Quantum simulation of excited states from parallel contracted quantum eigensolvers

TL;DR

This paper introduces a scalable quantum algorithm based on contracted quantum eigensolvers for efficiently computing multiple excited states of molecules and solids, leveraging the Rayleigh-Ritz variational principle.

Contribution

It generalizes the ground-state contracted quantum eigensolver to compute multiple excited states simultaneously using a novel anti-Hermitian approach.

Findings

Successfully applied to model and chemical Hamiltonians

Demonstrated scalability and efficiency of the excited-state CQEs

Compared different implementations showing promising results

Abstract

Computing excited-state properties of molecules and solids is considered one of the most important near-term applications of quantum computers. While many of the current excited-state quantum algorithms differ in circuit architecture, specific exploitation of quantum advantage, or result quality, one common feature is their rooting in the Schr\"odinger equation. However, through contracting (or projecting) the eigenvalue equation, more efficient strategies can be designed for near-term quantum devices. Here we demonstrate that when combined with the Rayleigh-Ritz variational principle for mixed quantum states, the ground-state contracted quantum eigensolver (CQE) can be generalized to compute any number of quantum eigenstates simultaneously. We introduce two excited-state (anti-Hermitian) CQEs that perform the excited-state calculation while inheriting many of the remarkable features of the original ground-state version of the algorithm, such as its scalability. To showcase our approach, we study several model and chemical Hamiltonians and investigate the performance of different implementations.