Solving the Traveling Salesman Problem with Quantum Self-Attention Networks

The Traveling Salesman Problem (TSP), a well-known NP-hard problem, has intrigued computer scientists and mathematicians for over two centuries. In recent years, end-to-end deep reinforcement learning algorithms have been increasingly employed to tackle the TSP. However, these algorithms typically rely on classical neural networks, which face challenges such as a high number of training parameters and the necessity for large training datasets. This paper proposes a novel approach that integrates quantum computing with transformer modeling to address these challenges. By utilizing variational quantum circuits within the encoder and employing a quantum self-attentive neural network, we train the model using deep reinforcement learning algorithms. Experimental results on benchmark datasets demonstrate that the quantum self-attentive neural network model significantly outperforms existing classical neural network models. This new approach not only substantially reduces the number of training parameters and the size of the training dataset while solving the TSP problem, but also achieves superior optimization results compared to classical neural networks.