Problems And Solutions In Quantum Computing And Quantum Information (4th Edition)

by Willi-hans Steeb, Yorick Hardy

Overview

'This is a very useful book which helps to understand the concepts of quantum computing and quantum information by well presented problems and detailed solutions … It is highly recommended for beginners as well as for advanced researchers.'
zbMATHQuantum computing and quantum information are two of the fastest growing and most exciting research fields in physics. Entanglement, teleportation and the possibility of using the non-local behavior of quantum mechanics to factor integers in random polynomial time have also added to this new interest.This book presents a huge collection of problems in quantum computing and quantum information together with their detailed solutions, which will prove to be invaluable to students as well as researchers in these fields. Each chapter gives a comprehensive introduction to the topics. All the important concepts and areas such as quantum gates and quantum circuits, product Hilbert spaces, entanglement and entanglement measures, teleportation, Bell states, Bell measurement, Bell inequality, Schmidt decomposition, quantum Fourier transform, magic gate, von Neumann entropy, quantum cryptography, quantum error corrections, quantum games, number states and Bose operators, coherent states, squeezed states, Gaussian states, coherent Bell states, POVM measurement, quantum optics networks, beam splitter, phase shifter and Kerr Hamilton operator are included. A chapter on quantum channels has also been added. Furthermore a chapter on boolean functions and quantum gates with mapping bits to qubits is included.The topics range in difficulty from elementary to advanced. Almost all problems are solved in detail and most of the problems are self-contained. Each chapter also contains supplementary problems to challenge the reader. Programming problems with Maxima and SymbolicC++ implementations are also provided.

Product Details

ISBN-13:	9789813238404
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	04/24/2018
Pages:	556
Product dimensions:	6.00(w) x 9.00(h) x 1.19(d)

Table of Contents

Preface v

Notation xi

I Finite-Dimensional Hilbert Spaces 1

1 Qubits 3

1.1 Introduction 3

1.2 Solved Problems 5

1.3 Supplementary Problems 27

2 Kronecker Product and Tensor Product 31

2.1 Introduction 31

2.2 Solved Problems 33

2.3 Supplementary Problems 59

3 Matrix Properties 65

3.1 Introduction 65

3.2 Solved Problems 67

3.3 Supplementary Problems 108

4 Density Operators 115

4.1 Introduction 115

4.2 Solved Problems 117

4.3 Supplementary Problems 139

5 Trace and Partial Trace 141

5.1 Introduction 141

5.2 Solved Problems 143

5.3 Supplementary Problems 153

6 Boolean Functions and Quantum Gates 155

6.1 Introduction 155

6.2 Solved Problems 157

6.3 Supplementary Problems 173

7 Unitary Transforms and Quantum Gates 175

7.1 Introduction 175

7.2 Solved Problems 177

7.3 Supplementary Problems 208

8 Entropy 209

8.1 Introduction 209

8.2 Solved Problems 211

8.3 Supplementary Problems 225

9 Measurement 227

9.1 Introduction 227

9.2 Solved Problems 229

9.3 Supplementary Problems 249

10 Entanglement 251

10.1 Introduction 251

10.2 Solved Problems 253

10.3 Supplementary Problems 293

11 Bell Inequality 295

11.1 Introduction 295

11.2 Solved Problems 297

11.3 Supplementary Problems 306

12 Teleportation 307

12.1 Introduction 307

12.2 Solved Problems 308

12.3 Supplementary Problems 318

13 Cloning 319

13.1 Introduction 319

13.2 Solved Problems 320

13.3 Supplementary Problems 324

14 Quantum Algorithms 325

14.1 Introduction 325

14.2 Solved Problems 327

14.3 Supplementary Problems 349

15 Quantum Error Correction 351

15.1 Introduction 351

15.2 Solved Problems 353

15.3 Supplementary Problem 358

16 Quantum Cryptography 359

16.1 Introduction 359

16.2 Solved Problems 360

16.3 Supplementary Problem 368

17 Quantum Channels 369

17.1 Introduction 369

17.2 Solved Problems 371

17.3 Supplementary Problems 384

II Infinite-Dimensional Hilbert Spaces 385

18 Bose Operators and Number States 387

18.1 Introduction 387

18.2 Solved Problems 389

18.3 Supplementary Problems 417

19 Coherent States 421

19.1 Introduction 421

19.2 Solved Problems 423

19.3 Supplementary Problems 437

20 Squeezed States 439

20.1 Introduction 439

20.2 Solved Problems 441

20.3 Supplementary Problems 457

21 Trace and Partial Trace 461

21.1 Introduction 461

21.2 Solved Problems 462

21.3 Supplementary Problems 468

22 Entanglement 469

22.1 Introduction 469

22.2 Solved Problems 471

22.3 Supplementary Problems 487

23 Continuous Variable Teleportation 489

23.1 Introduction 489

23.2 Solved Problems 489

23.3 Supplementary Problem 493

24 Swapping and Cloning 495

24.1 Introduction 495

24.2 Solved Problems 495

24.3 Supplementary Problems 500

25 Homodyne Detection 501

25.1 Introduction 501

25.2 Solved Problems 502

25.3 Supplementary Problems 504

26 Hamilton Operators 505

26.1 Introduction 505

26.2 Solved Problems 506

26.3 Supplementary Problems 519

Bibliography 521

Index 535