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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.
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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.
Kuldeep Singh Kaswan, PhD, is Professor in the School of Computing Science and Engineering at Galgotias University, Greater Noida, India. He is co-editor of the upcoming Wiley title Swarm Intelligence: An Approach from Natural to Artificial.
Jagjit Singh Dhatterwal, PhD, is Associate Professor in the Department of Artificial Intelligence & Data Science at Koneru Lakshmaiah Education Foundation, Vaddeswaram, AP, India. He is co-editor of the upcoming Wiley title Swarm Intelligence: An Approach from Natural to Artificial.
Anupam Baliyan, PhD, is Professor of Engineering and Technology at Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India.
Shalli Rani, PhD, is Professsor of Engineering and Technology at Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India. She is co-editor of the Wiley title IoT-enabled Smart Healthcare Systems, Services and Applications.
1 INTRODUCTION OF QUANTUM COMPUTING…
1.1 Introduction
1.2 What is the exact Meaning of Quantum Computing
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
1.8 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
1.12 Conclusion
2 MERITS AND DEMERITS OF QUANTUM COMPUTING………
2.1 Introduction
2.2 Quantum as Mathematical Computation
2.3 Complexity in Quantum
2.4 Advantages and Disadvantages of the Quantum Computational Model
2.5 Additional Advantages of Quantum Computing
2.6 Additional Disadvantages of Quantum Computing
2.7 Hybridization of Quantum Computing
2.8 Structure of QRAM
2.9 Algorithm in Quantum Computing
2.9.1 Designing of Quantum Algorithm
2.10 Alteration in Quantum Blocks
3 TOOLS ANF TECHNIQUES ON QUANTUM THEORY.…
3.1 Classical Information
3.2 Information Content in a Signal
3.3 Theory of Information and Entropy
3.4 Probability Basic
3.5 The No-Cloning Theorem
3.6 Trace Distance
3.7 Fidelity
3.8 Entanglement Of Formation and Concurrence
3.9 Information Content and Entropy
4 BUILDING BLOCKS OF QUANTUM COMPUTING……...
4.1 Single-Qubit
4.1.1 The Quantum Mechanics of Photon Polarization
4.2 Multi-Qubit
4.2.1 Quantum State Spaces
4.2.2 Direct Sums of Vector Spaces
4.2.3 Tensor Products of Vector Spaces
4.2.4 The state spaces of an n-Qubit System
4.2.5 Entangled States
4.2.6 Basics of Multi-Qubit Measurement
4.3 Measurement of Multi-Qubit
4.3.1 Notation for Mathematical Operations Using the Bra/Ket System Developed by Dirac
4.3.2 Projection Operators for Measurement
4.3.3 The Measurement Postulate
4.3.4 EPR Paradox and Bell’s Theorem
4.3.5 Setup for Bell’s Theorem
4.3.6 What Quantum Mechanics Predicts
4.3.7 Applying Bell's Theorem to the Predictions of Any Local Theory of Hidden Variables
4.3.8 Bell’s Inequality
4.4 State of Quantum Transformation
4.4.1 Single-step transformations
4.4.2 Impossible Transformations: The No-Cloning Principle
4.4.3 The Pauli Transformations
4.4.4 The Hadamard Transformation
4.4.5 Multiple-Qubit Transformations from Single-Qubit Transformations
4.4.6 The Controlled-NOT and Other Singly Controlled Gates
4.4.7 Dense Coding
4.4.8 Classical Bits in Dense Coding
4.4.9 Quantum Teleportation
4.4.10 Realizing Unitary Transformations as Quantum Circuits
4.4.11 Decomposition of Single-Qubit Transformations
4.4.12 Singly Controlled Single-Qubit Transformations
4.4.13 Multiply Controlled Single-Qubit Transformations
4.4.14 General Unitary Transformations
4.4.15 A Universally Approximating Set of Gates
