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