Quantum Computing Environments

Preface
Acknowledgments
Contents
About the Editors
1 Quantum Information Processing
	1.1 Schrødinger Equation
	1.2 Linear Algebra for Quantum Information Processing and Quantum Computing
		1.2.1 Linear Vector Space
		1.2.2 Hilbert Space
	1.3 Postulates of Quantum Mechanics
		1.3.1 Positive Operator Valued Measure (POVM)
	1.4 Entanglement
		1.4.1 Bell's Theorem
			1.4.1.1 A Game of Communication Between Two Parties
			1.4.1.2 A Quantum Mechanical Strategy
	1.5 Quantum Circuit
		1.5.1 Classical Circuit
		1.5.2 Reversible Computation
		1.5.3 Quantum Gates
		1.5.4 Pauli Group
		1.5.5 Clifford Group
		1.5.6 C3 Group
			1.5.6.1 No Cloning Theorem
	1.6 Quantum Algorithms
		1.6.1 Deutsch Algorithm
			1.6.1.1 Phase Kickback
			1.6.1.2 Back to Deutsch Algorithm
		1.6.2 Deutsch Jozsa Algorithm
			1.6.2.1 Classical Approach
			1.6.2.2 Quantum Approach
		1.6.3 Simon Algorithm
			1.6.3.1 Classical Approach
			1.6.3.2 Quantum Approach
		1.6.4 Bernstein–Vazirani Algorithm
			1.6.4.1 Classical Approach
			1.6.4.2 Quantum Approach
		1.6.5 Grover Algorithm
			1.6.5.1 Classical Approach
			1.6.5.2 Quantum Approach
			1.6.5.3 Geometric Approach to Grover Algorithm
	References
2 Quantum Compiling
	2.1 Introduction
	2.2 Layered Architecture and Quantum Compiling Stack
		2.2.1 The Five-Layer Architecture of Quantum Computers
		2.2.2 Description of the Five Layers of Quantum Computers
		2.2.3 Transposing the Five-Layer Architecture to Adiabatic Quantum Computers
	2.3 Quantum Compiling of Gate-Model Quantum Computers
		2.3.1 Gate-Model Quantum Computers
		2.3.2 The Standard Circuit Model
		2.3.3 The Quantum Compiling Problem
		2.3.4 The Solovay–Kitaev Theorem
		2.3.5 Beyond the Solovay–Kitaev Theorem
	2.4 Quantum Firmware for Adiabatic Quantum Computers
		2.4.1 Layer 1—Physical: The Annealing Process
		2.4.2 Layer 2—Virtual: AQC Topology
		2.4.3 Layer 3—Quantum Error Correction
		2.4.4 Layer 4—Logical: Implementing QUBO and HUBO Problems on D-Wave
		2.4.5 Layer 5—Algorithms: AQC as a Sampler
	2.5 Commercial Solutions for Quantum Firmware and Quantum Compiling
		2.5.1 Major Players in the Quantum Compiler Market
		2.5.2 Products for Quantum Compiling
		2.5.3 Future of the Quantum Compiling
	References
3 The Future Quantum Internet
	3.1 Introduction
	3.2 The Quantum Internet Fundamentals
		3.2.1 Single Qubit
		3.2.2 Multi-Qubits
		3.2.3 Entanglement and Bell States
		3.2.4 No-cloning Theorem
	3.3 Entanglement in Quantum Networks
		3.3.1 Entanglement-Based Quantum Network Applications
		3.3.2 Quantum Error Correction
	3.4 Teleportation and Entanglement Swapping
	3.5 Entanglement Distillation
	3.6 Quantum Repeaters
	3.7 Quantum Internet Architecture
		3.7.1 Goals of a Quantum Internet Architecture
		3.7.2 Physical Layer
		3.7.3 Link Layer
	3.8 Quantum Internet's Applications and Use Cases
		3.8.1 Control Plane Applications
		3.8.2 Quantum Security
		3.8.3 Fast Byzantine Negotiation
		3.8.4 Position Verification Mechanisms
			3.8.4.1 Quantum Verification Protocols (1D-QPVθ)
		3.8.5 Increasing the Data Rate Between Nodes: Superdense Codes
		3.8.6 Empowered Channel Capacity and Noise Resilience
	3.9 Quantum Empowered Optimization and Artificial Intelligence
		3.9.1 Network Clock Synchronization
		3.9.2 User Plane Applications
		3.9.3 Quantum Computing as a Service
	3.10 Direct and Distributed Quantum Computing
	3.11 Quantum Internet in the Space
	3.12 How Far Is a Quantum Internet from Reality?
	References
4 Quantum Radar
	4.1 Introduction
	4.2 Theory
		4.2.1 Quantum Sensor Types
		4.2.2 Separable and Non-separable States
		4.2.3 Coherent and Squeezed States
		4.2.4 Effect of Amplification on Quantum Noise
		4.2.5 Fundamental Limits on Quantum Measurements
	4.3 Proposals and Experiments on Quantum Radar
		4.3.1 Interferometric Quantum Radars
		4.3.2 Quantum Illumination-Based Quantum Radars
			4.3.2.1 Introduction on Continuous Variables and Gaussian States
			4.3.2.2 Two-Mode Squeezed Vacuum Beam
			4.3.2.3 Quantum Illumination with Gaussian States
			4.3.2.4 Quantum Illumination with Gaussian States in Optical Domain
			4.3.2.5 Quantum Illumination with Gaussian States in Microwave Domain
	4.4 Discussion and Comparison of Quantum Radar Techniques
	4.5 A General Comparison of Quantum Radar and Classical Radar
	4.6 Conclusion and Outlook: Potential of Practical Applications of Quantum Radar
	References
5 Quantum Finance
	5.1 Quantum Currency
	5.2 Quantum Coin
	5.3 Quantum Blockchain and Post-Quantum Blockchain
	5.4 Quantum Cheques and Quantum E-Cheques
		5.4.1 Quantum Cheques
		5.4.2 Quantum e-Cheques as Multiparty Quantum Secrete Sharing
		5.4.3 Transferring Quantum E-Cheques in Nonsecured Channels
		5.4.4 Conclusion
	5.5 Quantum Risk Management
	5.6 Forecasting of Time Series
	5.7 Portfolio Creation
	References
6 Future Perspectives of Quantum Applications Using AI
	6.1 Introduction
	6.2 Quantum Internet and Satellite and Underwater Communication Using Teleportation Techniques
	6.3 Countering Cyberattacks on Quantum Key Distribution Using ML Models on Security, Privacy, and Cryptography
	6.4 Quantum Sensing by Applying AI Learned Techniques to Detect Early Cancer and Improved Treatment
	6.5 Designing Quantum Materials Using AI and Machine Learning
	6.6 Quantum Dots
		6.6.1 Introduction
		6.6.2 Applications of Quantum Dots (Fig. 6.4)
			6.6.2.1 Biomedicine
			6.6.2.2 Photovoltaic
			6.6.2.3 Graphene Quantum Dots
			6.6.2.4 Display Devices
			6.6.2.5 Agriculture
			6.6.2.6 Data Storage
	References
Index