  Carriers such as electrons and holes inside the Brillouin zone of complex
semiconducting materials can form bound states (excitons, biexcitons etc.). For
obtaining the corresponding eigenstates (e.g. through Wannier or Bethe Salpeter
equation) and dynamics (e.g. cluster expansion) the number of involved
electrons and holes as well as the accuracy is limited by the appearing high
dimensional tensors (i.e. wavefunctions or correlations). These tensors can be
efficiently represented and manipulated via tensor network methods. We show how
tensor networks formulated via classic logic gates can be used to treat
electron-hole complexes inside the Brillouin zone. The method is illustrated
for the exciton and biexciton states of a single layer transition metal
dichalcogenide MoS$_2$ like model system.
