Quantum Computing

<ul style="list-style-type: none;"> <li>Preface</li> <li>1 Complex Numbers, Vector Space, and Dirac Notation <ul style="list-style-type: none;"> <li>1.1 Complex Numbers</li> <li>1.2 Complex Conjugation</li> <li>1.3 Vector Space</li> <li>1.4 Basis Set</li> <li>1.5 Dirac Notation <ul style="list-style-type: none;"> <li>1.5.1 Ket</li> <li>1.5.2 Bra</li> </ul></li> <li>1.6 Inner Product</li> <li>1.7 Linearly Dependent and Independent Vectors</li> <li>1.8 Dual Vector Space</li> <li>1.9 Computational Basis</li> <li>1.10 Outer Product</li> <li>References</li> </ul></li> <li>2 Basics of Quantum Mechanics <ul style="list-style-type: none;"> <li>2.1 Limitations of Classical Physics <ul style="list-style-type: none;"> <li>2.1.1 Blackbody Radiation</li> <li>2.1.2 Planck’s Constant</li> </ul></li> <li>2.2 Photoelectric Effect</li> <li>2.3 Classical Electromagnetic Theory</li> <li>2.4 Rutherford’s Model of the Atom</li> <li>2.5 Bohr’s Model of Atoms</li> <li>2.6 Particle and Wave Nature of Light</li> <li>2.7 Wave Function</li> <li>2.8 Postulates of Quantum Mechanics</li> <li>References</li> </ul></li> <li>3 Matrices and Operators <ul style="list-style-type: none;"> <li>3.1 Matrices</li> <li>3.2 Square Matrices</li> <li>3.3 Diagonal (or Triangular) Matrix</li> <li>3.4 Operators <ul style="list-style-type: none;"> <li>3.4.1 Rules for Operators</li> </ul></li> <li>3.5 Linear Operator</li> <li>3.6 Commutator</li> <li>3.7 Matrix Representation of a Linear Operator</li> <li>3.8 Symmetric Matrix</li> <li>3.9 Transpose Operation</li> <li>3.10 Orthogonal Matrices</li> <li>3.11 Identity Operator</li> <li>3.12 Adjoint Operator</li> <li>3.13 Hermitian Operator</li> <li>3.14 Unitary Operators <ul style="list-style-type: none;"> <li>3.14.1 Properties of Unitary Operators</li> </ul></li> <li>3.15 Projection Operator</li> <li>References</li> </ul></li> <li>4 Boolean Algebra, Logic Gates, and Quantum Information Processing <ul style="list-style-type: none;"> <li>4.1 Boolean Algebra</li> <li>4.2 Classical Circuit Computation Model</li> <li>4.3 Universal Logic Gates</li> <li>4.4 Quantum Computation</li> <li>4.5 The Quantum Bit and Its Representations</li> <li>4.6 Superposition in Quantum Systems</li> <li>4.7 Quantum Register</li> <li>References</li> </ul></li> <li>5 Quantum Gates and Circuits <ul style="list-style-type: none;"> <li>5.1 X Gate</li> <li>5.2 Y Gate</li> <li>5.3 Z Gate</li> <li>5.4 (Square Root of NOT) Gate</li> <li>5.5 Hadamard Gate</li> <li>5.6 Phase Gate</li> <li>5.7 T Gate</li> <li>5.8 Reversible Logic</li> <li>5.9 CNOT Gate</li> <li>5.10 Controlled-U Gate</li> <li>5.11 Reversible Gates <ul style="list-style-type: none;"> <li>5.11.1 Fredkin Gate (Controlled Swap Gate)</li> <li>5.11.2 Toffoli Gate (Controlled-Controlled-NOT)</li> <li>5.11.3 Peres Gate</li> </ul></li> <li>References</li> </ul></li> <li>6 Tensor Products, Superposition, and Quantum Entanglement <ul style="list-style-type: none;"> <li>6.1 Tensor Products</li> <li>6.2 Multi-Qubit Systems</li> <li>6.3 Superposition</li> <li>6.4 Entanglement</li> <li>6.5 Decoherence</li> <li>References</li> </ul></li> <li>7 Teleportation and Superdense Coding <ul style="list-style-type: none;"> <li>7.1 Quantum Teleportation</li> <li>7.2 No-Cloning Theorem</li> <li>7.3 Superdense Coding</li> <li>References</li> </ul></li> <li>8 Quantum Error Correction <ul style="list-style-type: none;"> <li>8.1 Classical Error-Correcting Codes</li> <li>8.2 Quantum Error-Correcting Codes</li> <li>8.3 Shor’s 3-Qubit Bit-Flop Code</li> <li>8.4 Error Correction <ul style="list-style-type: none;"> <li>8.4.1 Bit-Flip Error Correction</li> <li>8.4.2 Phase Error Correction</li> </ul></li> <li>8.5 Shor’s 9 Qubit Code</li> <li>References</li> </ul></li> <li>9 Quantum Algorithms <ul style="list-style-type: none;"> <li>9.1 Deutsch’s Algorithm</li> <li>9.2 Deutsch–Jozsa Algorithm</li> <li>9.3 Grover’s Search Algorithm <ul style="list-style-type: none;"> <li>9.3.1 Details of Grover’s Algorithm</li> </ul></li> <li>9.4 Shor’s Factoring Algorithm</li> <li>References</li> </ul></li> <li>10 Quantum Cryptography <ul style="list-style-type: none;"> <li>10.1 Principles of Information Security</li> <li>10.2 One-Time Pad</li> <li>10.3 Public Key Cryptography</li> <li>10.4 RSA Coding Scheme</li> <li>10.5 Quantum Cryptography</li> <li>10.6 Quantum Key Distribution</li> <li>10.7 BB84</li> <li>10.8 Ekart 91</li> <li>References</li> </ul></li> <li>Index</li> </ul>