  An impossibility theorem on approximately simulating quantum non-integrable
Hamiltonian systems is presented here. This result shows that there is a
trade-off between the unitary property and the energy expectation conservation
law in time-descretization of quantum non-integrable systems, whose classical
counterpart is Ge-Marsden's impossibility result about simulating classically
non-integrable Hamiltonian systems using integration schemes preserving
symplectic (Lie-Poisson) property.
