Quantum Algorithms for Cryptographically Significant Boolean Functions: An IBMQ Experience

Description

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.  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