Five Experimental Tests on the 5-Qubit IBM Quantum Computer

The 5-qubit quantum computer prototypes that IBM has given open access to on the cloud allow the implementation of real experiments on a quantum processor. We present the results obtained in five experimental tests performed on these computers: dense coding, quantum Fourier transforms, Bell's inequality, Mermin's inequalities (up to $n=5$) and the construction of the prime state $|p_3\rangle$. These results serve to assess the functioning of the IBM 5Q chips.