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We present an extension of many-body downfolding methods to reduce theresources required in the quantum phase estimation (QPE) algorithm. In thispaper, we focus on the Schrieffer--Wolff (SW) transformation of the electronicHamiltonians for molecular systems that provides significant simplifications ofquantum circuits for simulations of quantum dynamics. We demonstrate that byemploying Fock-space variants of the SW transformation (or rank-reducingsimilarity transformations (RRST)) one can significantly increase the localityof the qubit-mapped similarity transformed Hamiltonians. The practicalutilization of the SW-RRST formalism is associated with a series ofapproximations discussed in the manuscript. In particular, amplitudes thatdefine RRST can be evaluated using conventional computers and then encoded onquantum computers. The SW-RRST QPE quantum algorithms can also be viewed as anextension of the standard state-specific coupled-cluster downfolding methods toprovide a robust alternative to the traditional QPE algorithms to identify theground and excited states for systems with various numbers of electrons usingthe same Fock-space representations of the downfolded Hamiltonian.The RRSTformalism serves as a design principle for developing new classes ofapproximate schemes that reduce the complexity of quantum circuits.

Fock-space Schrieffer--Wolff transformation: classically-assisted rank-reduced quantum phase estimation algorithm