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Variational Quantum Eigensolver (VQE) method is the way to derive the wavefunctions from their eigen energies using quantum computers. But, the methodsto utilize the superposition states between them haven't been developed yet.The method to calculate the off diagonal element of observables between twostates derived by VQE method requires large numbers of gate operations forNoisy Intermediate Scale Quantum (NISQ) devices. We proposed the novel methodto drive the superposition state between the states the derived by VQE method.We call it Frame superposition cluster (FSC) method. Using the method, weconfirmed that dipole transition moment could be calculated with the highestaccuracy compared to other methods.

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