Excited States from ADAPT-VQE convergence path in Many-Body Problems: application to nuclear pairing problem and $H_4$ molecule dissociation

TL;DR

This paper introduces a quantum algorithm leveraging ADAPT-VQE convergence paths to accurately compute low-lying excited states in many-body systems, demonstrated on nuclear pairing and $H_4$ molecule dissociation.

Contribution

It presents a novel quantum space diagonalization method using ADAPT-VQE paths for excited states, improving accuracy with minimal quantum resource overhead.

Findings

Accurately computes excited states in many-body systems.

Demonstrates effectiveness on nuclear pairing problems.

Shows versatility with $H_4$ molecule dissociation.

Abstract

A quantum computing algorithm is proposed to obtain low-lying excited states in many-body interacting systems. The approximate eigenstates are obtained by using a quantum space diagonalization method in a subspace of states selected from the convergence path of the ADAPT-VQE (adaptive derivative-assembled pseudo-Trotter Ansatz variational quantum eigensolver) towards the ground state of the many-body problem. This method is shown to be accurate with only a small overhead in terms of quantum resources required to get the ground state. We also show that the quantum algorithm might be used to facilitate the convergence of the ADAPT-VQE method itself. Successful applications of the technique are made to like-particle pairing as well as neutron-proton pairing. Finally, the $H_4$ molecule's dissociation also illustrates the technique, demonstrating its accuracy and versatility.