QUANTUM COMPUTING A helpful introduction to all aspects of quantum computing Quantum computing is a field combining quantum mechanics—the physical science of nature at the scale of atoms and subatomic particles—and information science. Where ordinary computing uses bits, logical values whose position can either be 0 or 1, quantum computing is built around qubits, a fundamental unit of quantum information which can exist in a superposition of both states. As quantum computers are able to complete certain kinds of functions more accurately and efficiently than computers built on classical binary logic, quantum computing is an emerging frontier which promises to revolutionize information science and its applications. This book provides a concise, accessible introduction to quantum computing. It begins by introducing the essentials of quantum mechanics that information and computer scientists require, before moving to detailed discussions of quantum computing in theory and practice. As quantum computing becomes an ever-greater part of the global information technology landscape, the knowledge in Quantum Computing will position readers to join a vital and highly marketable field of research and development. The book’s readers will also find: Detailed diagrams and illustrations throughout A broadly applicable quantum algorithm that improves on the best-known classical algorithms for a wide range of problems In-depth discussion of essential topics including key distribution, cluster state quantum computing, superconducting qubits, and more Quantum Computing is perfect for advanced undergraduate and graduate students in computer science, engineering, mathematics, or the physical sciences, as well as for researchers and academics at the intersection of these fields who want a concise reference.

Table of Contents:
Preface xiii Author Biography xv 1 Introduction of Quantum Computing 1 1.1 Introduction 1 1.2 What Is the Exact Meaning of Quantum Computing? 2 1.2.1 What Is Quantum Computing in Simple Terms? 2 1.3 Origin of Quantum Computing 3 1.4 History of Quantum Computing 5 1.5 Quantum Communication 19 1.6 Build Quantum Computer Structure 19 1.7 Principle Working of Quantum Computers 21 1.7.1 Kinds of Quantum Computing 21 1.8 Quantum Computing Use in Industry 23 1.9 Investors Invest Money in Quantum Technology 24 1.10 Applications of Quantum Computing 26 1.11 Quantum Computing as a Solution Technology 29 1.11.1 Quantum Artificial Intelligence 29 1.11.2 How Close Are We to Quantum Supremacy? 30 1.12 Conclusion 30 References 31 2 Pros and Cons of Quantum Computing 33 2.1 Introduction 33 2.2 Quantum as a Numerical Process 33 2.3 Quantum Complexity 34 2.4 The Pros and Cons of the Quantum Computational Framework 36 2.5 Further Benefits of Quantum Computing 37 2.6 Further Drawbacks to Quantum Computing 38 2.7 Integrating Quantum and Classical Techniques 38 2.8 Framework of QRAM 39 2.9 Computing Algorithms in the Quantum World 40 2.9.1 Programming Quantum Processes 42 2.10 Modification of Quantum Building Blocks 42 References 43 3 Methods and Instrumentation for Quantum Computing 45 3.1 Basic Information of Quantum Computing 45 3.2 Signal Information in Quantum Computing 47 3.3 Quantum Data Entropy 47 3.4 Basics of Probability in Quantum Computing 50 3.5 Quantum Theorem of No-Cloning 52 3.6 Measuring Distance 53 3.7 Fidelity in Quantum Theory 58 3.8 Quantum Entanglement 62 3.9 Information Content and Entropy 66 References 71 4 Foundations of Quantum Computing 73 4.1 Single-Qubit 73 4.1.1 Photon Polarization in Quantum Computing 73 4.2 Multi-qubit 76 4.2.1 Blocks of Quantum States 76 4.2.2 Submission of Vector Space in Quantum