  This paper establishes the tractability of finding the optimal Nash
equilibrium, as well as the optimal social solution, to a discrete congestion
game using a gate-model quantum computer. The game is of the type originally
posited by Rosenthal in the 1970's. To find the optimal Nash equilibrium, we
formulate an optimization problem encoding based on potential functions and
path selection constraints, and solve it using the Quantum Alternating Operator
Ansatz. We compare this formulation to its predecessor, the Quantum Approximate
Optimization Algorithm. We implement our solution on an idealized simulator of
a gate-model quantum computer, and demonstrate tractability on a small
two-player game. This work provides the basis for future endeavors to apply
quantum approximate optimization to quantum machine learning problems, such as
the efficient training of generative adversarial networks using potential
functions.
