We discuss an extension of the Massively Parallel Quantum Computer Simulator by a gate level error model which covers operational errors and decoherence. Applying this error model to the Quantum Fourier Transformation (the kernel of Shor's algorithm) and Grover's quantum search algorithm, one finds that the QFT circuit is more robust to operational inaccuracies than Grover's algorithm on comparable scales. Critical parameters can be derived which give a first estimate of tolerable error thresholds. At present ion traps are regarded as the most promising technology for the realization of quantum computers due to the long coherence time of trapped ions. We discuss Hamiltonian based dynamical ion-trap simulations which have been developed in collaboration with the experimental working group of Prof. Rainer Blatt. In contrast to standard approaches no approximations like the rotating wave approximation or an expansion in the Lamb-Dicke parameter are required which allow for very accurate simulations. This permits to identify critical system parameters which limit the stability of the experiment.