  The similarity between objects is significant in a broad range of areas.
While similarity can be measured using off-the-shelf distance functions, they
may fail to capture the inherent meaning of similarity, which tends to depend
on the underlying data and task. Moreover, conventional distance functions
limit the space of similarity measures to be symmetric and do not directly
allow comparing objects from different spaces. We propose using quantum
networks (GQSim) for learning task-dependent (a)symmetric similarity between
data that need not have the same dimensionality. We analyze the properties of
such similarity function analytically (for a simple case) and numerically (for
a complex case) and showthat these similarity measures can extract salient
features of the data. We also demonstrate that the similarity measure derived
using this technique is $(\epsilon,\gamma,\tau)$-good, resulting in
theoretically guaranteed performance. Finally, we conclude by applying this
technique for three relevant applications - Classification, Graph Completion,
Generative modeling.
