  The recently developed Projective Quantum Eigensolver (PQE) offers an elegant
procedure to evaluate the ground state energies of molecular systems on quantum
computers. However, the noise in available quantum hardware can result in
significant errors in computed outcomes, limiting the realization of quantum
advantage. Although PQE comes equipped with some degree of inherent noise
resilience, any practical implementation with apposite accuracy would require
additional routines to suppress the errors further. In this work, we propose a
way to enhance the efficiency of PQE by developing an optimal framework for
introducing Zero Noise Extrapolation (ZNE) in the nonlinear iterative procedure
that outlines the PQE; leading to the formulation of ZNE-PQE. For this method,
we perform a detailed analysis of how various components involved in it affect
the accuracy and efficiency of the reciprocated energy convergence trajectory.
Moreover, we investigate the reasons behind the improvements observed in
ZNE-PQE over conventional PQE by performing a comparative analysis of their
residue norm landscape. This approach is expected to facilitate practical
applications of quantum computing in fields related to molecular sciences,
where it is essential to determine molecular energies accurately.
