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

TL;DR

The paper introduces PSHO, a new classical-quantum hybrid method for estimating eigenstate energies on quantum computers, which converges to eigenvalues without complex optimization.

Contribution

It proposes the power of sine Hamiltonian operator (PSHO), a novel approach that avoids ansatz circuit design and nonlinear optimization in quantum eigenvalue estimation.

Findings

Successfully applied to H4 and LiH molecules

Converges to eigenvalues with increasing power

Avoids complex variational optimization

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.