Computing 77 4.2.3 Vector Spacing in Quantum Blocks 77 4.2.4 States of n-Qubit Technology 79 4.2.5 States of Entangled 81 4.2.6 Classical Measuring of Multi-Qubit 84 4.3 Measuring of Multi-Qubit 87 4.3.1 Mathematical Functions in Quantum Operations 87 Example 88 4.3.2 Operator Measuring Qubits Projection 89 4.3.3 The Measurement Postulate 94 4.3.4 EPR Paradox and Bell’s Theorem 99 4.3.5 Layout of Bell’s Theorem 101 4.3.6 Statistical Predicates of Quantum Mechanics 101 4.3.7 Predictions of Bell’s Theorem 102 4.3.8 Bell’s Inequality 103 4.4 States of Quantum Metamorphosis 105 4.4.1 Solitary Steps Metamorphosis 106 4.4.2 Irrational Metamorphosis: The No-Cloning Principle 107 4.4.3 The Pauli Transformations 109 4.4.4 The Hadamard Metamorphosis 109 4.4.5 Multi-Qubit Metamorphosis from Single-Qubit 109 4.4.6 The Controlled-NOT and Other Singly Controlled Gates 110 4.4.7 Opaque Coding 113 4.4.8 Basic Bits in Opaque Coding 114 4.4.9 Quantum Message Teleportation 114 4.4.10 Designing and Constructing Quantum Circuits 116 4.4.11 Single Qubit Manipulating Quantum State 116 4.4.12 Controlling Single-Qubit Metamorphosis 117 4.4.13 Controlling Multi Single-Qubit Metamorphosis 117 4.4.14 Simple Metamorphosis 119 4.4.15 Unique Setup Gates 121 4.4.16 The Standard Circuit Model 122 References 123 5 Computational Algorithm Design in Quantum Systems 125 5.1 Introduction 125 5.2 Quantum Algorithm 125 5.3 Rule 1 Superposition 126 5.4 Rule 2 Quantum Entanglement 130 5.5 Rule 3 Quantum Metrology 132 5.6 Rule 4 Quantum Gates 133 5.7 Rule 5 Fault-Tolerant Quantum Gates 134 5.8 Quantum Concurrency 138 5.9 Rule 7 Quantum Interference 139 5.10 Rule 8 Quantum Parallelism 141 5.11 Summary 143 References 144 6 Optimization of an Amplification Algorithm 145 6.1 Introduction 145 6.2 The Effect of Availability Bias 146 6.2.1 Optimization of an Amplification Algorithm 147 6.2.2 Specifications of the Mathematical Amplification Algorithm 149 6.3 Quantum Amplitude Estimation and Quantum Counting 149 6.4 An Algorithm for Quantitatively Determining Amplitude 150 6.4.1 Mathematical Description of Amplitude Estimation Algorithm 151 6.5 Counting Quantum Particles: An Algorithm 151 6.5.1 Mathematical Description of Quantum Counting Algorithm 152 6.5.2 Related Algorithms and Techniques 152 References 153 7 Error-Correction Code in Quantum Noise 155 7.1 Introduction 155 7.2 Basic Forms of Error-Correcting Code in Quantum Technologies 156 7.2.1 Single Bit-Flip Errors in Quantum Computing 156 7.2.2 Single-Qubit Coding in Quantum Computing 161 7.2.3 Error-Correcting Code in Quantum Technology 162 7.3 Framework for Quantum Error-Correcting Codes 163 7.3.1 Traditional Based on Error-Correcting Codes 164 7.3.2 Quantum Error Decode Mechanisms 166 7.3.3 Correction Sets in Quantum Coding Error 167 7.3.4 Quantum Errors Detection 168 7.3.5 Basic Knowledge Representation of Error-Correcting Code 170 7.3.6 Quantum Codes as a Tool for Error Detection and Correction 173 7.3.7 Quantum Error Correction Across Multiple Blocks 176 7.3.8 Computing on Encoded Quantum States 177 7.3.9 Using Linear Transformation of Correctable Codes 177 7.3.10 Model of Classical Independent Error 178 7.3.11 Independent Quantum Inaccuracies Models 179 7.4 Coding Standards for CSS 182 7.4.1 Multiple Classical Identifiers 182 7.4.2 Traditional CSS Codes Satisfying a Duality Consequence 183 7.4.3 Code of Steane 186 7.5 Codes for Stabilizers 187 7.5.1 The Use of Binary Indicators in Quantum Correction of Errors 188 7.5.2 Using Pauli Indicators to Fix Errors in Quantum Techniques 188 7.5.3 Using Error-Correcting Stabilizer Algorithms 189 7.5.4 Stabilizer State Encoding Computation 191 7.6 A Stabilizer