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

TL;DR

This paper introduces a Fock-space Schrieffer--Wolff transformation to simplify quantum Hamiltonians, enhancing the efficiency of quantum phase estimation algorithms for molecular systems by increasing Hamiltonian locality.

Contribution

It extends many-body downfolding methods with a Fock-space SW transformation, enabling resource-efficient quantum simulations and providing a new class of approximate schemes for quantum circuits.

Findings

Increased locality of Hamiltonians improves quantum simulation efficiency.

Amplitudes for RRST can be computed classically and encoded on quantum computers.

The method offers a robust alternative to traditional QPE for electronic state identification.

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.