Solving the traveling salesman problem on 2 (N-1)! qubits with a variational quantum Kolmogorov--Arnold network: exact-gradient CVaR training and generalization over time-dependent graphs
The Variational Quantum Kolmogorov-Arnold Network (VQKAN) solves the Traveling Salesman Problem (TSP) by using quantum circuits to emulate transformer matrices. It uses exact-gradient training based on Conditional Value at Risk (CVaR) to find optimal tours. The method scales reliably to ten sites and generalizes across time-dependent graphs, showing potential for solving complex, real-world optimization problems.