Two loop corrections for single top quark production

Single-top-quark production enables us to study the nature of the weak interaction and to measure directly the Cabibbo-Kobayashi-Maskawa matrix element Vtb. For a detailed analysis of this process, precise theoretical predictions are required. The results available in the literature include the leading-order QCD corrections which are found to be small. Since in leading-order QCD no color exchange between the two incoming quarks is allowed, one can expect that higher-order QCD corrections may give a significant contribution. It is thus important to take these corrections into account. One important ingredient to extend the accuracy of the available predictions are the two-loop amplitudes. In this talk we discuss the methods used to assess the two-loop corrections and show first results for specific color configuration.