Treating nodes and singularities in quantum simulation of electronic structure: A sampling technique using multiple time steps

Quantum simulation of the electronic structure of atoms and molecules provides a rigorous upper bound to the true ground-state energy in these systems. Two approximations that are normally invoked, the short-time approximation for the Green’s function and the fixed-node approximation for the true ground-state wave function, are investigated. It is found that certain approximations to the short-time Green’s function introduce significant errors in the wave function near the nodes and Coulomb singularities. These errors can cause the rigorous upper bound to be violated. Introducing a multiple-time-step method we will show how this can be treated properly.