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

• URL: http://arxiv.org/abs/2211.10529v1
• Date: Fri, 18 Nov 2022 23:06:57 GMT
• Title: Fock-space Schrieffer--Wolff transformation: classically-assisted rank-reduced quantum phase estimation algorithm
• Authors: Karol Kowalski, Nicholas P. Bauman
• Abstract summary: In this paper, we focus on the Schrieffer--Wolff (SW) transformation of the electronic Hamiltonians for molecular systems. We demonstrate that by employing Fock-space variants of the SW transformation one can significantly increase the locality of the qubit-mapped similarity transformed Hamiltonians. The RRST formalism serves as a design principle for developing new classes of approximate schemes that reduce the complexity of quantum circuits.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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