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Submit a ProposalClassical and Quantum Principal Component Analysis in Data Engineering
One Line Description
This essential resource bridges the gap between classical data limitations and the future of computing, giving you the scalable, quantum-accelerated PCA strategies needed to conquer todays massive, high-dimensional datasets.
Description
With the rapid growth of big data in fields such as genomics, internet traffic analysis, and social network data, traditional principal component analysis methods have reached their limits in terms of scalability and computational efficiency. This volume delves into cutting-edge advancements in principal component analysis (PCA), particularly focusing on its applications in handling high-dimensional and large-scale datasets. It also provides practical insights into how PCA can be applied to fields such as machine learning, bioinformatics, and finance. Through real-world case studies, hands-on examples, and guidance on implementing PCA using modern software tools and libraries, the book presents essential principles in quantum information theory and quantum algorithms, establishing the groundwork necessary to comprehend how quantum computing may expedite and improve PCA procedures. This work examines quantum algorithms for matrix decomposition, analyzes the computational benefits of quantum PCA compared to classical approaches, and showcases real applications in quantum machine learning, encryption, and quantum chemistry. Ultimately, this book will serve as a valuable resource for researchers, students, and professionals looking to the future of high-dimensional data analysis and how to apply efficient, scalable methods to PCA in their work.
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With the rapid growth of big data in fields such as genomics, internet traffic analysis, and social network data, traditional principal component analysis methods have reached their limits in terms of scalability and computational efficiency. This volume delves into cutting-edge advancements in principal component analysis (PCA), particularly focusing on its applications in handling high-dimensional and large-scale datasets. It also provides practical insights into how PCA can be applied to fields such as machine learning, bioinformatics, and finance. Through real-world case studies, hands-on examples, and guidance on implementing PCA using modern software tools and libraries, the book presents essential principles in quantum information theory and quantum algorithms, establishing the groundwork necessary to comprehend how quantum computing may expedite and improve PCA procedures. This work examines quantum algorithms for matrix decomposition, analyzes the computational benefits of quantum PCA compared to classical approaches, and showcases real applications in quantum machine learning, encryption, and quantum chemistry. Ultimately, this book will serve as a valuable resource for researchers, students, and professionals looking to the future of high-dimensional data analysis and how to apply efficient, scalable methods to PCA in their work.
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Author / Editor Details
Abhishek Kumar, PhD is an Assistant Director and Associate Professor in the Computer Science and Engineering Department at Chandigarh University, Punjab, India with more than 13 years of experience. He has published more than 50 books and more than 170 publications in reputed, peer-reviewed national and international journals, books, and conferences. His research areas include artificial intelligence, renewable energy image processing, computer vision, data mining, and machine learning.
Abhishek Kumar, PhD is an Assistant Director and Associate Professor in the Computer Science and Engineering Department at Chandigarh University, Punjab, India with more than 13 years of experience. He has published more than 50 books and more than 170 publications in reputed, peer-reviewed national and international journals, books, and conferences. His research areas include artificial intelligence, renewable energy image processing, computer vision, data mining, and machine learning.
J.P. Ananth, PhD is a Professor and Dean in the Internal Quality Assurance Cell at the Sri Krishna College of Engineering and Technology, Coimbatore, India. His research work has been documented in many journals and serves as a reviewer for several international journals and conferences. His research interests include computer vision, pattern recognition, artificial intelligence, and data analytics.
S. Oswalt Manoj, PhD is an Associate Professor in the Department of Computer Science and Engineering at the Sri Krishna College of Engineering and Technology, Tamil Nadu, India. He has more than 100 publications in reputed, peer-reviewed national and international journals, books, and conferences, three published books, and ten patents. His research areas include big data analytics, artificial intelligence, computer vision, machine learning, deep learning, and cloud computing.
Navneet Kaur, PhD is a Professor in the Department of Computer Science and Engineering at Chandigarh University, Mohali, India. She has published many research articles in reputed journals, conferences, and book chapters. Her research interests include wireless sensor networks, wireless body area networks, AI, and cloud computing.
A. Jayanthiladevi, PhD is a Professor of Computer Engineering at Marwadi University. With a strong commitment to ground-breaking research, she has published numerous impactful works in international journals and conferences. Her expertise spans computational life sciences, artificial intelligence, mobile communications, machine learning, quantum computing, and health informatics.
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Table of Contents
Foreword
Preface
1. Integrating Quantum Learning and Principal Component Analysis: From Eigenvectors to Qubits
N. Kousika, M. S. C. Sujitha, R. Rajshree and G. Renugadevi
1.1 Introduction
1.1.1 Classical PCA: The Foundation
1.2 Quantum Computing: A New Paradigm
1.2.1 The Development of QPCA
1.2.2 Advantages of Quantum PCA
1.2.3 Challenges and Frontiers
1.2.4 Emerging Applications
1.2.5 Comparing Classical and Quantum PCA
1.3 Performance and Practical Considerations of QPCA
1.3.1 Hybrid Algorithm Design and Real-World Applications of QPCA
1.4 Quantum Machine Learning Horizons and Future Outlook
1.5 Conclusion
Bibliography
2. Applications in Quantum Cryptography: Harnessing Quantum Principles for Next-Generation Security
Manu Y., Tanuja, Niveditha N. M., Rudresh N. C. and Ravikiran H. N.
