Analysis of Multiscale Quantum Harmonic Oscillator Algorithm Based on a New Multimode Objective Function

The wavefunction is an important element of the multiscale quantum harmonic oscillator algorithm (MQHOA). To verify the physical model and the multimode optimization performance of the MQHOA for multimode optimization in this paper, we define a multidimensional harmonic-Gaussian potential function. When the wavefunction of the MQHOA for multimode optimization and the probability amplitude of an ammonia molecule are compared, the ground-state wavefunction can reflect the probability distribution of the two-state ammonia molecule. We obtain the extrema of the proposed function using the Hessian matrix and optimize the proposed function with the multimode algorithm. The experiments show that the multimode algorithm can determine the extrema of the proposed function with appropriate parameters. Changes in the proposed function barriers have little effect on the optimization ability of the multimode algorithm. The optimization ability of the multimode algorithm is determined by its own wavefunction.