Basics of Quantum Computation

1 What is the point in Quantum Computation 1

1.1 Preview 1

1.2 A First View of the Advantages 5

1.3 Is Physics Nothing Else But Computation ? 12

2 First Quantum Computations 15

2.1 Quantum Bits, or Qubits 15

2.2 Single Qubit Gates 18

2.3 Composite Quantum Systems and Entanglement 21

2.4 Multiple Qubit Gates 28

2.5 Classical Computations on Quantum Computers 30

2.6 Keeping Quantum Gates Simple 33

3 Two Strange Phenomena 39

3.1 No-Cloning 39

3.2 Teleportation 44

4 Bell’s Inequalities 53

4.1 Boole Type Inequalities 56

4.2 The Bell Eff ect 58

4.3 Bell’s Inequalities 61

4.4 Locality versus Nonlocality 64

5 The Deutsch-Jozsa Algorithm 67

5.1 A Simple Case of Quantum Parallelism 67

5.2 Massive Quantum Parallelism 69

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5.3 The Deutsch Algorithm 72

5.4 The Deutsch-Jozsa Algorithm 75

Bibliography 79-Basics of Quantum Computation 1 What is the point in Quantum Computation 1 1.1 Preview 1 1.2 A First View of the Advantages 5 1.3 Is Physics Nothing Else But Computation? 12 2 First Quantum Computations 15 2.1 Quantum Bits, or Qubits 15 2.2 Single Qubit Gates 18 2.3 Composite Quantum Systems and Entanglement 21 2.4 Multiple Qubit Gates 28 2.5 Classical Computations on Quantum Computers 30 2.6 Keeping Quantum Gates Simple 33 3 Two Strange Phenomena 39 3.1 No-Cloning 39 3.2 Teleportation 44 4 Bell' s Inequalities 53 4.1 Boole Type Inequalities 56 4.2 The Bell Effect 58 4.3 Bell' s Inequalities 61 4.4 Locality versus Nonlocality 64 5 The Deutsch-Jozsa Algorithm 67 5.1 A Simple Case of Quantum Parallelism 67 5.2 Massive Quantum Parallelism 69 ii 5.3 The Deutsch Algorithm 72 5.4 The Deutsch-Jozsa Algorithm 75 Bibliography 79