  We present a novel input model for general second-quantized Hamiltonians of
relativistic or non-relativistic many-fermion systems. This input model
incorporates the fermionic anticommutation relations, particle number
variations, and respects the symmetries of the Hamiltonian. Based on our input
model, we propose a hybrid framework for spectral calculations on future
quantum hardwares. We provide explicit circuit designs and the associated gate
cost and circuit depth. We demonstrate our framework by solving the low-lying
spectra of ${^{42}}Ca$ and ${^{46}}Ca$. Our input model provides new pathways
to solving the spectra and time evolutions of the relativistic and
nonrelativistic many-fermion systems.
