This chapter delves into superconducting qubits, starting with the essentials of superconductivity and circuit design. Central to this discussion is the Josephson junction, a key element in creating superconducting qubits. The text focuses on the transmon, the archetype in this field, while acknowledging other designs. Initialization of the transmon involves sophisticated dilution refrigerators, a process that is also examined. Additionally, the principles of circuit quantum electrodynamics (QED) are introduced as the framework for qubit control and measurement. Attention is then given to noise sources and their effect on superconducting qubits, with insights that apply to various qubit systems. The chapter wraps up by highlighting the strengths and challenges of superconducting qubits for quantum computing.

Appendix K: this appendix is an introduction to another very active and promising domain of quantum physics, named circuit quantum electrodynamics (cQED), dealing with the quantum properties of macroscopic objects consisting of superconducting electrical circuits. In an LC circuit the energy is quantized, and charge and flux are two quantum canonical conjugate quantities that do not commute. Their quantum fluctuations are bound by a Heisenberg inequality. A Josephson junction inserted in the circuit introduces strong nonlinearities in the system, which breaks the equidistance between the energy levels and makes the circuit look like a qubit, called a transmon. Cooling at mK temperatures is necessary to have quantum effects dominate over thermal effects. The circuit is embedded in a resonant cavity, and the system bears many analogies with cavity QED and Jaynes–Cummings formalism for coupled photons and atoms. One can perform nondestructive read-out and control of the transmon, as well as phase-sensitive, quantum-limited amplification, with nonlinearities that are much stronger than the ones used in quantum optics.