Fig. 1: Scaling of the number of Zeno measurements.
Number of measurements, obtained from Corollary 3, required in QAOA with Zeno dynamics to maintain a maximum out-of-constraint probability of \({\delta }_{\max }\) (hence, a minimum in-constraint probability of \(1-{\delta }_{\max }\)) for the B = ∑jxj (✖ marker) and \(B=\left\vert +\right\rangle \left\langle +\right\vert\) (✚ marker) mixers with 3 qubits. Color denotes the minimum in-constraint probability \(1-{\delta }_{\max }\), as indicated by the legend. Note that this is the scaling required to ensure the desired minimum in-constraint probability for the worst-case initial state (i.e., Equation (37)) and is potentially more pessimistic than what is observed in practice. Many more measurements are required for B = ∑jxj as the number of measurements grows quadratically with number of qubits. Note that due to periodicity, the evolution time, β, can be constrained to \(| \beta | \le \frac{\pi }{2}\) for B = ∑jxj and ∣β∣ ≤ π for \(B=\left\vert +\right\rangle \left\langle +\right\vert\).