4.4.16 The Standard Circuit Model
5 ALGORITHM STRUCTURE OF QUANTUM COMPUTING……
5.1 Introduction
5.2 Quantum Algorithm
5.3 Quantum Computing Rule 1
5.4 Quantum Computing Rule 2
5.5 Quantum Computing Rule 3
5.6 Quantum Computing Rule 4
5.7 Quantum Computing Rule 5
5.8 Quantum Computing Rule 6
5.9 Quantum Computing Rule 7
5.10 Quantum Computing Rule 8
6 ALGORITHM OF AMPLITUDE AMPLIFICATION …………………….
6.1 Introduction
6.2 Availability Bias
6.3 Amplitude Amplification Algorithm
6.3.1 Mathematical details for the amplitude amplification algorithm
6.4 Quantum Amplitude Estimation and Quantum Counting
6.5 The quantum amplitude estimation algorithm
6.5.1 Mathematical description of amplitude estimation algorithm
6.6 The Quantum Counting Algorithm
6.7 Searching Without Knowing the Success Probability
7 ERROR CORRECTION CODE IN QUANTUM NOISE …………
7.1 Introduction
7.2 Basic forms of Error-Correcting Code in Quantum Technologies
7.1.1 Single Bit-Flip Errors in Quantum Computing
7.1.2 Single Qubit Coding in Quantum Computing
7.1.3 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 The Classical Independent Error Model
7.3.11 Quantum Independent Error Models
7.4 CSS Codes
7.4.1 Dual Classical Codes
7.4.2 CSS Codes Built Using Traditional Codes That Meet a Duality Consequence
7.4.3 The Steane Code
7.5 Stabilizer Codes
7.5.1 Binary Observables for Quantum Error Correction
7.5.2 Error-Correcting Pauli Observables in Quantum Systems
7.5.3 Correcting Errors using Stabilizer Code
7.5.4 Computing on the Encoded Stabilizer States
7.6 CSS Codes as Stabilizer Codes
8 FAULT TOLERANCE IN QUANTUM COMPUTING
8.1 Introduction
8.2 Setting the Stage for Robust Quantum Computation
8.3 Fault-Tolerant Computation Using Steane’s Code
8.3.1 The Problem with Syndrome Computation
8.3.2 Fault-Tolerant Syndrome Extraction and Error Correction
8.3.3 Fault-Tolerant Gates for Steane’s Code
8.3.4 Fault-Tolerant Measurement
8.3.5 Fault-Tolerant State Preparation of |π/4
8.4 Robust Quantum Computation
8.4.1 Concatenated Coding
8.4.2 A Threshold Theorem
9 CRYPTOGRAPHY IN QUANTUM COMPUTING
9.1 Introduction of RSA Encryption
9.2 A Brief Overview of RSA Encryption
9.3 Basic Quantum Cryptography
9.4 An Example Attack: The Controlled Not Attack
9.5 The B92 Protocol
9.6 The E91 Protocol
10 BUILDING CLUSTERS IN QUANTUM COMPUTING
10.1 Introduction
10.1.1 Cluster States
10.2 Cluster States Preparation
10.3 Adjacency Matrices
10.4 Stabilizer States
10.4.1 Aside: Entanglement Witness
10.5 Cluster State Processing
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 The Quantum Core
11.10.2 Classical Extraction of the Period from the Measured Value
11.10.3 The Efficiency of Shor’s Algorithm
11.11 Omitting the Internal Measurement
11.12 Generalizations
11.13 Grover’s Algorithm use Solve sets of problems
11.13.1 Outline method of superposition
11.13.2 Setup of Black Box
11.13.3 The Iteration Step
11.13.4 How Many Iterations?
11.14 Good State Functions
11.14.1 The Two-Dimensional Geometry
11.15 Optimality of Grover’s Algorithm
11.15.1 Reduction to Three Inequalities
11.16 DE randomization of Grover’s Algorithm and Amplitude Amplification
11.16.1 Approach 1: Modifying Each Step
11.16.2 Approach 2: Modifying Only the Last Step
11.16.3 Unknown Number of Solutions
11.16.4 Varying the Number of Iterations
11.16.5 Quantum Counting
12 APPLICATIONS OF QUANTUM COMPUTING
12.1 Introduction
12.2 Teleportation Steps
12.3 The Peres Partial Transposition Condition
12.4 Entanglement Swapping
12.5 Superdense Coding
Index
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