2025/06/05 by Kobori, Takumi, Kosugi, Taichi, Nishi, Hirofumi +2
#FOS: Physical sciences #Quantum Physics (quant-ph)
paper · doi:10.48550/arxiv.2506.04663
Various methods have been explored to prepare the spin-adapted ground state, the lowest energy state within the Hilbert space constrained by externally specified values of the total spin magnitude and the spin-z component. In such problem settings, variational and non-variational methods commonly incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. While in variational approaches, only O(n_\textrmspin2) measurements are required for the calculation of the penalty terms for the total spin magnitude, non-variational approaches, such as probabilistic imaginary-time evolution or adiabatic time evolution, are expected to be more computationally intensive, requiring O(n_\textrmspin4) gates naively. This paper proposes a new procedure based on non-variational quantum algorithms to obtain the spin-adapted ground state. The proposed method consists of two steps: the first step is to prepare a spin-magnitude adapted state and the second step is post-processing for the desired Sz. By separating into two steps, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from O(n_\textrmspin4) to O(n_\textrmspin2). We conducted numerical experiments for spin-1/2 Heisenberg ring models and manganese trimer systems. The results confirmed the effectiveness of our method, demonstrating a significant reduction in gate complexity and validating its practical usefulness.