An Analytic Approach of the Time Propagator near Nodes in the Quantum Simulation of Electronic Ground States Using One-Dimensional System

Quantum simulation of the electronic structure of the atoms and molecules provides a rigorous upper bound to the true ground states energy in these systems. Short time approximation for the Green's function is investigated. It is found that certain approximations to the short time Green's function introduce significant errors in the wavefunction near the nodes. These errors can cause the rigorous upper bound to be violated. We will introduce exactly solvable one-dimensional system and explicitly show how the ground state energy is affected by the approximations.