# We proposed a near-term quantum machine learning algorithm for computing the excited state properties of a molecule.

Kawai (intern) and Nakagawa from QunaSys Inc. proposed a near-term quantum machine learning algorithm for computing the excited state properties of a molecule, which are crucial for studies in quantum chemistry. The preprint of the paper is available on arXiv:

“Predicting excited states from ground state wavefunction by supervised quantum machine learning”

https://arxiv.org/abs/2002.12925

-> Published in Machine Learning: Science and Technology (29 October, 2020),

https://iopscience.iop.org/article/10.1088/2632-2153/aba183

**BACKGROUND**

Quantum computers with hundreds to thousands of quantum bits without fault-tolerance, so-called NISQ (Noisy Intermediate-Scale Quantum) devices are about to be realized. One of the applications of those near-term quantum devices is expected to be accurate computations of properties of molecules and solid-state materials in quantum chemistry and condensed-matter physics fields. In particular, variational quantum eigensolver (VQE) can compute the ground state and excited state energies of molecules and materials using the variational method.

**MOTIVATION**

Nevertheless, computing the properties of the excited states of molecules in studies of photochemistry and chemical reactions requires significantly larger computational cost compared with computations of ground state energy.

**METHODS & RESULTS**

Kawai (intern) and Nakagawa from QunaSys Inc. proposed a quantum machine learning algorithm to learn and predict the properties of the excited states of a molecular Hamiltonian from its ground state wavefunction. This algorithm processes a ground state wavefunction which is an output from another quantum algorithm computing a ground state (e.g. VQE) using a quantum circuit called a quantum reservoir and trains a classical machine learning unit from the measurement data of the output state from the reservoir. The reservoir converts a wavefunction, whose exact classical description necessitates exponentially-growing resources along with the system size, to classical data with linear growth requiring the realizable number of runs of the quantum circuit, so that the classical unit may learn them efficiently. In addition, in order to demonstrate the proposed scheme, we confirmed from numerical simulations that the algorithm can accurately predict the excitation energies and the transition dipole moment of small-scale molecules, even when inevitable noises of realistic NISQ devices are taken into consideration. For the simulations, we used a fast quantum circuit simulator called Qulacs.

**OUTLOOK**

This study showed the potential that our algorithm may compute the properties of the excited states of large-scale molecules and materials that cannot be simulated on a classical computer. We expect that it will significantly broaden the applications of the NISQ devices towards chemistry and material science.