Quantum computing is a promising paradigm to solve certain computational problems that are intractable for classical computers. Quantum computers manipulate bits of quantum information called qubits. Their development has gained momentum in recent years. Cloud providers offered the first quantum computers for commercial use via the cloud and continue to expand their quantum computing service offerings. Classical computing in the cloud uses virtualization to abstract from the physical computing resources to virtual resources. It enables resource sharing among multiple clients and dynamic allocation of resources to clients and applications. To this end, physical resources can be aggregated and partitioned to create customized virtual resources. In contrast, the logical execution of a quantum circuit that illustrates the computation is still tightly bound to the physical quantum device. Cloud users need to select a suitable physical quantum computer for their computations. If the calculation requires more qubits than the quantum computer has, the device cannot execute it. Otherwise, the execution of the quantum circuit blocks the entire quantum machine regardless of the qubit capacity used. This work develops a virtualization concept for quantum computing to separate the logical quantum computation from the underlying hardware. Aggregation and partitioning of quantum circuits decouple the one-to-one relationship between the computation of a quantum circuit and the execution hardware. The goal is to automate the mapping between the quantum circuits and appropriate physical quantum execution resources, including their aggregation and partitioning. The concept is implemented in a prototype and evaluated with modern quantum computers.