Implementation of excited state energy and its analytical derivatives for photochemical reaction simulations on NISQ devices

A primitive but still powerful form of quantum computers called Noisy Intermediate-Scale Quantum (NISQ) devices is about to be utilized for the real-world problems. NISQ devices have a few hundreds to thousands of qubits under highly precise control although they are not fault-tolerant.

A quantum chemistry calculation is one of the most promising applications of NISQ devices in the near future, and Variational Quantum Eigensolver (VQE) is the most featured algorithm to take advantage of NISQ devices in quantum chemistry.
Recently, numerous algorithms based on the VQE are proposed for solving problems that are hard for classical computers, such as calculations of electronic excited states of large molecular systems.

However, VQE-type algorithms are in general based on the variational principle, which makes it difficult to predict their performances when applied to actual molecular systems due to their heuristic nature.

In this study, using the high-speed simulator Qulacs, we implement VQE-type algorithms to calculate several physical properties (analytical energy derivatives and oscillator strengths) required for photochemical reaction simulations and create their unified benchmark of various proposed methods for small molecules compared with results from the classical computation.