Fig. 11: Simulation and hardware experiment results using QAOA with Zeno dynamics.
QAOA with p = 1 and Zeno dynamics was applied to solve a four-asset problem with an equality constraint 2x1 − x2 − x3 = 0 (a) and inequality constraint \(\mathop{\sum }\nolimits_{j = 1}^{4}{x}_{j}\le 2\) (b). The circuits were executed on a classical simulator and on the H1-2 quantum device. The oracles are implemented using arithmetic in the Fourier domain. For the equality constraint (a), the quantum conditional logic (QCL) implementation of the Fourier adder used one auxiliary qubit, and the version without QCL used three auxiliary qubits. The Fourier adder used for the inequality constraint (b) used four auxiliary qubits. Error bars indicate the standard error of the mean arising from finite sampling (2000 shots). The in-constraint probability 1 − δ grows with the number of measurements (N).
