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We propose a random circuit model that attempts to capture the behavior of noisy intermediate-scale quantum devices when used for variationally solving 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 optima implies that 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 the quantum approximate optimization algorithm for classical optimization problems with two-dimensional circuits.