Riemannian Optimization for Multi-Player Quantum Games on Product Unitary Manifolds

The paper extends the Eisert-Wilkens-Lewenstein quantum game to multiplayer settings with mixed strategies, where each player selects unitary operators and mixes them classically. It introduces the Unitary Strategy Matrix Exponential Algorithm (USMEA), a geometry-aware sequential method that jointly learns local unitary actions and mixing probabilities for each player. The authors analyze USMEA’s convergence under standard conditions and confirm the theory with numerical experiments, demonstrating how classical optimization can be integrated into engineered quantum strategic interactions.

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