  Several combinatorial optimization problems can be solved with NISQ devices
once that a corresponding quadratic unconstrained binary optimization (QUBO)
form is derived. The aim of this work is to drastically reduce the variables
needed for these QUBO reformulations in order to unlock the possibility to
efficiently obtain optimal solutions for a class of optimization problems with
NISQ devices. This is achieved by introducing novel tools that allow an
efficient use of slack variables, even for problems with non-linear
constraints, without the need to approximate the starting problem. We divide
our new techniques in two independent parts, called the iterative quadratic
polynomial and the master-satellite methods. Hence, we show how to apply our
techniques in case of an NP-hard optimization problem inspired by a real-world
financial scenario called Max-Profit Balance Settlement. We follow by
submitting several instances of this problem to two D-wave quantum annealers,
comparing the performances of our novel approach with the standard methods used
in these scenarios. Moreover, this study allows to appreciate several
performance differences between the D-wave Advantage and Advantage2 quantum
annealers.
