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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