Quantum Computing: A Shift from Bits to Qubits

Preface
Contents
Editors and Contributors
Scientific Theory for Quantum
Quantification of Correlations in Quantum States
1 Introduction
2 Quantum States and Entanglement
3 Quantum Correlations Beyond Entanglement as Dephasing Sensitivity
4 Genuine Multipartite Total Correlations
5 Conclusion and Remarks
References
From Quantum Mechanics to Quantum Computing
1 Introduction
2 Quantum State
3 Hilbert Space in Quantum Mechanics
3.1 Time Evolution
3.2 Quantum Mechanics and Measurements
4 Qubits and Two State systems
5 Composite Systems and Entanglement
5.1 Multiple Qubits
6 Mixed States and Density Matrix
7 Measurement Problem and Quantum Decoherence
7.1 Decoherence and Quantum Computing
8 Conclusion
References
Phase Space Quantization I: Geometrical Ideas
1 Introduction
2 Phase Space Radar Measurements
3 Symplectic Geometry
4 Symplectic Geometry and Holomorphic Automorphisms
5 Deformation Quantization
6 Hilbert Space Methods
7 Conclusions and Discussions
References
Phase Space Quantization II: Statistical Ideas
1 Introduction
2 Radar Signals and Quantum Wave Functions
2.1 The Heisenberg Group
2.2 Statistical Interpretation
2.3 Stationary Stochastic Processes
3 Statistical Models
3.1 The Statistical Model of Classical Mechanics
3.2 The Stochastic Phase Space
4 The Statistical Model of Signals in Phase Space
5 Non-commutative Signal Theory
5.1 Some Ideas from Quantum Statistical Models
5.2 Reproducing Kernels and Functions of Positive Type
5.3 Star Products in Co-adjoint Orbits
5.4 Star Quantization in the Bloch Sphere
6 Summary Conclusion and Future Work
References
Efficient Quantum Circuit for Karatsuba Multiplier
1 Introduction
1.1 Scope
1.2 Research Contributions
1.3 Process Overview
1.4 Background
1.5 Organization of the Paper
2 Methodology to Design Quantum Karatsuba Multiplier Circuit
3 Design of Proposed Quantum Circuit for GF (2n) Reversible Karatsuba Multiplier
3.1 Quantum Circuits for Karatsuba-Based Polynomial Multiplication
3.2 Quantum Circuit for GF (24) Karatsuba Multiplier
4 Methodology to Remove Garbage Outputs from Quantum Polynomial Multiplication Circuit Designs
5 Results and Discussion
6 Conclusion
References
Quantum Computing: Building Concepts
Quantum Concepts
1 Introduction
2 Representing Quantum States
3 Quantum Gates
3.1 Some Important Results
4 Quantum Entanglement
4.1 Executing on Simulator
4.2 Executing on Real Quantum Device
5 Output Visualization
6 Conclusion
References
Evolutionary Analysis: Classical Bits to Quantum Qubits
1 Introduction
2 Classical Computer
2.1 Classical Bits
3 Quantum Computer
3.1 Quantum Bits
3.2 Bloch Sphere
3.3 Quantum State Formats for Representing Classical Data
4 Comparative Analysis
5 Quantum Gates
5.1 Single Qubit Gate
5.2 Hadamard Gate
5.3 Phase-Shift Gate
5.4 Universal Quantum Gate
5.5 Measurement (Z Gate)
6 Conclusion
References
Non-silicon Computing with Quantum Superposition Entanglement Using Qubits
1 Introduction
2 Concept of Quantum Computing
3 Reversible Evolution in Quantum Computing
3.1 Basic Logic Gates in Classical Computing
3.2 Information and Entropy
3.3 Reversible Computing
4 Quantum Gates and Circuits
5 Quantum Superposition and Quantum Entanglement
5.1 Qubits
5.2 Quantum Superposition
5.3 Quantum Entanglement
5.4 Gates with Single-Qubit
5.5 The Bloch Sphere’s Rotations
5.6 Why Quantum Computing? (Keys to Take Away)
5.7 Scaling of Qubits
6 Quantum Tunneling
6.1 Impact of Quantum Tunneling on Classical Computing
6.2 Impact of Quantum Tunneling on Quantum Computing
7 Conclusion
References
Quantum Algorithms–Theory and Applications
A Reversible Hybrid Architecture for Multilayer Memory Cell in Quantum-Dot Cellular Automata with Minimized Area and Less Delay
1 Introduction
2 Background and Related Work
2.1 QCA Cell
2.2 Basic Gates
2.3 Clock Mechanism
2.4 Related Work
3 Proposed Structure
4 Result and Discussion
5 Conclusion
References
Quantum Neural Network for Image Classification Using TensorFlow Quantum
1 Introduction
2 Data Preparation
3 Building of Quantum Neural Network
4 Results and Discussions
5 Conclusions
References
Quantum Network Architecture and Its Topology
1 Introduction
2 Network Attributes
2.1 Types of Connection
2.2 Network Topology
2.3 Star Topology Network
2.4 Bus Topology Network
2.5 Tree Topology Network
2.6 Ring Topology Network
2.7 Hybrid Topology
3 Current Status of the Quantum Network and Its Development
References
Quantum Computing-Enabled Machine Learning for an Enhanced Model Training Approach
1 Introduction
2 Why Quantum Computers
3 Classical Bits and Qubits
4 Quantum Phenomenon
4.1 Superposition
4.2 Entanglement
5 Quantum Algorithms
5.1 Grover Algorithm
6 Machine Learning
7 Libraries
8 Libraries
9 Proposed Framework
10 Conclusion
References
Numerical Modeling of the Major Temporal Arcade Using a Quantum Genetic Algorithm
