  We propose a random circuit model to analyze the impact of noise on the
performance of variational quantum circuits for classical optimization
problems. Our model accounts for the propagation of arbitrary single qubit
errors through the circuit. We find that even with a small noise rate, the
quality of the obtained classical optima is low on average and a single-qubit
error rate of $1 / nD$, where $n$ is the number of qubits and $D$ is the
circuit depth, is needed for the possibility of a quantum advantage. We
estimate that this translates to an error rate lower than $10^{-6}$ using QAOA
for classical optimization problems with 2D circuits.