2.1 Introduction
2.2 Basics of Quantum Cryptography
2.2.1 Quantum Mechanics Basis for Cryptography
2.2.2 Main Differences: Classical vs. Quantum Security
2.3 Quantum Key Distribution (QKD)
2.3.1 BB84 Protocol
2.3.2 E91 Protocol
2.3.3 Implementations in Real Life
2.3.4 Advantages and Disadvantages
2.4 Applications
2.4.1 QSDC
2.4.2 Quantum Digital Signatures (QDSs)
2.4.3 Quantum Random Number Generators (QRNGs)
2.4.4 Quantum Blockchain and Quantum Voting Systems
2.4.5 Use in National and Defense Communications
2.5 Integration with Traditional Classifications
2.5.1 Quantum-Safe Supercryptography versus Quantum Cryptocard Purple
2.5.2 Key Integration Formula: Symmetric Key Encryption after QKD
2.5.3 Hybrid Cryptographic Model (Post-Quantum + Quantum)
2.5.4 Key Rate Equation in Quantum-Classical Integration
2.5.5 Hybrid Security
2.5.6 Classical-Quantum Communication Middleware
2.6 Current Challenges
2.6.1 Hardware Limitations
2.6.2 Scalability, Cost
2.7 Future Research Directions
2.7.1 Quantum Internet and Networks
2.7.2 Quantum and Post-Quantum Interoperability
2.7.3 Global Standards and Security
2.8 Conclusion
References
3. Quantum PCA in Machine Learning (ML)
V. Vanitha, Manoj Kumaran, L. Hari Prasath and R. Narmadha
3.1 Introduction
3.1.1 Motivation behind Quantum PCA
3.1.2 Major Problems and Limitations of Quantum PCA in ML
3.2 Fundamentals of PCA
3.2.1 Classical PCA: Mathematical Foundation
3.2.2 Eigenvalue Decomposition and Singular Value Decomposition
3.2.3 Limitations of Classical PCA in High-Dimensional Data
3.3 Fundamentals of QC about ML
3.3.1 Introduction to Quantum Gates and Qubits
3.3.2 Principles of Quantum Parallelism and Superposition
3.3.3 Advancing Dimensionality Reduction with QA
3.4 PCA
3.4.1 Mathematical Formulation of QPCA
3.4.2 Quantum Eigenvalue Estimation Techniques
3.4.3 Implementing QPCA with Quantum Circuits
3.4.4 Comparing Complexity to Classical PCA
3.4.5 Algorithm for QPCA
3.5 Applications of Quantum PCA in ML
3.5.1 Compression Techniques for Large-Scale Datasets
3.5.2 Applications in CV and Natural Language Processing (NLP)
3.5.3 Implications for Financial Modeling and Genomics
3.5.4 Applications in Computer Vision and NLP
3.5.5 Implications for Financial Modeling and Genomics
3.6 Experimental Validation and Benchmarking
3.6.1 Fully Functional QPCA Pipelines on Cloud Quantum Platforms
3.6.2 QPCA Implemented within Specific Domains
3.6.3 Regulatory and Ethical Frameworks
3.6.4 A Future Direction: QPCA in the Quantum-AI Future
3.7 Future Directions and Open Problems
3.7.1 Scalability of Real-Hardware Quantum PCA
3.7.2 Efficient Quantum Data Encoding
3.7.3 Hybrid Quantum-Classical Integration
3.7.4 Quantum Noise Resilience and Error Mitigation
3.7.5 Standards and Benchmarks
3.7.6 Discovering New Uses
3.7.7 Theoretical Boundaries and Complexity Analysis
3.8 Conclusion
References
4. Future Trends and Innovations in Quantum Principal Component Analysis (PCA)
Aneesh Pradeep, Raghavendra R., V. Vanitha, Mohamed Uvaze Ahamed and A. Jayanthiladevi
4.1 Introduction
4.2 Emerging Trends in QPCA
4.2.1 Hybrid Quantum-Traditional PCA Frameworks
4.2.2 Application of Variational Algorithms in QPCA
4.3 Hardware Innovations Driving QPCA
4.3.1 Quantum Random Access Memory (qRAM)
4.3.2 Error-Corrected Qubits and Fault-Tolerant Circuits
4.4 Application-Driven Innovations
4.4.1 Real-Time QPCA for Streaming Data
4.4.2 Quantum PCA for Graph and Network Analysis
4.5 Open Problems and Research Challenges
4.5.1 Quantum Data Preparation
4.5.2 Hardware Error Noise and Decoherence
4.5.3 Examining Quantum System Properties QPCA Provides Eigenvalues and Eigenvectors
4.5.4 Resource Improvements QPCA May Attempt to Handle the Data in Larger Dimensions, Thus Requiring an Exponential Number of Qubits and Gate Operations
4.6 Future Directions
4.6.1 Fully Realized QPCA Pipelines on Cloud Quantum Platforms
4.6.2 Customized Domain-Specific QPCA Implementations
4.6.3 Regulatory and Ethical Guidelines
4.7 Conclusion
Bibliography
5. Challenges in Scaling Quantum Principal Component Analysis (QPCA)
R. Kowsalya, A. Jayanthiladevi, John T. Mesia Dhas and J. Viji Gripsy
5.1 Introduction
5.2 A Review of the Literature
5.3 Proposed Methodology
5.3.1 Hybrid Quantum Classical Principal Component Analysis
5.3.2 Classical Preprocessing
5.3.3 Quantum Data Encoding
5.3.4 Quantum Covariance Estimation
5.3.5 SWAP Test for State Overlap Measurement
5.3.6 Error Mitigation Techniques
5.4 Results and Discussion
5.5 Conclusion
5.6 Further Nations
Bibliography
6. Open Research Directions in Quantum Principal Component Analysis (QPCA)
Aneesh Pradeep, A. Jayanthiladevi, B. N. Shobha, Shashikala S. V. and Naveen K. B.