Role for CSS Codes 195 References 196 8 Tolerance for Inaccurate Information in Quantum Computing 197 8.1 Introduction 197 8.2 Initiating Stable Quantum Computing 198 8.3 Computational Error Tolerance Using Steane’s Code 200 8.3.1 The Complexity of Syndrome-Based Computation 201 8.3.2 Error Removal and Correction in Fault-Tolerant Systems 202 8.3.3 Steane’s Code Fault-Tolerant Gates 204 8.3.4 Measurement with Fault Tolerance 206 8.3.5 Readying the State for Fault Tolerance 207 8.4 The Strength of Quantum Computation 208 8.4.1 Combinatorial Coding 208 8.4.2 A Threshold Theorem 210 References 211 9 Cryptography in Quantum Computing 213 9.1 Introduction of RSA Encryption 213 9.2 Concept of RSA Encryption 214 9.3 Quantum Cipher Fundamentals 216 9.4 The Controlled-Not Invasion as an Illustration 219 9.5 Cryptography B92 Protocol 220 9.6 The E91 Protocol (Ekert) 221 References 221 10 Constructing Clusters for Quantum Computing 223 10.1 Introduction 223 10.1.1 State of Clusters 223 10.2 The Preparation of Cluster States 224 10.3 Nearest Neighbor Matrix 227 10.4 Stabilizer States 228 10.4.1 Aside: Entanglement Witness 230 10.5 Processing in Clusters 231 References 233 11 Advance Quantum Computing 235 11.1 Introduction 235 11.2 Computing with Superpositions 236 11.2.1 The Walsh–Hadamard Transformation 236 11.2.2 Quantum Parallelism 237 11.3 Notions of Complexity 239 11.3.1 Query Complexity 240 11.3.2 Communication Complexity 241 11.4 A Simple Quantum Algorithm 242 11.4.1 Deutsch’s Problem 242 11.5 Quantum Subroutines 243 11.5.1 The Importance of Unentangling Temporary Qubits in Quantum Subroutines 243 11.5.2 Phase Change for a Subset of Basis Vectors 244 11.5.3 State-Dependent Phase Shifts 246 11.5.4 State-Dependent Single-Qubit Amplitude Shifts 247 11.6 A Few Simple Quantum Algorithms 248 11.6.1 Deutsch–Jozsa Problem 248 11.6.2 Bernstein–Vazirani Problem 249 11.6.3 Simon’s Problem 252 11.6.4 Distributed Computation 253 11.7 Comments on Quantum Parallelism 254 11.8 Machine Models and Complexity Classes 255 11.8.1 Complexity Classes 257 11.8.2 Complexity: Known Results 258 11.9 Quantum Fourier Transformations 260 11.9.1 The Classical Fourier Transform 261 11.9.2 The Quantum Fourier Transform 263 11.9.3 A Quantum Circuit for Fast Fourier Transform 263 11.10 Shor’s Algorithm 265 11.10.1 Core Quantum Phenomena 266 11.10.2 Periodic Value Measurement and Classical Extraction 267 11.10.3 Shor’s Algorithm and Its Effectiveness 268 11.10.4 The Efficiency of Shor’s Algorithm 269 11.11 Omitting the Internal Measurement 270 11.12 Generalizations 271 11.12.1 The Problem of Discrete Logarithms 272 11.12.2 Hidden Subgroup Issues 272 11.13 The Application of Grover’s Algorithm It’s Time to Solve Some Difficulties 274 11.13.1 Explanation of the Superposition Technique 275 11.13.2 The Black Box’s Initial Configuration 275 11.13.3 The Iteration Step 276 11.13.4 Various of Iterations 277 11.14 Effective State Operations 279 11.14.1 2D Geometry 281 11.15 Grover’s Algorithm and Its Optimality 283 11.15.1 Reduction to Three Inequalities 284 11.16 Amplitude Amplification using Discrete Event Randomization of Grover’s Algorithm 286 11.16.1 Altering Each Procedure 286 11.16.2 Last Stage Variation 287 11.16.3 Solutions: Possibly Infinite 288 11.16.4 Varying the Number of Iterations 289 11.16.5 Quantum Counting 290 11.17 Implementing Grover’s Algorithm with Gain Boosting 291 References 292 12 Applications of Quantum Computing 295 12.1 Introduction 295 12.2 Teleportation 295 12.3 The Peres Partial Transposition Condition 298 12.4 Expansion of Transportation 303 12.5 Entanglement Swapping 304 12.6 Superdense Coding 305 References 307 Index 309