Instituting Superconducting Qubits for Scientists and Engineers

In the last two decades, a spectacular development in the superconducting qubits has been accomplished experimentally as well as theoretically. The main reason for that is the realization that superconducting qubits can play a crucial role in the emergent field of quantum information processing and quantum computing. The interaction of superconducting qubits with the quantized electromagnetic field leads to make the circuit quantum electrodynamics, inspired by cavity quantum electrodynamics. The field of superconducting qubits and circuit QED is fast growing and branching to diverse applications in multidisciplinary fields. This makes it harder for first-time readers to follow-up. Therefore, this article is targeting to introduce in an intuitive way the topic of superconducting qubit and circuit QED by giving all the mathematical background, Lagrangian formalism for electric circuits, interaction Hamiltonian, and contextual physical interpretation essential to anew scientists and engineers planning to be specialized in this field as well as portraying a wide vantage for higher studies through the suggested recommendation resulted from the simulated examples and written code based on Python packages and Qiskit software. In this article, the superconducting qubits, transmon and fluxonium, are reviewed after introducing the abstract definition of a quantum bit. Moreover, light-matter interaction in fluxonium qubit and quantization of transmission line resonator are discussed briefly. Some of the simulated systems such as the energy levels of fluxonium as a function of offset flux are presented. Finally, applications of superconducting qubits in quantum computing and other fields such as quantum transistors, quantum machines and metamaterials are discussed. Index Terms Superconducting qubits, circuit QED, quantum logic gate, fluxonium, transmon.