  The search for new computational tasks of quantum chemistry that can be
performed on current quantum computers is important for the development of
quantum computing and quantum chemistry. Although calculations of chemical
reactions have a wide range of applications in quantum chemical calculations, a
quantum algorithm for obtaining activation energy $E_a$, which determines the
rate of chemical reactions, has not been performed. In this study, we propose a
quantum algorithm for the chemical reaction path optimization to obtain $E_a$.
In our algorithm, quantum circuits can be used not only for the energy
evaluation by the variational quantum eigensolver (VQE) but also for chemical
reaction path generation. The chemical reaction path is obtained by encoding
the initial reaction path to the circuit, operating parameterized gates, and
extracting the path information by measurement. The nudged elastic band method
was used for optimizing a reaction path, and the ground-state calculation for
each state on the path was performed by the VQE or the exact diagonalization
(ED). The proposed algorithm was applied to $\mathrm{H}_2 + \mathrm{H}
\rightarrow \mathrm{H}_2 + \mathrm{H}$ reaction, and we confirmed that $E_a$
was obtained accurately in the case of both the VQE and the ED. We also
obtained numerical results that the entanglement between the images accelerates
the path optimization. From these results, we show the feasibility of
performing fast and accurate chemical reaction calculations by using quantum
algorithms.
