This book is a timely report of the state-of-the-art analytical techniques in the domain of quantum algorithms related to Boolean functions. It bridges the gap between recent developments in the area and the hands-on analysis of the spectral properties of Boolean functions from a cryptologic viewpoint. Topics covered in the book include Qubit, Deutsch–Jozsa and Walsh spectrum, Grover’s algorithm, Simon’s algorithm and autocorrelation spectrum. The book aims at encouraging readers to design and implement practical algorithms related to Boolean functions. Apart from combinatorial techniques, this book considers implementing related programs in a quantum computer. Researchers, practitioners and educators will find this book valuable.
Author(s): Tharrmashastha SAPV, Debajyoti Bera, Arpita Maitra, Subhamoy Maitra
Series: SpringerBriefs in Computer Science
Publisher: Springer
Year: 2021
Language: English
Pages: 127
City: Singapore
Preface
Contents
About the Authors
1 Introduction
1.1 Qubit
1.2 Single Qubit Quantum Gates
1.3 Single Qubit Measurement
1.4 Multiple Qubits
1.5 Multi-Qubit Gates
1.6 Multi-Qubit Measurement
1.7 Quantum Teleportation
1.8 Superdense Coding
1.9 CHSH Game
References
2 Deutsch-Jozsa and Walsh Spectrum
2.1 Boolean Functions
2.2 Walsh Transform
2.3 Boolean Function Implementation: Classical to Quantum
2.4 The Deutsch Algorithm
2.5 The Deutsch-Jozsa Algorithm
2.6 The Bernstein-Vazirani Algorithm
2.7 Relation Between Deutsch-Jozsa and Walsh Spectrum
References
3 Grover's Algorithm and Walsh Spectrum
3.1 Grover's Algorithm
3.1.1 Geometric Interpretation of Grover's Algorithm
3.2 Finding Satisfying Inputs of a Boolean Function
3.3 Nonlinearity
3.4 Linearity Testing
3.5 Resiliency
References
4 Simon's Algorithm and Autocorrelation Spectrum
4.1 Simon's Algorithm
4.2 Autocorrelation Transform
4.2.1 Higher-Order Derivatives
4.2.2 Algorithm for Autocorrelation Sampling
4.3 Autocorrelation Estimation
4.4 Additional Implications
References
5 Conclusion and Research Direction
5.1 What Is Covered?
5.2 Recent Results
References
Index
