  The Quantum Approximate Optimization Algorithm (QAOA) is a variational
quantum algorithm for Near-term Intermediate-Scale Quantum computers (NISQ)
providing approximate solutions for combinatorial optimiz\-ation problems. The
QAOA utilizes a quantum-classical loop, consisting of a quantum ansatz and a
classical optimizer, to minimize some cost function, computed on the quantum
device. This paper presents an investigation into the impact of realistic noise
on the classical optimizer and the determination of optimal circuit depth for
the Quantum Approximate Optimization Algorithm (QAOA) in the presence of noise.
We find that, while there is no significant difference in the performance of
classical optimizers in a state vector simulation, the Adam and AMSGrad
optimizers perform best in the presence of shot noise. Under the conditions of
real noise, the SPSA optimizer, along with ADAM and AMSGrad, emerge as the top
performers. The study also reveals that the quality of solutions to some 5
qubit minimum vertex cover problems increases for up to around six layers in
the QAOA circuit, after which it begins to decline. This analysis shows that
increasing the number of layers in the QAOA in an attempt to increase accuracy
may not work well in a noisy device.