6.1 Introduction
6.2 Mathematical Formulation of QPCA
6.2.1 Classical PCA Basics
6.2.2 QPCA Model
6.2.3 QPCA Algorithm Steps
6.3 Open Research Directions in QPCA
6.3.1 QPCA for Noisy and Imperfect Datasets
6.3.2 Hybrid Quantum-Classical PCA Algorithms
6.3.3 QPCA for High-Dimensional Data Analysis
6.3.4 QPCA for Feature Selection in Machine Learning
6.3.5 QPCA for Real-Time Big Data Analytics
6.4 Challenges and Future Directions
6.4.1 Current Challenges in QPCA
6.4.2 Future Directions
6.5 Case Studies Related to QPCA
6.6 Conclusion
Bibliography
7. Holomorphic Hierophanies: Quantum PCA (HH-QPCA) as Liturgical Practice in Topological Data Sanctuaries
Thamba Meshach W., Soumya T. R., Vineet Kumar Chauhan, Baburao Gaddala and Ananraj I.
7.1 Introduction
7.1.1 The Crisis of Euclidean Assumptions
7.1.2 Beyond the Covariance Matrix: Holomorphic Compression
7.1.3 The Role of Holomorphic Eigenfunctions
7.1.4 Quaternion Encoding and SU(2) Manifold Projection
7.1.5 Feature Sanctification through Entanglement
7.1.6 Framing the Topological Sanctuary
7.2 Related Works
7.2.1 Classical Linear Models: PCA and Its Variants
7.2.2 Topological and Geometric Learning
7.2.3 Quantum and Holomorphic Eigendecomposition
7.2.4 Summary of Gaps and Opportunities
7.3 Model Formulation: Holomorphic Hierophanies Quantum PCA (HH-QPCA)
7.3.1 Quantum State Representation
7.3.2 Holomorphic Function Space Mapping
7.3.3 Quaternion Embedding and SU(2) Projection
7.3.4 Eigenvalue Purification and Feature Selection
7.4 Experimental Results and Validation
7.4.1 Datasets
7.4.2 Evaluation Metrics
7.4.3 Implementation Setup
7.4.4 Results and Analysis
7.4.5 Discussion
7.4.6 Limitations
7.5 Discussion and Future Directions
7.5.1 Strengths of HH-QPCA
7.5.2 Theoretical Contributions
7.5.3 Application Scope
7.5.4 Limitations
7.5.5 Future Directions
7.6 Conclusion
Bibliography
8. Eigenvalue Ephemera: Non-Abelian PCA Dynamics in Quantum-Holographic Image Reconstruction
Manidipa Roy, S. Nancy Lima Christy, P. K. Manoj Kumar, Shoba R. and A. Syed Ismail
8.1 Introduction
8.2 Literature Review
8.2.1 Limitations of Classical PCA in Quantum Contexts
8.2.2 Non-Abelian PCA and SU(2) Manifolds
8.2.3 Quantum-Holographic Image Reconstruction
8.3 Proposed Methodology
8.3.1 Quantum-Encoded Input and Problem Definition
8.3.2 Quaternion Mapping of Complex Photonic Data
8.3.3 Holomorphic Sparsity Operator for Feature Compactness
8.3.4 Embedding into SU(2) Lie Group Manifolds
8.3.5 Ephemeral Eigenvalue Tracking: Dynamic Stability Control
8.3.6 Quaternion-Valued Denoising with SU(2) Awareness
8.3.7 Non-Abelian Tensor Reassembly
8.3.8 Output Representation
8.3.9 Pseudocode Summary
8.3.10 System Performance Summary
8.4 Experimental Validation and Results
8.4.1 Dataset Description
8.4.2 Experimental Setup
8.4.3 Evaluation Metrics
8.4.4 Quantitative Performance Comparison
8.4.5 Visual Analytics and Graph-Based Interpretation
8.4.6 Qualitative Observations
8.4.7 Real-Time Case Study: Encrypted Holography
8.4.8 Ablation Study
8.4.9 Summary
8.5 Discussion and Future Scope
8.5.1 Comparative Insights
8.5.2 Practical Implications
8.5.3 Limitations and Opportunities
8.6 Conclusion
8.6.1 Final Remarks
Bibliography
9. Principal Component Analysis (PCA) in Machine Learning and Data Science
Srinibas Pattanaik, Disha Sharma and Alessandro Vinciarelli
9.1 Introduction
9.1.1 The Primary Ideas of PCA
9.1.2 Applications of Principal Component Analysis
9.2 Mathematical Principles of PCA
9.2.1 The Covariance Coefficient and Correlations Covariance and Correlation Determine the Connection between Two Variables
9.2.2 The Eigenvalues and Eigenvectors for PCA
9.3 Approaches for Executing PCA
9.4 PCA for Architecture and Selection of Features
9.4.1 PCA Variance
9.4.2 Comprehension of Data and Hypothesis
9.5 PCA Axis Visualization
9.6 Modifications and Approaches to PCA
9.7 Conclusion
References
10. Price Discovery, Hedging, and Market Efficiency: A Transformer-Based Analysis of Spot and Futures Markets in Indian Base Metal Commodities
Bhavani M. and Ilankadhir M.
