Quantum Computing : A New Era of Computing

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. Cover Title Page Copyright Contents Preface Author Biography Chapter 1 Introduction of Quantum Computing 1.1 Introduction 1.2 What Is the Exact Meaning of Quantum Computing? 1.2.1 What Is Quantum Computing in Simple Terms? 1.3 Origin of Quantum Computing 1.4 History of Quantum Computing 1.5 Quantum Communication 1.6 Build Quantum Computer Structure 1.7 Principle Working of Quantum Computers 1.7.1 Kinds of Quantum Computing 1.8 Quantum Computing Use in Industry 1.9 Investors Invest Money in Quantum Technology 1.10 Applications of Quantum Computing 1.11 Quantum Computing as a Solution Technology 1.11.1 Quantum Artificial Intelligence 1.11.2 How Close Are We to Quantum Supremacy? 1.12 Conclusion References References Chapter 2 Pros and Cons of Quantum Computing 2.1 Introduction 2.2 Quantum as a Numerical Process 2.3 Quantum Complexity 2.4 The Pros and Cons of the Quantum Computational Framework 2.5 Further Benefits of Quantum Computing 2.6 Further Drawbacks to Quantum Computing 2.7 Integrating Quantum and Classical Techniques 2.8 Framework of QRAM 2.9 Computing Algorithms in the Quantum World 2.9.1 Programming Quantum Processes 2.10 Modification of Quantum Building Blocks References Chapter 3 Methods and Instrumentation for Quantum Computing 3.1 Basic Information of Quantum Computing 3.2 Signal Information in Quantum Computing 3.3 Quantum Data Entropy 3.4 Basics of Probability in Quantum Computing 3.5 Quantum Theorem of No‐Cloning 3.6 Measuring Distance 3.7 Fidelity in Quantum Theory 3.8 Quantum Entanglement 3.9 Information Content and Entropy References Chapter 4 Foundations of Quantum Computing 4.1 Single‐Qubit 4.1.1 Photon Polarization in Quantum Computing 4.2 Multi‐qubit 4.2.1 Blocks of Quantum States 4.2.2 Submission of Vector Space in Quantum Computing 4.2.3 Vector Spacing in Quantum Blocks 4.2.4 States of n‐Qubit Technology 4.2.5 States of Entangled 4.2.6 Classical Measuring of Multi‐Qubit 4.3 Measuring of Multi‐Qubit 4.3.1 Mathematical Functions in Quantum Operations 4.3.2 Operator Measuring Qubits Projection 4.3.3 The Measurement Postulate 4.3.4 EPR Paradox and Bell's Theorem 4.3.5 Layout of Bell's Theorem 4.3.6 Statistical Predicates of Quantum Mechanics 4.3.7 Predictions of Bell's Theorem 4.3.8 Bell's Inequality 4.4 States of Quantum Metamorphosis 4.4.1 Solitary Steps Metamorphosis 4.4.2 Irrational Metamorphosis: The No‐Cloning Principle 4.4.3 The Pauli Transformations 4.4.4 The Hadamard Metamorphosis 4.4.5 Multi‐Qubit Metamorphosis from Single‐Qubit 4.4.6 The Controlled‐NOT and Other Singly Controlled Gates 4.4.7 Opaque Coding 4.4.8 Basic Bits in Opaque Coding 4.4.9 Quantum Message Teleportation 4.4.10 Designing and Constructing Quantum Circuits 4.4.11 Single Qubit Manipulating Quantum State 4.4.12 Controlling Single‐Qubit Metamorphosis 4.4.13 Controlling Multi Single‐Qubit Metamorphosis 4.4.14 Simple Metamorphosis 4.4.15 Unique Setup Gates 4.4.16 The Standard Circuit Model References Chapter 5 Computational Algorithm Design in Quantum Systems 5.1 Introduction 5.2 Quantum Algorithm 5.3 Rule 1 Superposition 5.4 Rule 2 Quantum Entanglement 5.5 Rule 3 Quantum Metrology 5.6 Rule 4 Quantum Gates 5.7 Rule 5 Fault‐Tolerant Quantum Gates 5.8 Quantum Concurrency 5.9 Rule 7 Quantum Interference 5.10 Rule 8 Quantum Parallelism 5.11 Summary References Chapter 6 Optimization of an Amplification Algorithm 6.1 Introduction 6.2 The Effect of Availability Bias 6.2.1 Optimization of an Amplification Algorithm 6.2.2 Specifications of the Mathematical Amplification Algorithm 6.3 Quantum Amplitude Estimation and Quantum Counting 6.4 An Algorithm for Quantitatively Determining Amplitude 6.4.1 Mathematical Description of Amplitude Estimation Algorithm 6.5 Counting Quantum Particles: An Algorithm 6.5.1 Mathematical Description of Quantum Counting Algorithm 6.5.2 Related Algorithms and Techniques References Chapter 7 Error‐Correction Code in Quantum Noise 7.1 Introduction 7.2 Basic Forms of Error‐Correcting Code in Quantum Technologies 7.2.1 Single Bit‐Flip Errors in Quantum Computing 7.2.2 Single‐Qubit Coding in Quantum Computing 7.2.3 Error‐Correcting Code in Quantum Technology 7.3 Framework for Quantum Error‐Correcting Codes 7.3.1 Traditional Based on Error‐Correcting Codes 7.3.2 Quantum Error Decode Mechanisms 7.3.3 Correction Sets in Quantum Coding Error 7.3.4 Quantum Errors Detection 7.3.5 Basic Knowledge Representation of Error‐Correcting Code 7.3.6 Quantum Codes as a Tool for Error Detection and Correction 7.3.7 Quantum Error Correction Across Multiple Blocks 7.3.8 Computing on Encoded Quantum States 