One of the main interests of quantum physics in this new millennium is the exploitation of quantum mechanical principles in technical applications.<br />One approach here is to use entanglement and superpositions of states to realize powerful algorithms capable of solving challenging computational tasks on a much faster time scale than a classical computer ever could. To find the quantum analogue of a classical bit one needs a quantum mechanical two level system that can be used to store and process quantum information. Most of the current approaches to find such a "qubit" have the intention to find a single system that is able to fulfill all desirable tasks. But actually most quantum systems are only favorable for very specific tasks (e.g storage, processing, data exchange,..), similar as it is in classical computing. For some qubits the main disadvantages is that their quantum state is very fragile. Those systems loose their "quantum information" (that is the possibility to store superpositions of their states coherently) easily. They "decohere" on a timescale that is much shorter then any more involving algorithm. Other systems can keep those superposition states for quite a while, but are so difficult to address that the number of operations that can be made is very limited. The task of a so called hybrid quantum system is now to combine the strengths of these different systems, using e.g.<br />one for manipulation and an other system for storage. Similar to a processor/memory architecture in conventional computers these systems could use a kind of bus system to couple between them.<br />The main task of this thesis was to make steps towards the realization of such a system using two different combinations of quantum systems. Both are planned to use superconducting qubits (transmons) as processor qubit and either atoms (ultra cold rubidium 87 ensembles) or solid state spin systems (Nitrogen Vacancies in diamonds - NV centers) as memory.