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This paper establishes the tractability of finding the optimal Nashequilibrium, as well as the optimal social solution, to a discrete congestiongame using a gate-model quantum computer. The game is of the type originallyposited by Rosenthal in the 1970's. To find the optimal Nash equilibrium, weformulate an optimization problem encoding based on potential functions andpath selection constraints, and solve it using the Quantum Alternating OperatorAnsatz. We compare this formulation to its predecessor, the Quantum ApproximateOptimization Algorithm. We implement our solution on an idealized simulator ofa gate-model quantum computer, and demonstrate tractability on a smalltwo-player game. This work provides the basis for future endeavors to applyquantum approximate optimization to quantum machine learning problems, such asthe efficient training of generative adversarial networks using potentialfunctions.

Finding the optimal Nash equilibrium in a discrete Rosenthal congestion game using the Quantum Alternating Operator Ansatz