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, which is called circuit quantum electrodynamics or circuit-QED. The goal of the theory is 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 comprehensive, theoretically oriented, overview of this subject for Master or PhD students in physics and electrical engineering.

Authors 3

1. Alessandro Ciani

   Forschungszentrum Jülich · QuTech · Delft University of Technology

   Affiliation as printed

   Institute for Quantum Computing Analytics, Peter Grünberg Institute, Forschungszentrum Jülich, Germany

   Department of Applied Mathematics, Faculty EEMCS, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands

   QuTech, Lorentzweg 1, 2628 CJ Delft, The Netherlands

2. David Peter Divincenzo

   Forschungszentrum Jülich · QuTech · Delft University of Technology

   Affiliation as printed

   Institute for Theoretical Nanoelectronics, Peter Grünberg Institute, Forschungszentrum Jülich, Germany

   Department of Applied Mathematics, Faculty EEMCS, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands

   QuTech, Lorentzweg 1, 2628 CJ Delft, The Netherlands

3. Barbara M. Terhal Aachen

   RWTH Aachen University · Forschungszentrum Jülich · Jülich Aachen Research Alliance · QuTech · Delft University of Technology

   Affiliation as printed

   Delft Institute of Applied Mathematics, Faculty of Electrical Engineering, Mathematics and Computer Science, Delft University of Technology | QuTech, The Netherlands

   Delft University of Technology (2020

   Institute: Institute for Quantum Computing Analytics (PGI-12), Forschungszentrum Jülich, 52425 Jülich, Germany

   Institute: Theoretical Nanoelectronics (PGI-2), Forschungszentrum Jülich, 52425 Jülich, Ger-many • JARA Institute for Quantum Information,

   RWTH Aachen University, 52074 Aachen, Germany