Frame Superposition Cluster: The method to derive the transition matrices in high accuracy

Abstract

Variational Quantum Eigensolver (VQE) method is the way to derive the wave functions from their eigenenergies using quantum computers. But, the methods to utilize the superposition states between them haven't been developed yet. The method to calculate the off-diagonal element of observables between two states derived by VQE method requires large numbers of gate operations for Noisy-Intermediate-Scale-Quantum (NISQ) devices. We propose the novel method to derive the superposition state between the states derived by VQE method. We call it Frame Superposition Cluster (FSC) method. Using the method, we confirmed that dipole transition moment could be calculated with the highest accuracy compared to other methods.