  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 (H). In PSHO, for
any reference state, the normalized energy of the sine Hamiltonian power state
can be determined. With the increase of the power, the initial reference state
can converge to the eigenstate with the largest absolute eigenvalue in the
coefficients of the expansion of reference state, and the normalized energy of
the sine Hamiltonian power state converges to Ei. The ground and excited state
energies of a Hamiltonian can be determined by taking different t 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.
