Power of Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers

• URL: http://arxiv.org/abs/2209.14801v2
• Date: Thu, 10 Nov 2022 04:02:24 GMT
• Title: Power of Sine Hamiltonian Operator for Estimating the Eigenstate Energies on Quantum Computers
• Authors: Qingxing Xie, Yi Song and Yan Zhao
• Abstract summary: We propose a new classical quantum hybrid method, named as power of sine Hamiltonian operator (PSHO) In PSHO, for any reference state, the normalized energy of the sine Hamiltonian power state can be determined. The performance of the PSHO method is demonstrated by numerical calculations of the H4 and LiH molecules.
• Score: 4.814804579035369
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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