Native quantum games from interacting discrete-time quantum walks

C. M. Chandrashekar, Subhashish Banerjee

Hong Mei Guo, Juheng Zhang, Gary J. Kœhler

Rashid Ahmad

We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by distinguishable quantum walkers, strategies correspond to local coin operations, and payoffs are defined as expectation values of physical observables. Using interacting discrete-time quantum walks as a concrete platform, we demonstrate numerically that competitive, cooperative, and asymmetric games admit stable stationary strategy profiles when the walkers are coupled, while no non-trivial equilibria exist in the absence of interaction. To clarify the game-theoretic structure, we derive an analytic perturbative decomposition of the payoff function in the weak-interaction regime, showing explicitly that strategic coupling originates from interaction-induced interference terms in the joint probability distribution. For a collision-based phase interaction, the payoff becomes non-separable at first order in the interaction strength and generically admits stationary points satisfying the Nash conditions. Our results provide a physically explicit realization of strategic interdependence in quantum transport processes and establish interacting quantum walks as a minimal platform for studying game-theoretic behavior emerging from unitary dynamics.

Clement Boateng Ampadu

We consider the discrete-time quantum walk in the plane, and present a quantum implementation of Parrondo's game for four players. Physical significance of the game strategies are also discussed.

Vladimir G. Ivancevic, Tijana T. Ivancevic

Ramón Alonso‐Sanz