Quantum Computing: A New Era of Computing [1 ed.] 1394157819, 9781394157815

Table of contents :
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