7.3.9 Using Linear Transformation of Correctable Codes 7.3.10 Model of Classical Independent Error 7.3.11 Independent Quantum Inaccuracies Models 7.4 Coding Standards for CSS 7.4.1 Multiple Classical Identifiers 7.4.2 Traditional CSS Codes Satisfying a Duality Consequence 7.4.3 Code of Steane 7.5 Codes for Stabilizers 7.5.1 The Use of Binary Indicators in Quantum Correction of Errors 7.5.2 Using Pauli Indicators to Fix Errors in Quantum Techniques 7.5.3 Using Error‐Correcting Stabilizer Algorithms 7.5.4 Stabilizer State Encoding Computation 7.6 A Stabilizer Role for CSS Codes References Chapter 8 Tolerance for Inaccurate Information in Quantum Computing 8.1 Introduction 8.2 Initiating Stable Quantum Computing 8.3 Computational Error Tolerance Using Steane's Code 8.3.1 The Complexity of Syndrome‐Based Computation 8.3.2 Error Removal and Correction in Fault‐Tolerant Systems 8.3.3 Steane's Code Fault‐Tolerant Gates 8.3.4 Measurement with Fault Tolerance 8.3.5 Readying the State for Fault Tolerance 8.4 The Strength of Quantum Computation 8.4.1 Combinatorial Coding 8.4.2 A Threshold Theorem References Chapter 9 Cryptography in Quantum Computing 9.1 Introduction of RSA Encryption 9.2 Concept of RSA Encryption 9.3 Quantum Cipher Fundamentals 9.4 The Controlled‐Not Invasion as an Illustration 9.5 Cryptography B92 Protocol 9.6 The E91 Protocol (Ekert) References Chapter 10 Constructing Clusters for Quantum Computing 10.1 Introduction 10.1.1 State of Clusters 10.2 The Preparation of Cluster States 10.3 Nearest Neighbor Matrix 10.4 Stabilizer States 10.4.1 Aside: Entanglement Witness 10.5 Processing in Clusters References Chapter 11 Advance Quantum Computing 11.1 Introduction 11.2 Computing with Superpositions 11.2.1 The Walsh–Hadamard Transformation 11.2.2 Quantum Parallelism 11.3 Notions of Complexity 11.3.1 Query Complexity 11.3.2 Communication Complexity 11.4 A Simple Quantum Algorithm 11.4.1 Deutsch's Problem 11.5 Quantum Subroutines 11.5.1 The Importance of Unentangling Temporary Qubits in Quantum Subroutines 11.5.2 Phase Change for a Subset of Basis Vectors 11.5.3 State‐Dependent Phase Shifts 11.5.4 State‐Dependent Single‐Qubit Amplitude Shifts 11.6 A Few Simple Quantum Algorithms 11.6.1 Deutsch–Jozsa Problem 11.6.2 Bernstein–Vazirani Problem 11.6.3 Simon's Problem 11.6.4 Distributed Computation 11.7 Comments on Quantum Parallelism 11.8 Machine Models and Complexity Classes 11.8.1 Complexity Classes 11.8.2 Complexity: Known Results 11.9 Quantum Fourier Transformations 11.9.1 The Classical Fourier Transform 11.9.2 The Quantum Fourier Transform 11.9.3 A Quantum Circuit for Fast Fourier Transform 11.10 Shor's Algorithm 11.10.1 Core Quantum Phenomena 11.10.2 Periodic Value Measurement and Classical Extraction 11.10.3 Shor's Algorithm and Its Effectiveness 11.10.4 The Efficiency of Shor's Algorithm 11.11 Omitting the Internal Measurement 11.12 Generalizations 11.12.1 The Problem of Discrete Logarithms 11.12.2 Hidden Subgroup Issues 11.13 The Application of Grover's Algorithm It's Time to Solve Some Difficulties 11.13.1 Explanation of the Superposition Technique 11.13.2 The Black Box's Initial Configuration 11.13.3 The Iteration Step 11.13.4 Various of Iterations 11.14 Effective State Operations 11.14.1 2D Geometry 11.15 Grover's Algorithm and Its Optimality 11.15.1 Reduction to Three Inequalities 11.16 Amplitude Amplification using Discrete Event Randomization of Grover's Algorithm 11.16.1 Altering Each Procedure 11.16.2 Last Stage Variation 11.16.3 Solutions: Possibly Infinite 11.16.4 Varying the Number of Iterations 11.16.5 Quantum Counting 11.17 Implementing Grover's Algorithm with Gain Boosting References Chapter 12 Applications of Quantum Computing 12.1 Introduction 12.2 Teleportation 12.3 The Peres Partial Transposition Condition 12.4 Expansion of Transportation 12.5 Entanglement Swapping 12.6 Superdense Coding References Index EULA "Quantum mechanics emerged as a branch of physics in the early 1900s to explain nature on the scale of atoms and led to advances such as transistors, lasers, and magnetic resonance imaging. The idea to merge quantum mechanics and information theory arose in the 1970s but garnered little attention until 1982, when physicist Richard Feynman gave a talk in which he reasoned that computing based on classical logic could not tractably process calculations describing quantum phenomena. Quantum computing is the study of how to use phenomena in quantum physics to create new ways of computing. Quantum computing is made up of qubits. Unlike a normal computer bit, which can be 0 or 1, a qubit can be either of those, or a superposition of both 0 and 1"-- Provided by publisher