An Introduction to Quantum Computing

Quantum Computation and Quantum Information

Contents xi 4.3 Controlled operations 177 4.4 Measurement 185 4.5 Universal quantum gates 188 4.5.1 Two-level unitary gates are universal 189 4.5.2 Single qubit and CNOTgates are universal 191 4.5.3 A discrete set of universal operations 194

A Gentle Introduction Eleanor Rieffel and Wolfgang Polak

2.1 The Quantum Mechanics of Photon Polarization 9 2.1.1 A Simple Experiment 10 2.1.2 A Quantum Explanation 11 2.2 Single Quantum Bits 13 2.3 Single-Qubit Measurement 16 2.4 A Quantum Key Distribution Protocol 18 2.5 The State Space of a Single-Qubit System 21 2.5.1 Relative Phases versus Global Phases 21

Quantum Mechanics - University of Texas at Austin

of quantum mechanics. After a brief review of probability theory, in Chapter 2, we shall start, in Chapter 3, by examining how many of the central ideas of quantum mechanics are a direct consequence of wave-particle duality—i.e., the concept that waves sometimes act as particles, and particles as waves.

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Quantum Computation and Quantum Information

2 Introduction to quantum mechanics 60 2.1 Linear algebra 61 2.1.1 Bases and linear independence 62 2.1.2 Linear operators and matrices 63 2.1.3 The Pauli matrices 65 2.1.4 Inner products 65 2.1.5 Eigenvectors and eigenvalues 68 2.1.6 Adjoints and Hermitian operators 69 2.1.7 Tensor products 71 2.1.8 Operator functions 75

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Quantum Mechanics Made Simple: Lecture Notes

Oct 05, 2012 · Chapter 1 Introduction 1.1 Introduction Quantum mechanics is an important intellectual achievement of the 20th century. It is one of the more sophisticated eld in physics that has a ected our understanding of nano-meter length scale systems important for chemistry, materials, optics, and electronics. ...

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Chapter 1 Quantum Computing Basics and Concepts

4 CHAPTER 1. QUANTUM COMPUTING BASICS AND CONCEPTS quantum mechanical theory and Section 1.5 presents the transition from quantum mechanics to quantum logic circuits and quantum computation. 1.3 Mathematical Preliminaries to Quantum Com-puting According to [Dir84] each physical system is associated with a separate Hilbert space H.

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Quantum mechanics in one dimension - TCM Group

Chapter 2 Quantum mechanics in one dimension Following the rules of quantum mechanics, we have seen that the state of a quantum particle, subject to a scalar potential V(r), is described by the time-dependent Schr¨odinger equation, i!∂tΨ(r,t)=HˆΨ(r,t), (2.1) where Hˆ = −!2∇2 2m + V(r) denotes the Hamiltonian. To explore its proper-

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Introduction to Renormalization

Chapter 1 Introduction Quantum eld theory provides a framework for the description of all fundamental interac-tions (strong, weak, electromagnetic, maybe gravity), phase transitions in particle physics,

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Introduction to quantum mechanics - Harvard University

2 CHAPTER 10. INTRODUCTION TO QUANTUM MECHANICS deal of quantum mechanics already, whether you realize it or not. The outline of this chapter is as follows. In Section 10.1 we give a brief history of the development of quantum mechanics. In Section 10.2 we write down, after some motivation,

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