10.1 Introduction
10.1.1 Nature-Inspired Intelligence: A Theoretical Framework
10.1.1.1 Why NII for Commodity Markets?
10.2 Literature Review
10.3 Methodology
10.3.1 Model Selection and Justification
10.3.2 Model Workflow
10.3.3 Data and Preprocessing
10.3.4 Transformer Forecasting Model
10.3.5 Benchmark Models
10.3.6 Price Discovery Analysis
10.3.7 Hedging Effectiveness Measures
10.3.8 Market Efficiency Test
10.4 Results and Discussion
10.4.1 Price Prediction Accuracy
10.4.2 Impact on Hedging and Market Participation
10.4.3 Market Efficiency Insights
10.4.4 Comparative Analysis of Forecasting Models
10.4.5 Forecasting Performance
10.4.6 Price Discovery Findings
10.4.7 Hedging Effectiveness
10.4.8 Market Efficiency Analysis
10.4.9 Discussion
10.5 Conclusion
References
11. Quantum Computing and Blockchain Security: Threats, Solutions, and Future Directions
Navya Mathur, Mokshita Bajpai, Vedika Murarka, Avani Joshi, Ramanathan Lakshmanan and N. Kousika
11.1 Introduction
11.2 Fundamentals of Quantum Computing
11.2.1 Building Blocks of Quantum Circuits
11.3 Structure of Blockchain
11.3.1 Working of Blockchain
11.4 Privacy and Security
11.4.1 Basic Security Properties of Blockchain Technology
11.4.2 Difficulties with Quantum Computing
11.5 Quantum Key Sharing Concept (Blockchain-Based QKD Platform)
11.5.1 Introduction of Quantum Key Sharing (QKS)
11.5.2 Key Components of a Blockchain-Based QKD Platform
11.5.2.1 QKD Protocol
11.5.2.2 Blockchain Integration
11.5.2.3 Network and Scalability Considerations
11.5.3 Applications of Blockchain-Based QKD Platforms
11.5.3.1 Critical Infrastructure Security
11.5.3.2 Financial and Banking Systems
11.5.3.3 IoT Networks
11.5.4 Challenges and Future Directions
11.6 Quantum-Inspired Algorithms: Quantum-Influenced Quantum Walks (QIQW)
11.6.1 Introduction to Quantum-Inspired Algorithms
11.6.2 Basics of Quantum Walks
11.6.2.1 Classical Random Walk
11.6.2.2 Quantum Walks
11.6.3 Properties of Quantum-Inspired Quantum Walks (QIQW)
11.6.4 Applications of QIQW
11.6.5 Challenges and Future Potential
11.7 IoT Smart City Infrastructure: Enhancing Blockchain Security through Quantum Computing
11.7.1 The Role of IoT in Smart Cities
11.7.2 Blockchain-Based Framework for Smart City
11.7.3 Challenges in Implementing Quantum-Enabled Blockchain
11.7.4 Comparison Analysis: Traditional versus Quantum Enabled Systems
11.7.5 Future Directions
11.7.6 Conclusion
11.8 The PDI Model with a Special Emphasis on Safety Issues
11.8.1 Overview of the PDI Model
11.8.2 Key Components of the PDI Model
11.8.3 Privacy Mechanisms in the PDI Model
11.8.4 Decentralization and Its Role in Safety
11.8.5 Addressing Quantum Computing Threats
11.8.6 Future Research Directions
11.9 Advances in Quantum Networks, Secret Codes, and the Way Machines Learn
11.9.1 Quantum Networks: The Next Frontier
11.9.2 Secret Codes: Quantum Encryption and Blockchain Security
11.9.2.1 Quantum Key Distribution (QKD)
11.9.2.2 Post-Quantum Cryptography
11.9.2.3 Quantum Blockchain
11.9.3 How Machines Learn: Quantum Machine Learning
11.9.3.1 Quantum Algorithms for Machine Learning
11.9.3.2 Hybrid Quantum-Classical Models
11.9.3.3 Secure ML Models on Quantum Networks
11.9.4 Challenges and Opportunities
11.10 Where Things Might Go in the Future
11.10.1 The Emerging Landscape of Quantum Computing and Blockchain Security
11.10.2 Advancing Quantum-Resistant Blockchain Protocols
11.10.2.1 Scalable Quantum-Resistant Algorithms
11.10.2.2 Lightweight Cryptographic Solutions
11.10.3 Quantum-Assisted Blockchain Performance Enhancements
11.10.4 Future Use Cases and Applications
11.10.4.1 Quantum-Secure Supply Chains
11.10.4.2 Quantum-Enhanced Healthcare Systems
11.10.4.3 Next-Generation Financial Systems
11.10.5 Challenges and Open Questions
11.11 Conclusion
Bibliography
12. Quantum PCA in Genomics Dimensionality Reduction in Biological Data
S. Ranjana Devi, R. C. Suganthee, E. Grace Mary Kanaga, S. Sadesh and S. Gokul
12.1 Introduction
12.2 Aim and Objectives
12.2.1 Aim
12.2.2 Objectives
12.3 Literature Review
12.4 Research Methodology
12.5 Tables of Quantum PCA in Genomics Dimensionality Reduction in Biological Data
12.5.1 Statement of the Problem
12.6 Further Suggestions for Research
12.7 Scope and Limitations
12.7.1 Limitations of Quantum PCA in Genomics Dimensionality Reduction
12.8 Hypothesis
12.9 Acknowledgments
12.10 Discussion
12.11 Conclusion
Bibliography
13. Randomized and Stochastic Algorithms for Large-Scale PCA
Barakkath Nisha U., Yasir Abdullah R., Sindhu V. and Sujatha T.
