Quantum Computing, 1st Edition

ISBN10: 1260123111 | ISBN13: 9781260123111

By Parag Lala

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ISBN10: 1260123111 | ISBN13: 9781260123111

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A self-contained, reader-friendly introduction to the principles and applications of quantum computing

Especially valuable to those without a prior knowledge of quantum mechanics, this electrical engineering text presents the concepts and workings of quantum information processing systems in a clear, straightforward, and practical manner. The book is written in a style that helps readers who are not familiar with non-classical information processing more easily grasp the essential concepts; only prior exposure to classical physics, basic digital design, and introductory linear algebra is assumed.

Quantum Computing: A Beginner’s Introduction presents each topic in a tutorial style with examples, illustrations, and diagrams to clarify the material. Written by an experienced electrical engineering educator and author, this is a self-contained resource, with all the necessary pre-requisite material included within the text.

Coverage includes:

• Complex Numbers, Vector Space, and Dirac Notation
• Basics of Quantum Mechanics
• Matrices and Operators
• Boolean Algebra, Logic Gates and Quantum Information Processing
• Quantum Gates and Circuit
• Tensor Products, Superposition and Quantum Entanglement
• Teleportation and Superdense Coding
• Quantum Error Correction
• Quantum Algorithms
• Quantum Cryptography

Preface
1 Complex Numbers, Vector Space, and Dirac Notation
- 1.1 Complex Numbers
- 1.2 Complex Conjugation
- 1.3 Vector Space
- 1.4 Basis Set
- 1.5 Dirac Notation
  - 1.5.1 Ket
  - 1.5.2 Bra
- 1.6 Inner Product
- 1.7 Linearly Dependent and Independent Vectors
- 1.8 Dual Vector Space
- 1.9 Computational Basis
- 1.10 Outer Product
- References
2 Basics of Quantum Mechanics
- 2.1 Limitations of Classical Physics
  - 2.1.1 Blackbody Radiation
  - 2.1.2 Planck’s Constant
- 2.2 Photoelectric Effect
- 2.3 Classical Electromagnetic Theory
- 2.4 Rutherford’s Model of the Atom
- 2.5 Bohr’s Model of Atoms
- 2.6 Particle and Wave Nature of Light
- 2.7 Wave Function
- 2.8 Postulates of Quantum Mechanics
- References
3 Matrices and Operators
- 3.1 Matrices
- 3.2 Square Matrices
- 3.3 Diagonal (or Triangular) Matrix
- 3.4 Operators
  - 3.4.1 Rules for Operators
- 3.5 Linear Operator
- 3.6 Commutator
- 3.7 Matrix Representation of a Linear Operator
- 3.8 Symmetric Matrix
- 3.9 Transpose Operation
- 3.10 Orthogonal Matrices
- 3.11 Identity Operator
- 3.12 Adjoint Operator
- 3.13 Hermitian Operator
- 3.14 Unitary Operators
  - 3.14.1 Properties of Unitary Operators
- 3.15 Projection Operator
- References
4 Boolean Algebra, Logic Gates, and Quantum Information Processing
- 4.1 Boolean Algebra
- 4.2 Classical Circuit Computation Model
- 4.3 Universal Logic Gates
- 4.4 Quantum Computation
- 4.5 The Quantum Bit and Its Representations
- 4.6 Superposition in Quantum Systems
- 4.7 Quantum Register
- References
5 Quantum Gates and Circuits
- 5.1 X Gate
- 5.2 Y Gate
- 5.3 Z Gate
- 5.4 (Square Root of NOT) Gate
- 5.5 Hadamard Gate
- 5.6 Phase Gate
- 5.7 T Gate
- 5.8 Reversible Logic
- 5.9 CNOT Gate
- 5.10 Controlled-U Gate
- 5.11 Reversible Gates
  - 5.11.1 Fredkin Gate (Controlled Swap Gate)
  - 5.11.2 Toffoli Gate (Controlled-Controlled-NOT)
  - 5.11.3 Peres Gate
- References
6 Tensor Products, Superposition, and Quantum Entanglement
- 6.1 Tensor Products
- 6.2 Multi-Qubit Systems
- 6.3 Superposition
- 6.4 Entanglement
- 6.5 Decoherence
- References
7 Teleportation and Superdense Coding
- 7.1 Quantum Teleportation
- 7.2 No-Cloning Theorem
- 7.3 Superdense Coding
- References
8 Quantum Error Correction
- 8.1 Classical Error-Correcting Codes
- 8.2 Quantum Error-Correcting Codes
- 8.3 Shor’s 3-Qubit Bit-Flop Code
- 8.4 Error Correction
  - 8.4.1 Bit-Flip Error Correction
  - 8.4.2 Phase Error Correction
- 8.5 Shor’s 9 Qubit Code
- References
9 Quantum Algorithms
- 9.1 Deutsch’s Algorithm
- 9.2 Deutsch–Jozsa Algorithm
- 9.3 Grover’s Search Algorithm
  - 9.3.1 Details of Grover’s Algorithm
- 9.4 Shor’s Factoring Algorithm
- References
10 Quantum Cryptography
- 10.1 Principles of Information Security
- 10.2 One-Time Pad
- 10.3 Public Key Cryptography
- 10.4 RSA Coding Scheme
- 10.5 Quantum Cryptography
- 10.6 Quantum Key Distribution
- 10.7 BB84
- 10.8 Ekart 91
- References
Index

About the Author

Parag Lala

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