New implementations for parallel processing applications using reversible systolic networks and the corresponding nano and field-emission controlled-switching components is introduced. The extensions of implementations to many-valued field-emission systolic networks using the introduced reversible systolic architectures are also presented. The developed implementations are performed in the reversible domain to perform the required parallel computing. The introduced systolic systems utilize recent findings in field emission and nano applications to implement the function of the basic reversible systolic network using nano controlled-switching. This includes many-valued systolic computing via carbon nanotubes and carbon field-emission techniques. The presented realization of reversible circuits can be important for several reasons including the reduction of power consumption, which is an important specification for the system design in several future and emerging technologies, and also achieving high performance realizations. The introduced implementations for non-classical systolic computation are new and interesting for the design within modern technologies that require optimal design specifications of high speed, minimum power and minimum size, which includes applications in adiabatic low-power signal processing.