The superconducting circuit companion -- an introduction with worked examples

TL;DR

This tutorial provides an accessible introduction to superconducting qubit circuit analysis, including coupling, control, noise effects, and higher-dimensional systems, with practical examples for new researchers.

Contribution

It offers a comprehensive, step-by-step guide to quantum circuit analysis for superconducting qubits, including worked examples and methods for multiqubit systems.

Findings

Basic circuit analysis methods for superconducting qubits

Techniques for modeling qubit couplings and gates

Analysis of noise effects in superconducting circuits

Abstract

This tutorial aims at giving an introductory treatment of the circuit analysis of superconducting qubits, i.e., two-level systems in superconducting circuits. It also touches upon couplings between such qubits and how microwave driving and these couplings can be used for single- and two-qubit gates, as well as how to include noise when calculating the dynamics of the system. We also discuss higher-dimensional superconducting qudits. The tutorial is intended for new researchers with limited or no experience with the field but should be accessible to anyone with a bachelor's degree in physics. The tutorial introduces the basic methods used in quantum circuit analysis, starting from a circuit diagram and ending with a quantized Hamiltonian, that may be truncated to the lowest levels. We provide examples of all the basic techniques throughout the discussion, while in the last part of the tutorial we discuss several of the most commonly used circuits for quantum-information applications. This includes both worked examples of single qubits and examples of how to analyze the coupling methods that allow multiqubit operations. In several detailed appendices, we provide the interested reader with an introduction to more advanced techniques for handling larger circuit designs.