  We present an extension of many-body downfolding methods to reduce the
resources required in the quantum phase estimation (QPE) algorithm. In this
paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic
Hamiltonians for molecular systems that provides significant simplifications of
quantum circuits for simulations of quantum dynamics. We demonstrate that by
employing Fock-space variants of the SW transformation (or rank-reducing
similarity transformations (RRST)) one can significantly increase the locality
of the qubit-mapped similarity transformed Hamiltonians. The practical
utilization of the SW-RRST formalism is associated with a series of
approximations discussed in the manuscript. In particular, amplitudes that
define RRST can be evaluated using conventional computers and then encoded on
quantum computers. The SW-RRST QPE quantum algorithms can also be viewed as an
extension of the standard state-specific coupled-cluster downfolding methods to
provide a robust alternative to the traditional QPE algorithms to identify the
ground and excited states for systems with various numbers of electrons using
the same Fock-space representations of the downfolded Hamiltonian.The RRST
formalism serves as a design principle for developing new classes of
approximate schemes that reduce the complexity of quantum circuits.
