Excited state calculations using variational quantum eigensolver with spin-restricted ans\"atze and automatically-adjusted constraints

TL;DR

This paper introduces a quantum computing method combining a spin-restricted ansatz with an automatically-adjusted constraint approach to accurately compute excited states and potential energy surfaces on noisy quantum devices.

Contribution

It presents the VQE/AC method that avoids pre-setting constraint weights, enabling smoother excited state calculations on quantum hardware.

Findings

Achieved energy errors within 2 kcal/mol on real quantum hardware.

Successfully computed excited states at key geometries of molecules.

Demonstrated potential for accurate quantum simulations of photophysical properties.

Abstract

The ground and excited state calculations at key geometries, such as the Frank-Condon (FC) and the conical intersection (CI) geometries, are essential for understanding photophysical properties. To compute these geometries on noisy intermediate-scale quantum devices, we proposed a strategy that combined a chemistry-inspired spin-restricted ansatz and a new excited state calculation method called the variational quantum eigensolver under automatically-adjusted constraints (VQE/AC). Unlike the conventional excited state calculation method, called the variational quantum deflation, the VQE/AC does not require the pre-determination of constraint weights and has the potential to describe smooth potential energy surfaces. To validate this strategy, we performed the excited state calculations at the FC and CI geometries of ethylene and phenol blue at the complete active space self-consistent field (CASSCF) level of theory, and found that the energy errors were at most 2 kcal mol$^{-1}$ even on the ibm_kawasaki device.