  We demonstrate a method that merges the quantum filter diagonalization (QFD)
approach for hybrid quantum/classical solution of the time-independent
electronic Schr\"odinger equation with a low-rank double factorization (DF)
approach for the representation of the electronic Hamiltonian. In particular,
we explore the use of sparse "compressed" double factorization (C-DF)
truncation of the Hamiltonian within the time-propagation elements of QFD,
while retaining a similarly compressed but numerically converged
double-factorized representation of the Hamiltonian for the operator
expectation values needed in the QFD quantum matrix elements. Together with
significant circuit reduction optimizations and number-preserving
post-selection/echo-sequencing error mitigation strategies, the method is found
to provide accurate predictions for low-lying eigenspectra in a number of
representative molecular systems, while requiring reasonably short circuit
depths and modest measurement costs. The method is demonstrated by experiments
on noise-free simulators, decoherence- and shot-noise including simulators, and
real quantum hardware.
