  Combinatorial optimization is one of the key candidates in the race for
practical quantum advantage. In this work, we introduce a new family of
quantum-enhanced optimizers and demonstrate how quantum machine learning models
known as quantum generative models can find lower minima than those found by
means of stand-alone state-of-the-art classical solvers. We present two new
quantum-enhanced optimization strategies. The first scheme leverages data
points evaluated during the optimization search from any quantum or classical
optimizer. In this scheme, we show how our quantum generative model boosts the
performance of classical solvers in hard-to-solve instances where the classical
solver is not capable of making progress as a stand-alone strategy. The second
quantum optimization strategy works as a stand-alone solver. Here we show its
superior performance when the goal is to find the best minimum within the least
number of cost function evaluations. Under this setting, we benchmark our
quantum-enhanced optimization strategies against several solvers, including
Bayesian optimizers which are known to be one of the best competing solvers in
such tasks. To illustrate our findings, these benchmarks are performed in the
context of the portfolio optimization problem by constructing instances from
the S&P 500 stock market index. We show that our quantum-inspired generative
models based on tensor networks generalize to unseen candidates with lower cost
function values than any of the candidates seen by the classical solvers. This
is the first demonstration of the generalization capabilities of quantum
generative models that brings real value in the context of an industrial-scale
application.
