  Operator spreading has profound implications in diverse fields ranging from
statistical mechanics and blackhole physics to quantum information. The usual
way to quantify it is through out-of-time-order correlators (OTOCs), which are
the quantum analog to Lyapunov exponents in classical chaotic dynamics. In this
work we explore the phenomenon of operator spreading in quantum simulation of
electronic structure in quantum computers. To substantiate our results, we
focus on a hydrogen chain $H_4$ and demonstrate that operator spreading is
enhanced when the chain is far from its equilibrium geometry. We also
investigate the dynamics of bipartite entanglement and its dependence on the
partition's size. Our findings reveal distinctive signatures closely resembling
area- and volume-laws in equilibrium and far-from-equilibrium geometries,
respectively. Our results provide insight of operator spreading of coherent
errors in quantum simulation of electronic structure and can be experimentally
implemented in various platforms available today.
