Accelerated spin-adapted ground-state preparation with nonvariational quantum algorithms

Abstract

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, nonvariational methods incorporate penalty terms into the original Hamiltonian to enforce the desired constraints. Such additional terms would require a quartic number of gates in terms of the number $n_{\text{spin}}$ of spins when naively implemented. To circumvent this computationally intensive scaling, this paper proposes a new nonvariational procedure to obtain the spin-adapted ground states that requires only quadratic scaling. The proposed method consists of two stages: the first stage is to prepare a spin-magnitude adapted state and the second stage is post-processing for the desired $S_z$. By separating into two stages, the procedure achieves the desired spin-adapted ground state while reducing the number of penalty terms from $O(n_{\text{spin}}^4)$ to $O(n_{\text{spin}}^2)$. 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.

arXiv comment13 pages, 8 figures; revised following peer review

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