Tutorial: Introduction to Quantum Circuits and Technologies

We introduce the fundamentals of quantum theory as applied to lumped element circuits and simple microwave systems assuming no prior knowledge in quantum mechanics. We will consider the Lagrangian and Hamiltonian analysis of these systems, and their corresponding canonical quantization. A short discussion of how these basic principles can be used to understand the operation of superconducting quantum computers will then be covered. These fundamental principles will be built on in the other talks in the workshop to look at a variety of modern problems in quantum circuits, methods, and algorithms as applied to microwave engineering.