Noisy Intermediate Scale Quantum (NISQ) devices are the current standard for executing quantum circuits. These devices are restricted by their limited qubit counts. This introduces a scalability issue when trying to execute larger quantum algorithms. Promising approaches like modular quantum computing architectures are currently being developed to solve the scalability, but they are still theoretical. So, in practice, multiple independent NISQ devices are utilized to solve the scalability issue. For this to be possible, the circuits must be cut, and each part must be placed on a different device called quantum circuit mapping. This process is not optimized yet. My thesis presents a solution approach that utilizes Quadratic Unconstrained Binary Optimization (QUBO) in order to optimize this process of placing the qubits of the circuits on multiple unrelated devices. The solution proved twice as useful for some types of inputs compared to the standard way of mapping currently utilized in practice while being less effective for other types of inputs.