  Reflecting the increasing interest in quantum computing, the variational
quantum eigensolver (VQE) has attracted much attentions as a possible
application of near-term quantum computers. Although the VQE has often been
applied to quantum chemistry, high computational cost is required for reliable
results because infinitely many measurements are needed to obtain an accurate
expectation value and the expectation value is calculated many times to
minimize a cost function in the variational optimization procedure. Therefore,
it is necessary to reduce the computational cost of the VQE for a practical
task such as estimating the potential energy surfaces (PESs) with chemical
accuracy, which is of particular importance for the analysis of molecular
structures and chemical reaction dynamics. A hybrid quantum-classical neural
network has recently been proposed for surrogate modeling of the VQE [Xia $et\
al$, Entropy 22, 828 (2020)]. Using the model, the ground state energies of a
simple molecule such as H2 can be inferred accurately without the variational
optimization procedure. In this study, we have extended the model by using the
subspace-search variational quantum eigensolver procedure so that the PESs of
the both ground and excited state can be inferred with chemical accuracy. We
also demonstrate the effects of sampling noise on performance of the
pre-trained model by using IBM's QASM backend.
