Quantum simulations of excited states with active-space downfolded Hamiltonians

TL;DR

This paper explores the use of double unitary coupled cluster (DUCC) Hamiltonians and quantum phase estimation (QPE) algorithms to accurately simulate excited states in strongly correlated molecular systems, enhancing quantum computational methods.

Contribution

It demonstrates the effectiveness of DUCC in describing excited states and highlights the role of QPE as a tool for identifying and verifying excited-state configurations.

Findings

DUCC Hamiltonians effectively describe excited states.

QPE can verify hypotheses about excited states.

Application to strongly correlated molecules shows promising results.

Abstract

Many-body techniques based on the double unitary coupled cluster ansatz (DUCC) can be used to downfold electronic Hamiltonians into low-dimensional active spaces. It can be shown that the resulting dimensionality reduced Hamiltonians are amenable for quantum computing. Recent studies performed for several benchmark systems using quantum phase estimation (QPE) algorithms demonstrated that these formulations can recover a significant portion of ground-state dynamical correlation effects that stem from the electron excitations outside of the active space. These results have also been confirmed in studies of ground-state potential energy surfaces using quantum simulators. In this letter, we study the effectiveness of the DUCC formalism in describing excited states. We also emphasize the role of the QPE formalism and its stochastic nature in discovering/identifying excited states or excited-state processes in situations when the knowledge about the true configurational structure of a sought after excited state is limited or postulated (due to the specific physics driving excited-state processes of interest). In this context, we can view the QPE algorithm as an engine for verifying various hypotheses for excited-state processes and providing statistically meaningful results that correspond to the electronic state(s) with the largest overlap with a postulated configurational structure. We illustrate these ideas on examples of strongly correlated molecular systems, characterized by small energy gaps and high density of quasi-degenerate states around the Fermi level.