An Introduction to Superconducting Qubits and Circuit Quantum Electrodynamics

TL;DR

This paper reviews the fundamental concepts of superconducting qubits and circuit quantum electrodynamics, focusing on their theoretical foundations and relevance to axion detection experiments.

Contribution

It provides a clear overview of the classical and quantum descriptions of superconducting circuits, including black box quantization methods, tailored for the Axion Dark Matter Experiment community.

Findings

Discussion of classical Lagrangians and Hamiltonians for LC circuits

Explanation of black box circuit quantization techniques

Application to weakly anharmonic qubits coupled to resonators

Abstract

A subset of the concepts of circuit quantum electrodynamics are reviewed as a reference to the Axion Dark Matter Experiment (ADMX) community as part of the proceedings of the 2nd Workshop on Microwave Cavities and Detectors for Axion Research. The classical Lagrangians and Hamiltonians for an LC circuit are discussed along with black box circuit quantization methods for a weakly anharmonic qubit coupled to a resonator or cavity.