Quantum computers have been shown to have tremendous potential in solving difficult problems in quantum chemistry. In this paper, we propose a new classical-quantum hybrid method, named as power of sine Hamiltonian operator (PSHO), to evaluate the eigenvalues of a given Hamiltonian (Ĥ). In PSHO, for any reference state $|{\phi }_0⟩$, the normalized energy of the ${\sin }^n(\hat{H}\tau )|{\phi }_0⟩$ state can be determined. With the increase of the power, the initial reference state can converge to the eigenstate with the largest $|\sin (E_i\tau )|$ value in the coefficients of the expansion of $|{\phi }_0⟩$, and the normalized energy of the ${\sin }^n(\hat{H}\tau )|{\phi }_0⟩$ state converges to E_i. The ground- and excited-state energies of a Hamiltonian can be determined by taking different τ values. The performance of the PSHO method is demonstrated by numerical calculations of the H₄ and LiH molecules. Compared with the current popular variational quantum eigensolver method, PSHO does not need to design the ansatz circuits and avoids the complex nonlinear optimization problems. PSHO has great application potential in near-term quantum devices.

中文翻译：

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正弦哈密顿算子在量子计算机上估计本征态能量的能力

量子计算机已被证明在解决量子化学中的难题方面具有巨大的潜力。在本文中，我们提出了一种新的经典-量子混合方法，称为正弦哈密顿量算子 (PSHO) 的幂，用于评估给定哈密顿量 ( Ĥ ) 的特征值。在 PSHO 中，对于任何参考状态$|{\phi }_0⟩$, 的归一化能量${罪}^n(\hat{H}\tau )|{\phi }_0⟩$状态可以确定。随着功率的增加，初始参考态可以收敛到最大的本征态$|罪({乙}_{\mathrm{一世}}\tau )|$膨胀系数中的值$|{\phi }_0⟩$，以及归一化的能量${罪}^n(\hat{H}\tau )|{\phi }_0⟩$状态收敛于E _i。哈密​​顿量的基态和激发态能量可以通过采用不同的 τ 值来确定。PSHO 方法的性能通过 H ₄和 LiH 分子的数值计算得到证明。与目前流行的变分量子本征求解方法相比，PSHO不需要设计拟态电路，避免了复杂的非线性优化问题。PSHO 在近期的量子器件中具有巨大的应用潜力。