Fig. 2: Performance of QAOA with Zeno dynamics and QAOA with constraints enforced using penalty terms.
Approximation ratio r and out-of-constraint probability δ (correspondingly 1 − δ in-constraint probability) achieved by QAOA with constraints enforced using penalty terms (dotted lines) on problems (a–d) with a single constraint, and by QAOA with Zeno dynamics (solid lines) on problems with a single (a–d) and multiple (e, f) constraint(s). The markers ✖ and ✚ indicate whether QAOA used the B = ∑jxj mixer or \(B=\left\vert +\right\rangle \left\langle +\right\vert\) mixer, respectively. For all single constraint problems, QAOA with Zeno dynamics produces a superior approximation ratio and in-constraint probability (solid line is above dotted line with the same color). As penalty factor tuning is prohibitively difficult for problems with multiple constraints (see the Results Section), for these problems only Zeno dynamics results are presented.
