Mesoscopic Physics meets Quantum Engineering

Sergey N Shevchenko

• Publisher: WSPC
• Year: 2019
• ISBN:
  9789811201417
• Topic: Scienze fisiche
• Subtopic: Teoria quantistica

Quantum mechanics was initially constructed to describe objects on atomic and subatomic scales. However, in the last decades, quantum mechanics has been revisited and its use extended to the study and description of macroscopic distinct states. This is accomplished by modeling basic objects of mesoscopic physics, such as superconducting quantum circuits and low-dimensional structures derived from a two-dimensional electronic gas. In recent years, these devices support the study of fundamental systems such as a two-level quantum system, or qubit, as an object for manipulations and applications. This book will provide an introduction to quantum computation and quantum information, based on quantum physics, solid-state theory, and theory of computing. We will become familiar with this important field and explore how it is inseparably linked to basic notions of physics such as superposition, entanglement, and quantum dynamics. Then we will consider superconducting and mesoscopic systems, as well as a series of phenomena, where important are the spectra quantization, interference, and charge discreteness.

This book derives its content from a lecture course designed for graduate students and postdocs who are acquainted with quantum mechanics and statistical physics. In particular, it was developed together with the lecture series taught to 5th year students of the Department of Physics and Technology in V N Karazin Kharkiv National University.

Contents:

• Quantum Engineering
• Superposition, Entanglement, and Quantum Computation
• Quantum Mechanics of Qubits
• Superconducting Quantum Circuits
• Normal Quantum Circuits
• Circuit Quantum Electrodynamics
• Conclusion
• Bibliography
• Index

Readership: Graduate students and researchers in the field.Quantum Engineering;Quantum Dynamical Effects;Two-Level System;Qubit;Superconducting Qubits;Quantum Dots;Quantum Wires;Landau-Zener-Stuckelberg-Majorana Interference;Josephson Effect;Rabi Oscillations;Multi-Photon Excitations;Circuit QED0 Key Features:

• Adapted for delivering lectures: this contains relatively simple derivations and schemes prepared for easy reproducing on the blackboard. The presentation is self-sufficient and does not require any other source. Book contains elements which supplement standard courses like Quantum Mechanics and Statistical Physics
• Covers several modern subfields, such as Quantum Dynamics, Superconducting and Semiconducting Qubits, Low-Dimensional Structures, Circuit Quantum Electrodynamics, with which every modern student in Physics should be familiarized
• The introductory material is useful for professionals as well, since it presents concise and important features in the emergent field of quantum engineering

Chapter 1

SUPERPOSITION, ENTANGLEMENT, AND QUANTUM COMPUTATION

“One of the goals of quantum computation and quantum information is to develop tools which sharpen our intuition about quantum mechanics, and make its predictions more transparent to human minds.”

[Nielsen and Chuang 2010]

The last three decades bore witness to the emergence of the new research field, Quantum Computations (also known as Quantum Information). Quantum Computations assumes the study of problems related to the processing and transfer of information using the laws and objects of quantum mechanics. The theory of quantum information appeared at the intersection of earlier fields such as information theory, computer sciences, and quantum mechanics. The formalism and methodology of quantum optics, condensed matter theory, and cryptography are also incorporated.

As we will discuss below in more detail, the long-standing goal of the theory of quantum computations is the development of a quantum computer.⁵ The realizations of the quantum search algorithm, quantum cryptography, and quantum simulators are intermediate-scale problems researchers are considering.⁶

On the other hand, tasks and problems formulated by quantum computation theory stimulate the development and broadening understanding of quantum physics laws. It is this last thesis of quantum information theory that is the locomotive of the present lecture course. In this chapter we will give an introduction to quantum information theory, and, using the language of this theory, show how the basic notions of quantum mechanics can be described.

1.1.Quantum computers

Even though different aspects of quantum information theory are present in quantum physics from its very foundation, it is common to consider the R. Feynman talk at the conference some 35 years ago to be the beginning (see Footnote 4 on page 3; note that the idea of quantum computations was proposed by Yu. Manin in 1980⁷). In that speech, Feynman discussed principal difficulties with simulating quantum-mechanical systems with a usual (classical) computer. For that, he proposed to construct principally new computers, based on the laws of quantum mechanics. This thesis was later strictly grounded and developed. Maybe, it will be this very application — the simulation of quantum systems — that will become an important realization of quantum computations (see Footnote 6 on page 7).

Another reason leading to the search for new principles of calculations, is the shift in size of manufacturing elements of classical computers to nanometer scales, where the laws of quantum mechanics are relevant. Impressively, the development of computer technology during the last fifty years obeyed Moore’s law with high accuracy. This law predicted the doubling of computation power for the same price every two years. To date, the progress was mainly due to miniaturization of the elements. And now, when the characteristic scales have shrunk down to the order of a few nanometers, quantum phenomena must inevitably be taken into account. However, quantum interference and fluctuations are ruinous for the operation principles of a classical computer. Thus the necessity in searching for new models of informatization arises, and so the paradigm of a quantum computer appeared. Despite the existing series of problems of principle, many specialists believe that a quantum computer ...

Table of contents

• Cover Page
• Title Page
• Copyright Page
• Abstract
• Contents
• 0. Quantum Engineering
• 1. Superposition, Entanglement, and Quantum Computation
• 2. Quantum Mechanics of Qubits
• 3. Superconducting Quantum Circuits
• 4. Normal Quantum Circuits
• 5. Circuit Quantum Electrodynamics
• Bibliography
• Index