2022/11/18 by Karol Kowalski, Kowalski, Karol, Nicholas P. Bauman +1
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Physics of Superconductivity and Magnetism #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2211.10529
openalex publication_date 2022/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.