Hybrid quantum-classical algorithms for solving quantum chemistry in Hamiltonian–wave-function space

The variational quantum eigensolver (VQE) typically optimizes parameters in a circuit to prepare eigenstates for system. Its application many problems may involve group of Hamiltonians, e.g., Hamiltonian molecule is function the nuclear configurations. In this paper we incorporate derivatives into VQE and develop some hybrid quantum-classical algorithms, which explore both wave-function spaces solving chemistry more efficiently. For geometry optimization, propose mutual gradient-descent algorithm that updates wave alternately, can give rapid convergence towards equilibrium structures molecules as demonstrated numerical simulations. Moreover, speed up calculation energy potential surface, establish differential equations govern how optimized change with intrinsic Hamiltonian. Our study suggests direction systems efficiently by considering function.