Classical versus quantum errors in quantum computation of dynamical systems

The stability of the quantum algorithm simulating the quantum dynamics of a system with different regimes, ranging from global chaos to integrability, was analyzed. The behavior of the fidelity of quantum motion was compared in different regimes when the system's parameters were perturbed or when there were unitary errors in the quantum gates implementing the quantum algorithms. It was observed that while the first kind of errors had a classical limit, the second one had no classical analog. It was presented that, whereas in the classical errors the decay of fidelity was very sensitive to the dynamical regime, in the quantum errors it was almost independent of the dynamical behavior of the simulated systems.