13.1 Introduction
13.1.1 Why Scale Matters for PCA in Modern Systems
13.1.2 Limitations of Classical PCA in High Dimensions
13.1.3 The Rise of Randomized and Stochastic PCA
13.1.4 Motivating Scenarios and Design Goals
13.1.5 Minimal Mathematical Framing
13.1.6 What Practitioners Need in Production
13.1.7 Contributions and Chapter Organization
13.2 Background and Related Work
13.2.1 Classical PCA and Its Scaling Bottlenecks
13.2.2 Randomized PCA: Sketches, Power Steps, and Modern Refinements
13.2.3 Stochastic and Online PCA: Single-Pass Learning Under Constraints
13.2.4 Choosing Test Matrices and Managing Numerical Hygiene
13.2.5 Data Quality, Anomalies, and Why Pre-Processing Matters
13.2.6 Hybrid and Systems-Level Patterns
13.2.7 Positioning and Takeaways
13.3 Framework of Randomized and Stochastic Algorithms
13.3.1 Ingest, Centering, and Data-Quality Gates
13.3.2 Randomized PCA Branch (Few-Pass Sketching)
13.3.3 Stochastic/Online PCA Branch (Single-Pass Updates)
13.3.4 Proposed Method: Sketch-Then-Refine Hybrid (SRH)
13.3.5 Distributed Coordination and Serving
13.3.6 Operational Knobs and Defaults
13.4 Applications of Hybrid Swarm Intelligence
13.4.1 Randomized PCA Batch Acceleration at Scale
13.5 Experimental Results and Performance Analysis
13.6 Conclusion
References
14. Distributed and Incremental PCA for Real-Time Applications
Barakkath Nisha U., Yasir Abdullah R., Palani S., Ramprasath J. and Sivaganesan D.
14.1 Introduction
14.1.1 Why Distributed and Incremental
14.1.2 Limits of Classical PCA in Real-Time Pipelines
14.1.3 Our Perspective and Contributions
14.1.4 Reader’s Guide
14.2 Background and Related Work
14.2.1 Classical PCA and Scaling Limits
14.2.2 Distributed PCA: Sketches, Fusion, and Coordination
14.2.3 Incremental (Online) PCA: Single-Pass Subspace Tracking
14.2.4 Numerical Hygiene and Privacy in Production
14.2.5 Data Quality at Ingest: Anomaly-Aware Gates
14.2.6 Domain Evidence from IoT, WSN, and Edge Analytics
14.2.7 What the 2024–2025 Evidence Adds
14.2.8 Synthesis and Gaps
14.3 Framework of Randomized and Stochastic Algorithms
14.3.1 System Architecture
14.3.2 Local Incremental Update at the Worker
14.3.3 Coordinator Side Fusion and Serving
14.3.4 Anomaly-Aware Ingest
14.3.5 Monitoring and Control Loops
14.3.6 Privacy, Robustness, and Fault Tolerance
14.3.7 Operational Defaults and Small Recipes
14.4 Experimental Results and Performance Analysis
14.5 Conclusion
Bibliography
15. Quantum Palimpsests: Eigenvector Erasure and the Rebirth of Latent Space in Holographic Mnemonic Sanctuaries
Shanmugha Priya R. K., Praveena R., B. Saritha, R. Radhika and Prithivirajan P. T.
15.1 Introduction
15.2 Related Work
15.2.1 Quantum Holonomy and Non-Abelian Encodings
15.2.2 Quantum Annealing and Eigenvalue Adaptation
15.2.3 LiDAR Point Clouds and Quantum Compression
15.2.4 Topological Measures via Sheaf Theory
15.2.5 Quantum Discord and Non-Classical Correlations
15.2.6 Applications in Astrobiology and Biosignature Mapping
15.2.7 Cosmological Eigenmapping and Quantum Sensing
15.3 Proposed Work
15.3.1 Introduction to the Adaptive Quantum Geometric Manifold (AQGM)
15.3.2 Integration of Non-Abelian Gauge Theories
15.3.3 Application to LiDAR Point Cloud Compression
15.4 Experimental Setup and Results
15.4.1 Environment Configuration
15.4.2 Dataset Specifications
15.4.3 Evaluation Metrics
15.4.4 Performance Results
15.4.5 Comparative Analysis
15.5 Ablation Study
15.5.1 Experimental Setup
15.5.2 Comparative Results
15.5.3 Insights
15.5.4 Mathematical Drop in TDL
15.6 Conclusion and Future Work
15.6.1 Future Work
References
Index
Back to Top
Foreword
Preface
1. Integrating Quantum Learning and Principal Component Analysis: From Eigenvectors to Qubits
N. Kousika, M. S. C. Sujitha, R. Rajshree and G. Renugadevi
1.1 Introduction
1.1.1 Classical PCA: The Foundation
1.2 Quantum Computing: A New Paradigm
1.2.1 The Development of QPCA
1.2.2 Advantages of Quantum PCA
1.2.3 Challenges and Frontiers
1.2.4 Emerging Applications
1.2.5 Comparing Classical and Quantum PCA
1.3 Performance and Practical Considerations of QPCA
1.3.1 Hybrid Algorithm Design and Real-World Applications of QPCA
1.4 Quantum Machine Learning Horizons and Future Outlook
1.5 Conclusion
Bibliography
2. Applications in Quantum Cryptography: Harnessing Quantum Principles for Next-Generation Security
Manu Y., Tanuja, Niveditha N. M., Rudresh N. C. and Ravikiran H. N.
