  Quantum computers are expected to offer advantages over classical computers
for combinatorial optimization. Here, we introduce a feedback-based strategy
for quantum optimization, where the results of qubit measurements are used to
constructively assign values to quantum circuit parameters. We show that this
procedure results in an estimate of the combinatorial optimization problem
solution that improves monotonically with the depth of the quantum circuit.
Importantly, the measurement-based feedback enables approximate solutions to
the combinatorial optimization problem without the need for any classical
optimization effort, as would be required for the quantum approximate
optimization algorithm (QAOA). Numerical analyses are presented that
investigate the utility of this feedback-based protocol for the
graph-partitioning problem MaxCut.
