  Excited states of molecules lie in the heart of photochemistry and chemical
reactions. The recent development in quantum computational chemistry leads to
inventions of a variety of algorithms that calculate the excited states of
molecules on near-term quantum computers, but they require more computational
burdens than the algorithms for calculating the ground states. In this study,
we propose a scheme of supervised quantum machine learning which predicts the
excited-state properties of molecules only from their ground state wavefunction
resulting in reducing the computational cost for calculating the excited
states. Our model is comprised of a quantum reservoir and a classical machine
learning unit which processes the measurement results of single-qubit Pauli
operators with the output state from the reservoir. The quantum reservoir
effectively transforms the single-qubit operators into complicated multi-qubit
ones which contain essential information of the system, so that the classical
machine learning unit may decode them appropriately. The number of runs for
quantum computers is saved by training only the classical machine learning
unit, and the whole model requires modest resources of quantum hardware that
may be implemented in current experiments. We illustrate the predictive ability
of our model by numerical simulations for small molecules with and without
noise inevitable in near-term quantum computers. The results show that our
scheme well reproduces the first and second excitation energies as well as the
transition dipole moment between the ground states and excited states only from
the ground state as an input. We expect our contribution will enhance the
applications of quantum computers in the study of quantum chemistry and quantum
materials.
