A Primer on Quantum Computing (eBook)

Preface 6
Acknowledgments 8
Contents 9
1 Introduction 11
References 14
2 Bits and Qubits 16
2.1 The Classical Computer and Reversibility 16
2.2 Review of Quantum Mechanics for Quantum Computation 20
2.3 Quantum Circuits 30
2.4 Universal Gates 37
2.5 Computational Simulations 40
References 42
3 Grover's Algorithm for Unstructured Search 44
3.1 Introduction 44
3.2 Geometric Visualization 48
3.3 A Small Example for Grover's Algorithm 51
3.4 Generalization 55
3.5 Grover Operator in Terms of Universal Gates 58
3.6 Computational Simulations 61
References 63
4 Shor's Algorithm for Integer Factorization 65
4.1 A Reduction of Integer Factorization to Order Finding 66
4.2 Quantum Algorithm to Calculate the Order 67
4.3 The Quantum Discrete Fourier Transform 71
4.4 Generalization by Means of an Example 74
4.5 Fourier Transform in Terms of the Universal Gates 78
4.6 Computational Simulations 84
References 84
5 Quantum Walks 86
5.1 Classical Random Walks 86
5.2 Coined Quantum Walks 88
5.2.1 Generalizing by Means of Examples 91
5.3 Staggered Quantum Walks 93
5.3.1 Tessellation Cover and the Evolution Operator 93
5.3.2 An Example Using the Diamond Ring of Size 9 96
5.3.3 Diamond Ring of Size N 99
5.3.4 Reproducing the Flip-Flop Coined Model 104
References 107
6 Conclusion and Further Remarks 109
References 111
Index 112