Quantum computers are being developed to solve certain problems faster than classical computers. Instead of using classical bits, they use quantum bits (qubits) that utilize quantum effects. At Chalmers University of Technology, researchers have already built a quantum chip consisting of two superconducting transmon qubits and are trying to build systems with more qubits. To assist in that process, they make numerical simulations of the quantum systems. However, these simulations face an intrinsic computational limitation: the Hilbert space of the system grows exponentially with the number of qubits. In order to mitigate the problem: the simulations should be made as efficient as possible, by applying certain approximations, while still obtaining accurate results. The aim of this project is to compare several of these approximations, to see how accurate they are and how fast they run on a classical computer. This is done by modelling the qubits as quantum anharmonic oscillators and testing several cases: varying the energy levels of the qubits, increasing the number of qubits, and testing the rotating-wave approximation (RWA). These cases were tested by implementing two-qubit gates on the system. The simulations were all made using the Python library QuTiP. The results show that one should simulate using at least one energy level higher than the maximum energy level required for the gate to function. For larger systems, the RWA will make a big difference in simulation times, while still giving relatively accurate results. When using the RWA, the number of levels used does not seem to affect the results significantly and one could therefore use the lowest possible energy levels that can simulate the system.