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arXiv:1610.03438 · International Journal of Circuit Theory and Applications

Introduction to quantum electromagnetic circuits

Uri Vool, Michel Devoret

Published Jun 5, 2017• 312 citations
arXivHTMLPDF

Abstract

Summary The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture notes, has three main parts. The first part describes how to construct a Hamiltonian for a general circuit, which can include dissipative elements. The second part describes the quantization of the circuit, with an emphasis on the quantum treatment of dissipation. The final part focuses on the Josephson nonlinear element and the main linear building blocks from which superconducting circuits are assembled. It also includes a brief review of the main types of superconducting artificial atoms, elementary multi‐level quantum systems made from basic circuit elements. Copyright © 2017 John Wiley & Sons, Ltd.

DOI
10.1002/cta.2359

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Summary The article is a short opinionated review of the quantum treatment of electromagnetic circuits, with no pretension to exhaustiveness. This review, which is an updated and modernized version of a previous set of Les Houches School lecture notes, has three main parts. The first part describes how to construct a Hamiltonian for a general circuit, which can include dissipative elements. The second part describes the quantization of the circuit, with an emphasis on the quantum treatment of dissipation. The final part focuses on the Josephson nonlinear element and the main linear building blocks from which superconducting circuits are assembled. It also includes a brief review of the main types of superconducting artificial atoms, elementary multi‐level quantum systems made from basic circuit elements. Copyright © 2017 John Wiley & Sons, Ltd.
The new and rapidly growing field of circuit QED offers extremely exciting prospects for learning about and exercising intimate control over quantum systems, providing flexible, engineerable design and strong nonlinearities and interactions in systems consisting of microwave radiation fields and fixed artificial "atoms". These notes aim to provide a non-expert introduction to the field of circuit QED, to give a basic appreciation of the promise and challenges of the field, along with a number of key concepts that will hopefully be useful for the reader who is new to the field and beginning to explore the research literature. They were written as a pedagogical text designed to complement a course delivered to third-year undergraduate students. After a introductory section which discusses why studying circuit QED might be worthwhile and interesting, I introduce the basic theory tools from quantum optics and quantum information which are needed to understand the key elements of circuit QED. I also provide a brief overview of superconductivity, focussing on the concepts which are most relevant to operation in the regimes of interest in circuit QED. I then describe the three main types of superconducting qubits, and finally give a basic introduction to decoherence and mixture and how they relate to quantum behaviour in electronic circuits.
Summary A new engineering discipline called ‘quantum technology’ is emerging. Nanotechnology and cryotechnology enable engineers to develop devices and integrated circuits in which quantum phenomena have dominant sway. Macroscopic finite‐state ‘artificial atoms’ are realized exploiting superconductive Josephson effect, and these ‘atoms’ exchange microwave photons in superconductive microwave circuits. The achievements of cavity quantum electrodynamics in quantum optics are mimicked in the microwave frequency range. The new technology is dubbed circuit quantum electrodynamics. This paper tries to call the attention of engineers majoring in circuit theory and design on the challenges they face in designing quantum circuits. Modeling and simulation of quantum circuit components are reviewed. Approximate closed quantum system models as well as more accurate open system models are introduced in the case of single quantum devices and composite quantum systems. The effects of amplitude damping and phase damping are illustrated by simulation. The role of classical resistors in quantum circuits is investigated. Special attention is given to the almost standardized technology developed for superconductive microwave quantum circuits. Open problems are identified that circuit designers face in developing computer‐aided‐design tools for quantum circuits. Copyright © 2017 John Wiley & Sons, Ltd.
Superconducting qubits are solid state electrical circuits fabricated using techniques borrowed from conventional integrated circuits. They are based on the Josephson tunnel junction, the only non-dissipative, strongly non-linear circuit element available at low temperature. In contrast to microscopic entities such as spins or atoms, they tend to be well coupled to other circuits, which make them appealling from the point of view of readout and gate implementation. Very recently, new designs of superconducting qubits based on multi-junction circuits have solved the problem of isolation from unwanted extrinsic electromagnetic perturbations. We discuss in this review how qubit decoherence is affected by the intrinsic noise of the junction and what can be done to improve it.
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.
In the last 25 years a new understanding has evolved of the role of information in quantum mechanics. At the same time there has been tremendous progress in atomic/optical physics and condensed matter physics, and particularly at the interface between these two formerly distinct fields, in developing experimental systems whose quantum states are long-lived and which can be engineered to perform quantum information processing tasks. These lecture notes will present a brief introduction to the basic theoretical concepts behind this `second quantum revolution.' These notes will also provide an introduction to `circuit QED.' In addition to being a novel test bed for non-linear quantum optics of microwave electrical circuits which use superconducting qubits as artificial atoms, circuit QED offers an architecture for constructing quantum information processors.
Abstract Superconductivity manifests macroscopic quantum phenomena. A superconducting circuit composed of Josephson junctions, Cooper pair boxes, and rf-/dc-SQUID, properly miniaturized, becomes quantized and demonstrates Rabi oscillations and entanglement. In this paper, we offer an overview of this approach. We begin with an introduction of the history and elementary theory of superconductivity. Then we describe the building blocks of superconducting classical circuits and derive their canonical quantizations. The set-up of qubits and superconducting quantum logic gates are then examined. Finally, ways to make measurements are discussed.