Fig. 4: QAOA heuristics in the presence of realistic hardware noise: increasing problem size for a fixed number of rounds.

The approximation ratio averaged over 60 random graphs of increasing number of nodes n and fixed number of rounds p = 4 is plotted. The black, green, and red curves respectively correspond to noise-free training, noisy training with noise-free final cost evaluation, and noisy training with noisy final cost evaluation. a For a problem size of 8 nodes or larger, the noisily-trained approximation ratio falls below the performance guarantee of the classical Goemans-Williamson algorithm. b The depth of the circuit (red curve) scales linearly with the number of qubits, confirming we are in a regime where we would expect to observe Noise-Induced Barren Plateaus.