Figure 4

Pareto frontier of QAOA parameters with respect to approximation ratio and the in-constraint probability for 14 (a) and 20 (b) qubits. Each color plots a different problem instance for a given number of qubits. When solving a constrained-optimization problem using QAOA, the parameter optimization strategy has to be tuned to arrive at the desired point on the Pareto frontier. Directly optimizing the objective (6) would lead to choosing the righmost point of the frontier, which in the case of the 20 qubit instance presented in (c) corresponds to approximation ratio equal to that of random guess. In (c), each dot corresponds to one value of \(\mathbf {\beta }, \mathbf {\gamma }\) from a grid search in parameter space. Thick dashed line shows the Pareto frontier and the thin dotted line marks the approximation ratio of a random solution. The red \(\times\) marker indicates the parameters chosen for the experiments shown above.