  The quantum approximate optimization algorithm (QAOA) is widely seen as a
possible usage of noisy intermediate-scale quantum (NISQ) devices. We analyze
the algorithm as a bang-bang protocol with fixed total time and a randomized
greedy optimization scheme. We investigate the performance of bang-bang QAOA on
MAX-2-SAT, finding the appearance of phase transitions with respect to the
total time. As the total time increases, the optimal bang-bang protocol
experiences a number of jumps and plateaus in performance, which match up with
an increasing number of switches in the standard QAOA formulation. At large
times, it becomes more difficult to find a globally optimal bang-bang protocol
and performances suffer. We also investigate the effects of changing the
initial conditions of the randomized optimization algorithm and see that better
local optima can be found by using an adiabatic initialization.
