Fock-Space Schrieffer–Wolff Transformation: Classically-Assisted Rank-Reduced Quantum Phase Estimation Algorithm

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