VQE Algorithm in Quantum Chemistry
Xiangjun Tan · Highlights in Science Engineering and Technology · 2022
For a complex quantum system, the dimensionality of the Hamiltonian grows exponentially with the size of the system, making it difficult to perform fast large-scale simulations and calculations on a classical computer. The first Variational Quantum Eigenvalue solver (VQE) proposed by Peruzzo et al. This gives the possibility of highly accurate molecular simulations and calculations in the field of quantum chemical computing. VQE is roughly based on the principle of using a quantum computer and set up a trial wave function |ψ(θ)⟩=U(θ)|ψ0⟩ to measure the energy expectation of the wave function |ψ(θ)⟩ at the corresponding initialization parameter, and then using a classical optimization algorithm to iterate θ0→θn over the energy to minimum until convergence. The significance of this paper is to verify the accuracy as well as the feasibility of the VQE algorithm for the calculation of LiH molecules in STO-3g basis, and to perform an error analysis and to verify the exponential acceleration of the classical algorithm implementation. These results shed light on guiding further exploration focusing on quantum computingt.