Development of symmetry-preserving variational quantum algorithms for solving many-body problems

Abstract

This work focuses on developing efficient quantum algorithms for solving many-body quantum problems by implementing variational quantum eigensolver (VQE) associated with shallow quantum circuits without optimization issues such as Barren plateaus. This research aims to overcome the disadvantages of hardware-efficient ansatz (HEA) through a novel approach that would incorporate circuit optimization methods together with symmetry-preserving techniques. We propose to modify the standard VQE algorithm to compute materials, molecules, and electronic structures on a quantum computing simulator. The decomposition of the diagonalization of the Hamiltonian into block-diagonalized form with Householder transformation allows the define symmetry-preserving cost functions and to setup iterative processes. The resulting circuits become shallower, and optimization is simplified. Numerical results show in detail the effectiveness of this solver by showing shallower circuits and achieving higher performances compared to the standard VQE approaches. We implement and test the algorithm for the ground-state properties of H2, LiH, HeH+, H− 3 and H4. We compared various variational approaches to the fidelity of the results with full configuration interaction (FCI) and showed that the method introduced here can surpass the standard VQE in both accuracy and efficiency. These advancements offer a promising path for achieving practical quantum simulations on near-term quantum devices.