QUANTUM COMPUTING

Preface 9
1 Fundamentals of Quantum Physics 13
1.1 Key Equations and Physical Constants 13
1.2 Solved Problems 15
1.3 Short Questions 18
1.4 Exercises 18
1.4.1 General Properties 18
1.4.2 Photoelectric Effect 19
1.4.3 Wave-Particle Duality 19
1.4.4 Heisenberg's Uncertainty Principle 20
1.4.5 Schrödinger's Wave Equation 21
1.4.6 Bohr's Atom and Quantum Numbers 22
2 Quantum Computing: Gates and Circuits 25
2.1 Definitions 25
2.2 Solved problems 26
2.3 Short questions 30
2.4 Exercises 31
2.4.1 1-qubit operations 31
2.4.2 Rotation matrices and the Bloch sphere 32
2.4.3 N-qubit operations 33
2.4.4 Quantum circuits 34
3 Quantum Computing: Applications 41
3.1 Definitions 41
3.2 Solved Problems 41
3.3 Short Questions 43
3.4 Exercises 44
3.4.1 No-cloning Theorem and Quantum Parallelism 44
3.4.2 EPR-Bell State Generators and Measurement 44
3.4.3 Superdense Coding 45
3.4.4 Teleportation 46
3.4.5 Distributed Quantum Computing 50
4 Quantum Measurements 53
4.1 Definitions 53
4.2 Solved Problems 54
4.3 Short Questions 56
4.4 Exercises 56
5 Quantum Algorithms 63
5.1 Solved Problems 64
5.2 Short Questions 67
5.3 Exercises 67
5.3.1 Deutsch-Jozsa Algorithm 67
5.3.2 Grover Algorithm 68
5.3.3 Quantum Fourier Transform and Shor Algorithm 69
6 Quantum Processors 73
6.1 Definitions 73
6.2 Solved problems 76
6.3 Short Questions 79
6.4 Exercises 80
6.4.1 Optical elements 80
6.4.2 Optical Setups 82
6.4.3 Ion Trap Quantum Computing 84
7 Quantum Communication 87
7.1 Quantum Protocol Definitions 87
7.2 Solved Problems 89
7.3 Short Questions 90
7.4 Exercises 90
7.4.1 RSA Cryptography 90
7.4.2 BB84 Protocol 91
7.4.3 B92 protocol 94
7.4.4 E91 Protocol 94
Appendix A. Brief Summary of Linear Algebra 99
Appendix B. Solutions to Selected Short Question 103
Appendix C. Solutions to Selected Problems 107
Bibliography

Quantum technology is one of the most promising and challenging ?elds in contemporary science. Quantum computing, quantum cryptography, and more generally quantum information technologies claim that they, in the short term, will change our paradigm of classical computing and communications. Concepts such as duality, superposition, entanglement, teleportation and many others seem to be closer to magic or science fiction than to everyday human experience. However, herein lies also the unlimited power of human thought, which mathematics and physics help us to go beyond our immediate experience of the world. This book, oriented toward undergraduate students pursuing Bachelor's Degrees in Engineering, draws on the experience of the authors during nearly ten years of work in this ?eld. The book consists of a comprehensive list of exercises with increasing degrees of di?culty. Additional material such as solved problems and a basic compilation of theory is also included in each chapter. The list of topics, which include among others, quantum computing, quantum teleportation, superdense coding, quantum processors or quantum communication protocols, intended for opening doors that will motivate students to continue delving into the ?eld of quantum technologies, which has only just begun to be explored.