  Adiabatic quantum computing is implemented on specialized hardware using the
heuristics of the quantum annealing algorithm. This setup requires the
addressed problems to be formatted as discrete quadratic functions without
constraints and the variables to take binary values only. The problem of
finding Nash equilibrium in two-player, non-cooperative games is a two-fold
quadratic optimization problem with constraints. This problem was formatted as
a single, constrained quadratic optimization in 1964 by Mangasarian and Stone.
Here, we show that adding penalty terms to the quadratic function formulation
of Nash equilibrium gives a quadratic unconstrained binary optimization (QUBO)
formulation of this problem that can be executed on quantum annealers. Three
examples are discussed to highlight the success of the formulation, and an
overall, time-to-solution (hardware + software processing) speed up of seven to
ten times is reported on quantum annealers developed by D-Wave System.
