Realistic lower bounds for the factorization time of large numbers on a quantum computer

We investigate the time T a quantum computer requires to factorize a given number dependent on the number of bits L required to represent this number. We stress the fact that in most cases one has to take into account that the execution time of a single quantum gate is related to the decoherence time of the qubits that are involved in the computation. Although exhibited here only for special systems, this inter-dependence of decoherence and computation time seems to be a restriction in many current models for quantum computers and leads to the result that the computation time T scales much stronger with L than previously expected.