2.1 Introduction
2.2 Basics of Quantum Cryptography
2.2.1 Quantum Mechanics Basis for Cryptography
2.2.2 Main Differences: Classical vs. Quantum Security
2.3 Quantum Key Distribution (QKD)
2.3.1 BB84 Protocol
2.3.2 E91 Protocol
2.3.3 Implementations in Real Life
2.3.4 Advantages and Disadvantages
2.4 Applications
2.4.1 QSDC
2.4.2 Quantum Digital Signatures (QDSs)
2.4.3 Quantum Random Number Generators (QRNGs)
2.4.4 Quantum Blockchain and Quantum Voting Systems
2.4.5 Use in National and Defense Communications
2.5 Integration with Traditional Classifications
2.5.1 Quantum-Safe Supercryptography versus Quantum Cryptocard Purple
2.5.2 Key Integration Formula: Symmetric Key Encryption after QKD
2.5.3 Hybrid Cryptographic Model (Post-Quantum + Quantum)
2.5.4 Key Rate Equation in Quantum-Classical Integration
2.5.5 Hybrid Security
2.5.6 Classical-Quantum Communication Middleware
2.6 Current Challenges
2.6.1 Hardware Limitations
2.6.2 Scalability, Cost
2.7 Future Research Directions
2.7.1 Quantum Internet and Networks
2.7.2 Quantum and Post-Quantum Interoperability
2.7.3 Global Standards and Security
2.8 Conclusion
References
3. Quantum PCA in Machine Learning (ML)
V. Vanitha, Manoj Kumaran, L. Hari Prasath and R. Narmadha
3.1 Introduction
3.1.1 Motivation behind Quantum PCA
3.1.2 Major Problems and Limitations of Quantum PCA in ML
3.2 Fundamentals of PCA
3.2.1 Classical PCA: Mathematical Foundation
3.2.2 Eigenvalue Decomposition and Singular Value Decomposition
3.2.3 Limitations of Classical PCA in High-Dimensional Data
3.3 Fundamentals of QC about ML
3.3.1 Introduction to Quantum Gates and Qubits
3.3.2 Principles of Quantum Parallelism and Superposition
3.3.3 Advancing Dimensionality Reduction with QA
3.4 PCA
3.4.1 Mathematical Formulation of QPCA
3.4.2 Quantum Eigenvalue Estimation Techniques
3.4.3 Implementing QPCA with Quantum Circuits
3.4.4 Comparing Complexity to Classical PCA
3.4.5 Algorithm for QPCA
3.5 Applications of Quantum PCA in ML
3.5.1 Compression Techniques for Large-Scale Datasets
3.5.2 Applications in CV and Natural Language Processing (NLP)
3.5.3 Implications for Financial Modeling and Genomics
3.5.4 Applications in Computer Vision and NLP
3.5.5 Implications for Financial Modeling and Genomics
3.6 Experimental Validation and Benchmarking
3.6.1 Fully Functional QPCA Pipelines on Cloud Quantum Platforms
3.6.2 QPCA Implemented within Specific Domains
3.6.3 Regulatory and Ethical Frameworks
3.6.4 A Future Direction: QPCA in the Quantum-AI Future
3.7 Future Directions and Open Problems
3.7.1 Scalability of Real-Hardware Quantum PCA
3.7.2 Efficient Quantum Data Encoding
3.7.3 Hybrid Quantum-Classical Integration
3.7.4 Quantum Noise Resilience and Error Mitigation
3.7.5 Standards and Benchmarks
3.7.6 Discovering New Uses
3.7.7 Theoretical Boundaries and Complexity Analysis
3.8 Conclusion
References
4. Future Trends and Innovations in Quantum Principal Component Analysis (PCA)
Aneesh Pradeep, Raghavendra R., V. Vanitha, Mohamed Uvaze Ahamed and A. Jayanthiladevi
4.1 Introduction
4.2 Emerging Trends in QPCA
4.2.1 Hybrid Quantum-Traditional PCA Frameworks
4.2.2 Application of Variational Algorithms in QPCA
4.3 Hardware Innovations Driving QPCA
4.3.1 Quantum Random Access Memory (qRAM)
4.3.2 Error-Corrected Qubits and Fault-Tolerant Circuits
4.4 Application-Driven Innovations
4.4.1 Real-Time QPCA for Streaming Data
4.4.2 Quantum PCA for Graph and Network Analysis
4.5 Open Problems and Research Challenges
4.5.1 Quantum Data Preparation
4.5.2 Hardware Error Noise and Decoherence
4.5.3 Examining Quantum System Properties QPCA Provides Eigenvalues and Eigenvectors
4.5.4 Resource Improvements QPCA May Attempt to Handle the Data in Larger Dimensions, Thus Requiring an Exponential Number of Qubits and Gate Operations
4.6 Future Directions
4.6.1 Fully Realized QPCA Pipelines on Cloud Quantum Platforms
4.6.2 Customized Domain-Specific QPCA Implementations
4.6.3 Regulatory and Ethical Guidelines
4.7 Conclusion
Bibliography
5. Challenges in Scaling Quantum Principal Component Analysis (QPCA)
R. Kowsalya, A. Jayanthiladevi, John T. Mesia Dhas and J. Viji Gripsy
5.1 Introduction
5.2 A Review of the Literature
5.3 Proposed Methodology
5.3.1 Hybrid Quantum Classical Principal Component Analysis
5.3.2 Classical Preprocessing
5.3.3 Quantum Data Encoding
5.3.4 Quantum Covariance Estimation
5.3.5 SWAP Test for State Overlap Measurement
5.3.6 Error Mitigation Techniques
5.4 Results and Discussion
5.5 Conclusion
5.6 Further Nations
Bibliography
6. Open Research Directions in Quantum Principal Component Analysis (QPCA)
Aneesh Pradeep, A. Jayanthiladevi, B. N. Shobha, Shashikala S. V. and Naveen K. B.
6.1 Introduction
6.2 Mathematical Formulation of QPCA
6.2.1 Classical PCA Basics
6.2.2 QPCA Model
6.2.3 QPCA Algorithm Steps
6.3 Open Research Directions in QPCA
6.3.1 QPCA for Noisy and Imperfect Datasets
6.3.2 Hybrid Quantum-Classical PCA Algorithms
6.3.3 QPCA for High-Dimensional Data Analysis
6.3.4 QPCA for Feature Selection in Machine Learning
6.3.5 QPCA for Real-Time Big Data Analytics
6.4 Challenges and Future Directions
6.4.1 Current Challenges in QPCA
6.4.2 Future Directions
6.5 Case Studies Related to QPCA
6.6 Conclusion
Bibliography
7. Holomorphic Hierophanies: Quantum PCA (HH-QPCA) as Liturgical Practice in Topological Data Sanctuaries
Thamba Meshach W., Soumya T. R., Vineet Kumar Chauhan, Baburao Gaddala and Ananraj I.
