  Methods to find the solution state for optimization problems encoded into
Ising Hamiltonians are a very active area of current research. In this work we
compare the quantum approximate optimization algorithm (QAOA) with multi-stage
quantum walks (MSQW). Both can be used as variational quantum algorithms, where
the control parameters are optimized classically. A fair comparison requires
both quantum and classical resources to be assessed. Alternatively, parameters
can be chosen heuristically, as we do in this work, providing a simpler setting
for comparisons. Using both numerical and analytical methods, we obtain
evidence that MSQW outperforms QAOA, using equivalent resources. We also show
numerically for random spin glass ground state problems that MSQW performs well
even for few stages and heuristic parameters, with no classical optimization.
