Lecture Notes on Quantum Electrical Circuits

Alessandro Ciani; David P. DiVincenzo; Barbara M. Terhal

doi:10.59490/tb.85

Lecture Notes on Quantum Electrical Circuits

Authors

Alessandro Ciani

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

https://orcid.org/0000-0002-8707-0532

David P. DiVincenzo

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

https://orcid.org/0000-0003-4332-645X

Barbara M. Terhal

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

https://orcid.org/0000-0003-0218-6614

DOI: https://doi.org/10.59490/tb.85

Keywords: superconducting electrical circuits, circuit-QED , quantum computing, Josephson junction, quantum information

Synopsis

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.

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Author Biographies

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

Alessandro Ciani is a postdoctoral scholar at Forschungszentrum Jülich. He received his PhD in 2019 from RWTH Aachen University. After two years spent at QuTech, TU Delft, he came back to Germany in 2021. His research focuses on superconducting qubits and on fundamental aspects of quantum computing and error correction.

David P. DiVincenzo, Institute for Theoretical Nanoelectronics, Peter Grünberg Institute, Forschungszentrum Jülich, Germany

David DiVincenzo is a research director at Forschungszentrum Jülich, professor of physics at RWTH Aachen University, and a part-time affiliate of QuTech, TU Delft. He received his PhD from the University of Pennsylvania and came to Germany after 25 years on the staff of the IBM Research Division in New York. He is a fellow of the APS and a member of the National Academy of Sciences of the US. His research interests focus on the physical implementation of high-quality solid-state qubits for quantum computing.

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

Barbara Terhal is a professor in the Department of Applied Mathematics, Faculty EEMCS at TU Delft and an affiliate of QuTech, TU Delft. She received her PhD from the University of Amsterdam (1999) and worked at IBM Research in New York from 2000 till 2010, and as professor of physics at RWTH Aachen from 2010 till 2017. She is a fellow of the APS and a member of the Royal Netherlands Academy of Arts and Sciences. Her research interests are in quantum error correction, in particular for superconducting qubits, and in understanding the computational and conceptual novelty of quantum information.