7.1 Introduction
7.1.1 The Crisis of Euclidean Assumptions
7.1.2 Beyond the Covariance Matrix: Holomorphic Compression
7.1.3 The Role of Holomorphic Eigenfunctions
7.1.4 Quaternion Encoding and SU(2) Manifold Projection
7.1.5 Feature Sanctification through Entanglement
7.1.6 Framing the Topological Sanctuary
7.2 Related Works
7.2.1 Classical Linear Models: PCA and Its Variants
7.2.2 Topological and Geometric Learning
7.2.3 Quantum and Holomorphic Eigendecomposition
7.2.4 Summary of Gaps and Opportunities
7.3 Model Formulation: Holomorphic Hierophanies Quantum PCA (HH-QPCA)
7.3.1 Quantum State Representation
7.3.2 Holomorphic Function Space Mapping
7.3.3 Quaternion Embedding and SU(2) Projection
7.3.4 Eigenvalue Purification and Feature Selection
7.4 Experimental Results and Validation
7.4.1 Datasets
7.4.2 Evaluation Metrics
7.4.3 Implementation Setup
7.4.4 Results and Analysis
7.4.5 Discussion
7.4.6 Limitations
7.5 Discussion and Future Directions
7.5.1 Strengths of HH-QPCA
7.5.2 Theoretical Contributions
7.5.3 Application Scope
7.5.4 Limitations
7.5.5 Future Directions
7.6 Conclusion
Bibliography
8. Eigenvalue Ephemera: Non-Abelian PCA Dynamics in Quantum-Holographic Image Reconstruction
Manidipa Roy, S. Nancy Lima Christy, P. K. Manoj Kumar, Shoba R. and A. Syed Ismail
8.1 Introduction
8.2 Literature Review
8.2.1 Limitations of Classical PCA in Quantum Contexts
8.2.2 Non-Abelian PCA and SU(2) Manifolds
8.2.3 Quantum-Holographic Image Reconstruction
8.3 Proposed Methodology
8.3.1 Quantum-Encoded Input and Problem Definition
8.3.2 Quaternion Mapping of Complex Photonic Data
8.3.3 Holomorphic Sparsity Operator for Feature Compactness
8.3.4 Embedding into SU(2) Lie Group Manifolds
8.3.5 Ephemeral Eigenvalue Tracking: Dynamic Stability Control
8.3.6 Quaternion-Valued Denoising with SU(2) Awareness
8.3.7 Non-Abelian Tensor Reassembly
8.3.8 Output Representation
8.3.9 Pseudocode Summary
8.3.10 System Performance Summary
8.4 Experimental Validation and Results
8.4.1 Dataset Description
8.4.2 Experimental Setup
8.4.3 Evaluation Metrics
8.4.4 Quantitative Performance Comparison
8.4.5 Visual Analytics and Graph-Based Interpretation
8.4.6 Qualitative Observations
8.4.7 Real-Time Case Study: Encrypted Holography
8.4.8 Ablation Study
8.4.9 Summary
8.5 Discussion and Future Scope
8.5.1 Comparative Insights
8.5.2 Practical Implications
8.5.3 Limitations and Opportunities
8.6 Conclusion
8.6.1 Final Remarks
Bibliography
9. Principal Component Analysis (PCA) in Machine Learning and Data Science
Srinibas Pattanaik, Disha Sharma and Alessandro Vinciarelli
9.1 Introduction
9.1.1 The Primary Ideas of PCA
9.1.2 Applications of Principal Component Analysis
9.2 Mathematical Principles of PCA
9.2.1 The Covariance Coefficient and Correlations Covariance and Correlation Determine the Connection between Two Variables
9.2.2 The Eigenvalues and Eigenvectors for PCA
9.3 Approaches for Executing PCA
9.4 PCA for Architecture and Selection of Features
9.4.1 PCA Variance
9.4.2 Comprehension of Data and Hypothesis
9.5 PCA Axis Visualization
9.6 Modifications and Approaches to PCA
9.7 Conclusion
References
10. Price Discovery, Hedging, and Market Efficiency: A Transformer-Based Analysis of Spot and Futures Markets in Indian Base Metal Commodities
Bhavani M. and Ilankadhir M.
