  The project uses QuTiP, a quantum computing framework, to simulate
interactions between two-qubits coupled with each other via three resonators.
The main aim of this project is to build machinery of techniques to understand
complex qubit-cavity interactions using QuTiP's functionalities. The system
simulated mimics the one constructed by McKay et. al. (M15) and the results of
the simulations closely agree with M15's experimental results. The effect of
the coupling strength between the qubits and the cavities is studied. It was
observed that stronger couplings generated larger separations between the
eigen-modes. Studies involving resonance were used to construct the iSWAP gate,
a universal quantum logic gate. This study showed the importance of external
thermal losses due to cavity dissipation, and qubit decay and dephasing. The
Landau-Zener model was tested for the case of multiple crossing; the model
motivated the comparison of three scenarios where the 2 qubits were coupled via
1 cavity, 3 cavities, and 6 cavities. The study concluded that having multiple
modes, which is a consequence of having multiple cavities, is advantageous for
transferring energy from the qubit to the cavity. Finally, the ac-Stark shift
was measured in the system and its dynamics showed excellent agreement with the
experimental results obtained by M15.