1 Introduction
2 Background
2.1 Database of Major Temporal Arcade Images
2.2 Gaussian Matched Filters
2.3 Spline Curves
2.4 Genetic Algorithms
2.5 Quantum Genetic Algorithms
2.6 Proposed Method for Modeling the Major Temporal Arcade
3 Computational Experiments
4 Conclusions
References
Entangled Quantum Neural Network
1 Introduction
2 Related Background
2.1 Quantum Entanglement
2.2 The Measurement on Density Matrix
2.3 Multi-layer Perceptron
3 The EQNN Framework
3.1 Quantum Entanglement Inspired Correlation Learning for Classification (QECA)
3.2 Quantum Correlation Revealed by Bell State for Classification Tasks (QCCA)
3.3 Strong Statistical Correlation Revealed by Quantum Entanglement for Supervised Learning (ECA)
3.4 Neural Network Model Reconstructed from Entangled Quantum States (QNN)
3.5 Discussion
4 Experiment Results
4.1 Baselines
4.2 Datasets
4.3 Hyper-Parameter Setting
5 Conclusions
References
Quantum Simulation Tools and Demonstrations
Exploring IBM Quantum Experience
1 Introduction
2 Navigating IBM Q Experience
2.1 Qiskit in Local Environment
3 IBM Quantum Composer
3.1 Visualise the States of Qubits
3.2 Generate Code Automatically
3.3 Make Our Very Own Quantum Circuit
3.4 Window for IBM Quantum Composer
4 IBM Quantum LAB
4.1 Quantum Circuits
4.2 Quantum Registers
4.3 Qiskit Backends
4.4 Qiskit Simulators
4.5 GHZ Circuit
5 Running Jobs on IBM Real Quantum Machines
6 The Quantum Teleportation Protocol
6.1 Simulating the Teleportation Protocol
6.2 Applications of Teleportation
7 Applications of Quantum Algorithms
8 IBM Q Experience in Research Field
9 Conclusion
References
Quantum Programming on Azure Quantum—An Open Source Tool for Quantum Developers
1 Introduction
2 Azure Quantum
2.1 Who is Azure Quantum For?
2.2 What AQ Offers?
2.3 What is QDK?
2.4 What is Offered by QDK?
2.5 Programming Language Supported by QDK
3 Quantum Program
3.1 Mathematics Required for Quantum Computing
3.2 Ways to Write Quantum Program
4 Quantum Simulators
4.1 Full State Simulator
4.2 Sparse Simulator
4.3 Toffoli Simulator
4.4 Noise Simulator
4.5 Resource Estimator
4.6 Quantum Trace Simulator
5 Azure Quantum Workspace
5.1 Create an Azure Quantum Workspace
5.2 Get Started with Q and an Azure Quantum Notebook
5.3 Submit a Quantum Circuit with Qiskit Using an Azure Quantum Workspace
6 Ways to Develop a Quantum Software
7 Conclusion
References
Survey of Open-Source Tools/Industry Tools to Develop Quantum Software
1 Introduction
2 Quantum Computer Vendors’ Toolkits
2.1 Microsoft Quantum Development Kit
2.2 Amazon Braket
2.3 Google Quantum AI
3 Survey of Open-Source Software
References
Simulating Quantum Principles: Qiskit Versus Cirq
1 Introduction
2 Superposition
3 Entanglement
4 Interference
5 Conclusion
References
Future Direction and Applications
Quantum Machine Learning in Prediction of Breast Cancer
1 Quantum Machine Learning
1.1 Introduction
1.2 Machine Learning
1.3 Deep Quantum Learning
2 Quantum Machine Learning Algorithms
