Multi-player conflict avoidance through entangled quantum walks

Quantum computing has the potential to solve complex problems faster and more efficiently than classical computing. It can achieve speedups by leveraging quantum phenomena like superposition, entanglement, and tunneling. Quantum walks (QWs) form the foundation for many quantum algorithms. Unlike classical random walks, QWs exhibit quantum interference, leading to unique behaviors such as linear spreading and localization. These properties make QWs valuable for various applications, including universal computation, time series prediction, encryption, and quantum hash functions. One emerging application of QWs is decision making. Previous research has used QWs to model human decision processes and solve multi-armed bandit problems. This paper extends QWs to collective decision making, focusing on minimizing decision-conflict cases where multiple agents choose the same option, leading to inefficiencies like traffic congestion or overloaded servers. Prior research using quantum interference has addressed two-player conflict avoidance but struggled with three-player scenarios. This paper proposes a novel method using QWs to entirely eliminate decision conflicts in three-player cases, demonstrating its effectiveness in collective decision making.