  In this paper, we introduce a quantum-enhanced algorithm for simulation-based
optimization. Simulation-based optimization seeks to optimize an objective
function that is computationally expensive to evaluate exactly, and thus, is
approximated via simulation. Quantum Amplitude Estimation (QAE) can achieve a
quadratic speed-up over classical Monte Carlo simulation. Hence, in many cases,
it can achieve a speed-up for simulation-based optimization as well. Combining
QAE with ideas from quantum optimization, we show how this can be used not only
for continuous but also for discrete optimization problems. Furthermore, the
algorithm is demonstrated on illustrative problems such as portfolio
optimization with a Value at Risk constraint and inventory management.
