Transmon as an Anharmonic Oscillator

This lecture explores the concept of a transmon as an anharmonic oscillator, discussing the Lagrangian, Hamiltonian, and quantization process. It delves into the conditions for the transmon to behave as a qubit, the role of the drive in the rotating frame, and the implementation of one-qubit gates. The lecture also covers the energy levels, the two-level approximation, and the requirements for high-fidelity single qubit operations in quantum computing. Various coupling strategies for entanglement between qubits are presented, including fixed coupling and tunable coupling methods. The lecture concludes with a detailed explanation of how to couple transmon qubits using direct capacitive coupling.