  A quantum sensor (QS) is able to measure various physical phenomena with
extreme sensitivity. QSs have been used in several applications such as atomic
interferometers, but few applications of a quantum sensor network (QSN) have
been proposed or developed. We look at a natural application of QSN --
localization of an event (in particular, of a wireless signal transmitter). In
this paper, we develop effective quantum-based techniques for the localization
of a transmitter using a QSN. Our approaches pose the localization problem as a
well-studied quantum state discrimination (QSD) problem and address the
challenges in its application to the localization problem. In particular, a
quantum state discrimination solution can suffer from a high probability of
error, especially when the number of states (i.e., the number of potential
transmitter locations in our case) can be high. We address this challenge by
developing a two-level localization approach, which localizes the transmitter
at a coarser granularity in the first level, and then, in a finer granularity
in the second level. We address the additional challenge of the impracticality
of general measurements by developing new schemes that replace the QSD's
measurement operator with a trained parameterized hybrid quantum-classical
circuit. Our evaluation results using a custom-built simulator show that our
best scheme is able to achieve meter-level (1-5m) localization accuracy; in the
case of discrete locations, it achieves near-perfect (99-100\%) classification
accuracy.
