Entanglement-assisted phase estimation algorithm for calculating dynamical response functions

TL;DR

This paper introduces an entanglement-assisted quantum phase estimation algorithm that improves the accuracy of dynamical response function calculations by reducing spectral leakage, demonstrated through simulations in multiple quantum many-body systems.

Contribution

It extends quantum phase estimation with optimal entangled states to better estimate excitation energies and transition probabilities, mitigating spectral leakage issues.

Findings

Peaks in energy spectra are more localized with entangled QPE.

The method achieves Heisenberg-limited scaling for estimation precision.

Numerical simulations validate improved spectral resolution across various systems.

Abstract

Dynamical response functions are fundamental quantities to describe the excited-state properties in quantum many-body systems. Quantum algorithms have been proposed to evaluate these quantities by means of quantum phase estimation (QPE), where the energy spectra are directly extracted from the QPE measurement outcomes in the frequency domain. Accurate estimation of excitation energies and transition probabilities with these QPE-based approaches is, however, challenging because of the problem of spectral leakage (or peak broadening) which is inherent in the QPE algorithm. To overcome this issue, in this work we consider an extension of the QPE-based approach adopting the optimal entangled input states, which is known to achieve the Heisenberg-limited scaling for the estimation precision. We show that with this method the peaks in the calculated energy spectra are more localized than those calculated by the original QPE-based approaches, suggesting the mitigation of the spectral leakage problem. By analyzing the probability distribution with the entangled phase estimation, we propose a simple scheme to better estimate both the transition energies and the corresponding transition probabilities of the peaks of interest in the spectra. The validity of our prescription is demonstrated by numerical simulations in various quantum many-body problems: the spectral function of a simple electron-plasmon model in condensed-matter physics, the dipole transitions of the H$_2$O molecule in quantum chemistry, and the electromagnetic transitions of the $^6$Li nucleus in nuclear physics.