Mitarai, Nakagawa of QunaSys Inc., and our advisor, Dr. Mizukami, published a paper (preprint) that proposed an algorithm to calculate molecular energy derivatives analytically on a quantum computer.

Theory of analytical energy derivatives for the variational quantum eigensolver

https://arxiv.org/abs/1905.04054

## Background

The development of noisy quantum computers, called Noisy Intermediate-Scale Quantum (NISQ) devices, is flourishing.NISQ devices are expected to be used in the fields of quantum chemistry and machine learning and are expected to be able to perform high-precision, large-scale calculations that conventional classical computers could not do.

In quantum chemistry calculations, the quantities obtained by differentiating the energy value of a molecule by some parameter ("energy derivative") is a very important amount. For example, you can find the most stable structure of a molecule by finding the energy derivatives of the bonding distance and angle of a molecule. In addition, energy derivatives are quantities that appear in most parts of quantum chemical calculations, such as a search for chemical reaction pathways and calculation of NMR spectra.

## Previous Problems

So far, when calculating energy derivatives of a molecule using a quantum computer, the only method used was taking numerical difference at two close points. However, NISQ devices have noise at the output, and it is extremely difficult to take accurate differences. Therefore, the calculation of energy derivatives has been a major obstacle in using quantum computers for quantum chemical calculations.

## Our Method and Result

Mitarai and Nakagawa of QunaSys Inc., and our advisor, Dr. Mizukami, proposed an algorithm for analytical calculation of molecular energy derivatives on a quantum computer. In this algorithm, the formula for obtaining the energy derivatives known in theoretical quantum chemistry was combined with the variational quantum eigensolver (VQE), which is a quantum algorithm using a NISQ device. Specifically, the analytical derivative can be calculated by measuring new inserted quantum gates before and after the rotating gate of the quantum circuit used to VQE calculation. We also show that this method can be applied not only to the derivatives of the ground state energy but also to the derivatives of the excited state energy which is more difficult to calculate with conventional classical computers.

## Future Prospects

The energy derivatives is a quantity that is widely used in the calculation of the properties of molecules and materials, and the proposed algorithm is an important step toward practical application to quantum chemical calculations in quantum computers. Based on this algorithm, various quantum chemical calculation methods are expected to be implemented on the quantum computer, and the power of the quantum computing will be demonstrated.