We introduce a constructive protocol that uses feedback from qubit measurements to solve discrete optimization problems on quantum computers.

The use of feedback removes the need for any classical optimization effort. The protocol could be used on quantum computers to solve discrete optimization problems with a range of applications spanning supply chain and logistics.

We motivate our protocol using quantum Lyapunov control theory and show that the use of feedback guarantees that the quality of the discrete optimization problem solution will improve with quantum circuit depth. The performance of the protocol towards solving the quintessential MaxCut problem on regular graphs is explored numerically.

For details see

“Feedback-based quantum optimization”, A. Magann, K. Rudinger, M. Grace, M. Sarovar. arXiv:2103.08619