Proposal of method to solve a Traveling Salesman Problem using Variational Quantum Kolmogorov-Arnold Network

Abstract: Traveling salesman problems (TSP) are one of the well-known combinatorial optimization problems that many groups tackle to solve. This problem appears in many types of combinational optimization, such as scheduling, route optimization, and circuit optimization. However, this problem is NP-hard, as the number of combinations increases exponentially as the number of sites increases. Quantum Annealers and Adiabatic Quantum Computers are good at solving it, and universal quantum computers are limited by the number of qubits they have. Therefore, we propose a novel approach that solves it using a Variational Quantum Kolmogorov-Arnold network (VQKAN). Our approach requires a smaller number of qubits than the former approaches on quantum computers. We confirmed that our approach can optimize the paths on the graphs whose length of each path is time-dependent, partial.