Analysis of nonlinear dynamics in a classical transmon circuit

Abstract

The focus of this thesis is on classical dynamics of a transmon qubit. First, we introduce the basic concepts of the classical circuit analysis and use this knowledge to derive the Lagrangians and Hamiltonians of an LC circuit, a Cooper-pair box, and ultimately we derive Hamiltonian for a transmon qubit. The transmon Hamiltonian is used to derive the equations of motion and also the meaning of these equations is discussed. Finally, the thesis is ended with some numerical results for the transmon equations of motion with a brief interpretation included.