Given the limitations of noisy-intermediate scale quantum (NISQ) computing, variational methods have become a ubiquitous approach to perform molecular electronic structure simulations using simple, short-depth circuits. By design, methods like the variational quantum eigensolver (VQE) build on the variational principle to target the minimal eigenenergy state of an observable, typically the Hamiltonian operator. These methods may be extended to recover higher-lying eigenvalues and their excited states using projectors that constrain the variational search space. An alternative approach is to use the quantum equation of motion (QEOM) algorithm, first presented by Ollitrault et al. (2019), to calculate the excited states and corresponding spectrum. This approach draws inspiration from classical EOM methods, which have a long history of development for solving many-body systems. In QEOM, an approximate ground state is prepared using VQE and then used to estimate elements of a secular equation. The secular equation defines the action of typical many-body excitation operators onto the ground state, which may be used to recover the corresponding excitation energies. Here we address the sensitivity of QEOM to the quality of ansatz used to approximate the ground state and the excitation operators. We examine the effect of the ground state on the computed energy spectrum by using a structured ansatz derived with the ADAPT-VQE algorithm (Grimsley et al., 2019). This adaptive algorithm refines the ground-state circuit ansatz by tuning excitation operators from a pre-defined set. We investigate the convergence of the energy spectrum as a function of the circuit ansatz evolution along the ADAPT-VQE algorithm, which provides feedback on the reachability of the ansatz. In the spirit of classical EOM techniques, we also discuss the extension of QEOM to include operators capable of ionization, electron attachment, and spin-flip by exploring the underlying Fock space in a controlled fashion.

Benchmarking the quantum equation of motion method using an adaptive ansatz

ACS Spring Meeting 2021

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.