NISQ algorithm for the matrix elements of a generic observable

TL;DR

This paper introduces a NISQ-compatible quantum algorithm for estimating both diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis, useful in physics and chemistry, without requiring eigenstate preparation.

Contribution

The paper presents a novel NISQ algorithm capable of estimating matrix elements without prior eigenstate preparation, broadening quantum computational tools for physical applications.

Findings

Numerical simulations show effective estimation of matrix elements.

The method works with randomly initialized trial functions.

No need for energy eigenstate preparation.

Abstract

The calculation of off-diagonal matrix elements has various applications in fields such as nuclear physics and quantum chemistry. In this paper, we present a noisy intermediate scale quantum algorithm for estimating the diagonal and off-diagonal matrix elements of a generic observable in the energy eigenbasis of a given Hamiltonian. Several numerical simulations indicate that this approach can find many of the matrix elements even when the trial functions are randomly initialized across a wide range of parameter values without, at the same time, the need to prepare the energy eigenstates.