Optimized meta-VQE Algorithm for Better Trend Learning of Ground State Energy

Using variational quantum eigensolver (VQE) algorithm to realize ground state energy calculation on noisy intermediate-scale quantum (NISQ) devices is widely applied in quantum physics, quantum chemistry, and other fields. It can simulate chemical molecules to solve the energy solution required by chemical reactions. This paper proposes an optimized cost function for the original meta-VQE and combines it with the quantum architecture search algorithm to break the limitation of the fixed structure. To expand the penalty degree of error and obtain more accurate results, two indicators are added to the original cost function including the slope error of discrete predicted value and accurate value as well as the error of the first value. The results show that the optimized algorithm can learn more characteristics of the ground state energy changing trend in the noise channel, and obtain a more accurate estimate of equilibrium bond length.