In many papers, the QAOA is shown to be intimately related to Quantum Annealing/Quantum Adiabatic Algorithm/Adiabatic Quantum Optimization.
The mixing operator in the QAOA is described by Hadfield as one that transfers probability amplitudes between states. Another post shows it also helps change the probability distribution, as evolving only under the cost Hamiltonian has no effect on the probabilities. It also prevents the possibility of being stuck in an eigenstate of the problem Hamiltonian. In Quantum Annealing, the driver is chosen such that it doesn't commute with the problem Hamiltonian and that it has an easy to construct ground state, after which the system is evolved adiabatically to find the ground state of the problem Hamiltonian. I also see how the QAOA is a discrete trotterization of Quantum Annealing.
I used Qiskit to implement the QAOA and tested them on a simple 3 node graph with 2 edges, a 4-regular 6 node graph and an 8 node 4-regular graph. In each case, I tried a variety of depths (p=3,6,12,24), the standard equal superposition initial state as well as random states. In all initial states I tried, I was able to find the MAXCUT solution. This to me seems strange, since the initial state is crucial to Quantum Annealing. In which case, how is the driver and the mixer related?
I also inspected the relationships between the optimized $\beta$s and $\gamma$s. Given that the QAOA is a trotterization of Quantum Annealing, and that we can think of these angles as the length of time the system is evolving under the operator, I expected to find an inverse relationship such that the values of the angles used for the Mixer unitary decrease in magnitude and the values of the angles used for the Phase unitary increase in magnitude as we move from the leftmost part of the circuit to the right. But this was not the case and no discernible pattern could be seen. Shouldn't there be a correlation to a progression in time? Or perhaps the progression is not linear?