Theoretical model and numerical simulation demonstrate approximate semidefinite program convergence under noise, indicating viable quantum optimization for weakly constrained systems.
Key Points
Variational quantum algorithms achieve convergence to approximate local optima for weakly constrained semidefinite programming where matrix dimension N exceeds constraint count M.
Numerical simulation of the algorithms on MaxCut problems demonstrates consistent convergence to approximate solutions even within noisy quantum settings.
Theoretical analysis extends the framework to general convex optimization classes with fewer constraints, highlighting broad utility across combinatorial optimization.