New Method for Tensor Networks in Combinatorial Optimization

A recent paper titled "Quick design of feasible tensor networks for constrained combinatorial optimization" by Hyakka Nakada, Kotaro Tanahashi, and Shu Tanaka presents a novel approach to solving constrained combinatorial optimization problems using tensor networks. The authors highlight the limitations of existing quantum gate methods, such as the quantum approximate optimization algorithm, which struggle with errors and scalability issues when applied to large-scale problems.

The study proposes a method that simplifies the design of tensor networks, allowing for feasible solutions to be identified without relying on complex penalty functions. The authors utilize elementary mathematics to construct tensor networks through nilpotent-matrix manipulation and algebraic determination of tensor parameters.

To validate their approach, the researchers applied their method to a facility location problem, demonstrating that feasible solutions emerged during the imaginary time evolution process, ultimately leading to optimal solutions. This research is expected to enhance the efficiency of tensor networks in practical applications, thereby broadening the scope of combinatorial optimization techniques available for complex problem-solving.

The findings are significant as they provide a more accessible framework for utilizing tensor networks in optimization tasks, potentially impacting various fields that rely on combinatorial optimization methods. The full paper can be accessed at arXiv:2409.01699.