Two-qubit operations on the Transmon qubit
We have seen that introducing a flux changes the difference in the energy levels of the system. This is used in order to couple different qubits, allowing for example the realisation of a c-phase gate. Do you think this gate is enough or should other 2-qubit gates be implemented as well? Why do you think people have implemented a c-phase gate instead of others?
Having a c-phase and a Hadamard allows you to have a c-not gate as well, meaning you have a universal set of gates.
The main reason to have a c-phase gate and not other ones is due to the difficulties in the physical implementation.