  Variational quantum algorithms offer fascinating prospects for the solution
of combinatorial optimization problems using digital quantum computers.
However, the achievable performance in such algorithms and the role of quantum
correlations therein remain unclear. Here, we shed light on this open issue by
establishing a tight connection to the seemingly unrelated field of quantum
metrology: Metrological applications employ quantum states of spin-ensembles
with a reduced variance to achieve an increased sensitivity, and we cast the
generation of such squeezed states in the form of finding optimal solutions to
a combinatorial MaxCut problem with an increased precision. By solving this
optimization problem with a quantum approximate optimization algorithm (QAOA),
we show numerically as well as on an IBM quantum chip how highly squeezed
states are generated in a systematic procedure that can be adapted to a wide
variety of quantum machines. Moreover, squeezing tailored for the QAOA of the
MaxCut permits us to propose a figure of merit for future hardware benchmarks.
