Lecture Notes on Quantum Electrical Circuits

Abstract

During the last 30 years, stimulated by the quest to build superconducting quantum processors, a theory of quantum electrical circuits has emerged, and this theory goes under the name of circuit quantum electrodynamics or circuit-QED. The theory aims to provide a quantum description of the most relevant degrees of freedom. The central objects to be derived and studied are the Lagrangian and the Hamiltonian governing these degrees of freedom. Central concepts in classical network theory such as impedance and scattering matrices can be used to obtain the Hamiltonian and Lagrangian description for the lossless (linear) part of the circuits. Methods of analysis, both classical and quantum, can also be developed for nonreciprocal circuits. These lecture notes aim at giving a pedagogical, theoretically oriented overview of this subject for Master or PhD students in physics and electrical engineering.