  Quantum machine learning algorithms have emerged to be a promising
alternative to their classical counterparts as they leverage the power of
quantum computers. Such algorithms have been developed to solve problems like
electronic structure calculations of molecular systems and spin models in
magnetic systems. However the discussion in all these recipes focus
specifically on targeting the ground state. Herein we demonstrate a quantum
algorithm that can filter any energy eigenstate of the system based on either
symmetry properties or on a predefined choice of the user. The work horse of
our technique is a shallow neural network encoding the desired state of the
system with the amplitude computed by sampling the Gibbs- Boltzmann
distribution using a quantum circuit and the phase information obtained
classically from the non-linear activation of a separate set of neurons. We
show that the resource requirements of our algorithm is strictly quadratic. To
demonstrate its efficacy, we use state-filtration in monolayer transition
metal-dichalcogenides which are hitherto unexplored in any flavor of quantum
simulations. We implement our algorithm not only on quantum simulators but also
on actual IBM-Q quantum devices and show good agreement with the results
procured from conventional electronic structure calculations. We thus expect
our protocol to provide a new alternative in exploring band-structures of
exquisite materials to usual electronic structure methods or machine learning
techniques which are implementable solely on a classical computer