2.1 Quantum Machine Learning Approaches
2.2 Grover Search Algorithm
2.3 Quantum Reinforcement Learning
2.4 Quantum Annealing
2.5 Quantum Neural Networks
2.6 Support Vector Machine
3 Breast Cancer
3.1 Introduction
3.2 Molecular Classification of Breast Cancer
3.3 Diagnosis of Breast Cancer
3.4 Breast Cancer Diagnostic Techniques
3.5 QML in Breast Cancer
4 Future Scope of Quantum Machine Learning for Breast Cancer Prediction
5 Conclusion
References
Understanding of Argon Fluid Sensor Using Single Quantum Well Through K-P Model: A Bio-medical Application Using Semiconductor Based Quantum Structure
1 Introduction
1.1 History
1.2 Fabrication
2 Quantum Well Structure
2.1 Modeling of Well (Infinite)
2.2 Finite Potential Well
3 Concept of Superlattices
4 Application
4.1 Saturable Absorber
4.2 Thermoelectrics
4.3 Solar Cell Devices
5 Mathematical Treatment for QW Structure
5.1 Bandgap Energy
5.2 Carrier Capture and Lifetime
5.3 Case: 2
6 Semiconductor Based on Quantum Structure
7 Semiconductor Based Quantum Structure for Bio-medical Application
8 Proposed Quantum Structure for Measurement of Argon Fluid
9 Result and Interpretation
10 Conclusions
References
A Study on Quantum Cryptography and Its Need
1 Introduction
2 Quantum Key Distribution (QKD)
2.1 Security of Quantum Key Distribution
3 BB84 Protocol
3.1 Detecting: The Eavesdropper, Eve
3.2 Distilling a Secret Key
4 Ekert 91 Protocol
5 Zhang’s Mask Authentication Protocol
5.1 Setup Phase
5.2 Signature-Masking Phase
5.3 Verification Phase
6 Quantum Signature Masked Authentication Protocol-Shi et al. [5]
6.1 Setup Phase
6.2 Signature-Masking Phase
6.3 Verification Phase
6.4 Correctness
7 Quantum Signature Masked Authentication Scheme-Fatahi and Afsheh [6]
7.1 Setup Phase
7.2 Signature-Masking Phase
7.3 Verification Phase
7.4 Correctness
8 Attacks and Security
8.1 Intercept Resend Attack
8.2 Man in the Middle Attack
8.3 Trojan Horses Attack
8.4 Denial of Service Attack (DOS)
8.5 Security of Quantum Key Distribution [2]
8.6 Attacks by Side Channels
9 Observation
10 Conclusion
References
Evolution of Quantum Machine Learning and an Attempt of Its Application for SDN Intrusion Detection
1 Introduction
2 Quantum Computing Terminologies
3 Past, Present, and Future of AI, ML, and QC
4 Experimentation
5 Conclusion
References
Implications of Deep Circuits in Improving Quality of Quantum Question Answering
1 Introduction
2 Literature Review
2.1 Question Classification
2.2 Quantum Machine Learning
3 Dataset
4 Feature Selection
4.1 Content and Non-content Words
4.2 Question Keywords
4.3 Wh-Words
4.4 Nouns
4.5 Verb Count
4.6 N-gram Probabilities
5 Variational Models
6 Quantum Support Vector Machines
7 Data Encoding
8 Experimental Setup
8.1 Application of Question Classification on a Pre-developed QA System
9 Results and Analysis
9.1 Performance of RBQA System While Using QSVM’s Best Classification Results as Features
10 Conclusion and Future Works
References