<p>The classical games of Rock-Paper-Scissors (RPS) and its extended variant, Rock-Paper-Scissors-Lizard-Spock (RPSLS), exemplify non-transitive logic and mixed-strategy Nash equilibria in game theory. This work presents a novel quantum implementation of these games using Grover’s search algorithm, demonstrating how quantum superposition and entanglement can transform classical gameplay. We develop a quantum circuit architecture that efficiently identifies winning strategies, with the RPSLS variant highlighting the scalability of our approach to larger strategy spaces. Furthermore, we introduce a novel quantum bit commitment protocol based on non-orthogonal RPSLS states, which serves as a pedagogical model for understanding security trade-offs in quantum cryptography. Our framework reveals deep parallels between the cyclic dominance of game strategies and quantum nonlocality through Hardy’s paradox, while offering practical applications in quantum optimization and secure communication. The proposed implementation is experimentally feasible on near-term quantum devices and provides an accessible platform for illustrating quantum algorithmic advantages in strategic decision-making.</p>