  The Integrated Side Lobe Ratio (ISLR) problem we consider here consists in
finding optimal sequences of phase shifts in order to minimize the mean squared
cross-correlation side lobes of a transmitted radar signal and a mismatched
replica. Currently, ISLR does not seem to be easier than the general polynomial
unconstrained binary problem, which is NP-hard. In our work, we aim to take
advantage of the exponential scalability of quantum computing to find new
optima, by solving the ISLR problem on a quantum annealer. This quantum device
is designed to solve quadratic optimization problems with binary variables
(QUBO). After proposing suitable formulation for different instances of the
ISLR, we discuss the performances and the scalability of our approach on the
D-Wave quantum computer. More broadly, our work enlightens the limits and
potential of the adiabatic quantum computation for the solving of large
instances of combinatorial optimization problems.
