Quantum Computing: A Gentle Introduction

✍ Scribed by Eleanor Rieffel, Wolfgang Polak

• Publisher: The MIT Press
• Year: 2011
• Tongue: English
• Leaves: 389
• Series: Scientific and Engineering Computation
• Edition: 1
• Category: Library

✦ Synopsis

The combination of two of the twentieth century's most influential and revolutionary scientific theories, information theory and quantum mechanics, gave rise to a radically new view of computing and information. Quantum information processing explores the implications of using quantum mechanics instead of classical mechanics to model information and its processing. Quantum computing is not about changing the physical substrate on which computation is done from classical to quantum but about changing the notion of computation itself, at the most basic level. The fundamental unit of computation is no longer the bit but the quantum bit or qubit. This comprehensive introduction to the field offers a thorough exposition of quantum computing and the underlying concepts of quantum physics, explaining all the relevant mathematics and offering numerous examples. With its careful development of concepts and thorough explanations, the book makes quantum computing accessible to students and professionals in mathematics, computer science, and engineering. A reader with no prior knowledge of quantum physics (but with sufficient knowledge of linear algebra) will be able to gain a fluent understanding by working through the book. The text covers the basic building blocks of quantum information processing, quantum bits and quantum gates, showing their relationship to the key quantum concepts of quantum measurement, quantum state transformation, and entanglement between quantum subsystems; it treats quantum algorithms, discussing notions of complexity and describing a number of simple algorithms as well as the most significant algorithms to date; and it explores entanglement and robust quantum computation, investigating such topics as quantifying entanglement, decoherence, quantum error correction, and fault tolerance.

✦ Table of Contents

Cover
......Page 1
Contents......Page 6
Preface......Page 12
1 Introduction......Page 16
I Quantum Building Blocks......Page 22
2 Single-Qubit Quantum Systems......Page 24
3 Multiple-Qubit Systems......Page 46
4 Measurement of Multiple-Qubit States......Page 62
5 Quantum State Transformations......Page 86
6 Quantum Versions of Classical Computations......Page 114
II Quantum Algorithms......Page 138
7 Introduction to Quantum Algorithms......Page 140
8 Shor’s Algorithm......Page 178
9 Grover’s Algorithm and Generalizations......Page 192
III Entangled Subsystems and Robust Quantum Computation......Page 218
10 Quantum Subsystems and Properties of Entangled States......Page 220
11 Quantum Error Correction......Page 260
12 Fault Tolerance and Robust Quantum Computing......Page 308
13 Further Topics in Quantum Information Processing......Page 326
Appendixes......Page 344
A Some Relations Between Quantum Mechanics and Probability Theory......Page 346
B Solving the Abelian Hidden Subgroup Problem......Page 356
Bibliography......Page 368
Notation Index......Page 380
Index......Page 384

✦ Subjects

Физика;Квантовая физика;Квантовые вычисления и квантовая информатика;