constrained optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem. Our results show the effectiveness of this construction and potential applications.
• Score: 5.904219009974901
• License: http://creativecommons.org/licenses/by/4.0/
• 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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