10.1 Introduction
10.1.1 Nature-Inspired Intelligence: A Theoretical Framework
10.1.1.1 Why NII for Commodity Markets?
10.2 Literature Review
10.3 Methodology
10.3.1 Model Selection and Justification
10.3.2 Model Workflow
10.3.3 Data and Preprocessing
10.3.4 Transformer Forecasting Model
10.3.5 Benchmark Models
10.3.6 Price Discovery Analysis
10.3.7 Hedging Effectiveness Measures
10.3.8 Market Efficiency Test
10.4 Results and Discussion
10.4.1 Price Prediction Accuracy
10.4.2 Impact on Hedging and Market Participation
10.4.3 Market Efficiency Insights
10.4.4 Comparative Analysis of Forecasting Models
10.4.5 Forecasting Performance
10.4.6 Price Discovery Findings
10.4.7 Hedging Effectiveness
10.4.8 Market Efficiency Analysis
10.4.9 Discussion
10.5 Conclusion
References
11. Quantum Computing and Blockchain Security: Threats, Solutions, and Future Directions
Navya Mathur, Mokshita Bajpai, Vedika Murarka, Avani Joshi, Ramanathan Lakshmanan and N. Kousika
11.1 Introduction
11.2 Fundamentals of Quantum Computing
11.2.1 Building Blocks of Quantum Circuits
11.3 Structure of Blockchain
11.3.1 Working of Blockchain
11.4 Privacy and Security
11.4.1 Basic Security Properties of Blockchain Technology
11.4.2 Difficulties with Quantum Computing
11.5 Quantum Key Sharing Concept (Blockchain-Based QKD Platform)
11.5.1 Introduction of Quantum Key Sharing (QKS)
11.5.2 Key Components of a Blockchain-Based QKD Platform
11.5.2.1 QKD Protocol
11.5.2.2 Blockchain Integration
11.5.2.3 Network and Scalability Considerations
11.5.3 Applications of Blockchain-Based QKD Platforms
11.5.3.1 Critical Infrastructure Security
11.5.3.2 Financial and Banking Systems
11.5.3.3 IoT Networks
11.5.4 Challenges and Future Directions
11.6 Quantum-Inspired Algorithms: Quantum-Influenced Quantum Walks (QIQW)
11.6.1 Introduction to Quantum-Inspired Algorithms
11.6.2 Basics of Quantum Walks
11.6.2.1 Classical Random Walk
11.6.2.2 Quantum Walks
11.6.3 Properties of Quantum-Inspired Quantum Walks (QIQW)
11.6.4 Applications of QIQW
11.6.5 Challenges and Future Potential
11.7 IoT Smart City Infrastructure: Enhancing Blockchain Security through Quantum Computing
11.7.1 The Role of IoT in Smart Cities
11.7.2 Blockchain-Based Framework for Smart City
11.7.3 Challenges in Implementing Quantum-Enabled Blockchain
11.7.4 Comparison Analysis: Traditional versus Quantum Enabled Systems
11.7.5 Future Directions
11.7.6 Conclusion
11.8 The PDI Model with a Special Emphasis on Safety Issues
11.8.1 Overview of the PDI Model
11.8.2 Key Components of the PDI Model
11.8.3 Privacy Mechanisms in the PDI Model
11.8.4 Decentralization and Its Role in Safety
11.8.5 Addressing Quantum Computing Threats
11.8.6 Future Research Directions
11.9 Advances in Quantum Networks, Secret Codes, and the Way Machines Learn
11.9.1 Quantum Networks: The Next Frontier
11.9.2 Secret Codes: Quantum Encryption and Blockchain Security
11.9.2.1 Quantum Key Distribution (QKD)
11.9.2.2 Post-Quantum Cryptography
11.9.2.3 Quantum Blockchain
11.9.3 How Machines Learn: Quantum Machine Learning
11.9.3.1 Quantum Algorithms for Machine Learning
11.9.3.2 Hybrid Quantum-Classical Models
11.9.3.3 Secure ML Models on Quantum Networks
11.9.4 Challenges and Opportunities
11.10 Where Things Might Go in the Future
11.10.1 The Emerging Landscape of Quantum Computing and Blockchain Security
11.10.2 Advancing Quantum-Resistant Blockchain Protocols
11.10.2.1 Scalable Quantum-Resistant Algorithms
11.10.2.2 Lightweight Cryptographic Solutions
11.10.3 Quantum-Assisted Blockchain Performance Enhancements
11.10.4 Future Use Cases and Applications
11.10.4.1 Quantum-Secure Supply Chains
11.10.4.2 Quantum-Enhanced Healthcare Systems
11.10.4.3 Next-Generation Financial Systems
11.10.5 Challenges and Open Questions
11.11 Conclusion
Bibliography
12. Quantum PCA in Genomics Dimensionality Reduction in Biological Data
S. Ranjana Devi, R. C. Suganthee, E. Grace Mary Kanaga, S. Sadesh and S. Gokul
12.1 Introduction
12.2 Aim and Objectives
12.2.1 Aim
12.2.2 Objectives
12.3 Literature Review
12.4 Research Methodology
12.5 Tables of Quantum PCA in Genomics Dimensionality Reduction in Biological Data
12.5.1 Statement of the Problem
12.6 Further Suggestions for Research
12.7 Scope and Limitations
12.7.1 Limitations of Quantum PCA in Genomics Dimensionality Reduction
12.8 Hypothesis
12.9 Acknowledgments
12.10 Discussion
12.11 Conclusion
Bibliography
13. Randomized and Stochastic Algorithms for Large-Scale PCA
Barakkath Nisha U., Yasir Abdullah R., Sindhu V. and Sujatha T.
13.1 Introduction
13.1.1 Why Scale Matters for PCA in Modern Systems
13.1.2 Limitations of Classical PCA in High Dimensions
13.1.3 The Rise of Randomized and Stochastic PCA
13.1.4 Motivating Scenarios and Design Goals
13.1.5 Minimal Mathematical Framing
13.1.6 What Practitioners Need in Production
13.1.7 Contributions and Chapter Organization
13.2 Background and Related Work
13.2.1 Classical PCA and Its Scaling Bottlenecks
13.2.2 Randomized PCA: Sketches, Power Steps, and Modern Refinements
13.2.3 Stochastic and Online PCA: Single-Pass Learning Under Constraints
13.2.4 Choosing Test Matrices and Managing Numerical Hygiene
13.2.5 Data Quality, Anomalies, and Why Pre-Processing Matters
13.2.6 Hybrid and Systems-Level Patterns
13.2.7 Positioning and Takeaways
13.3 Framework of Randomized and Stochastic Algorithms
13.3.1 Ingest, Centering, and Data-Quality Gates
13.3.2 Randomized PCA Branch (Few-Pass Sketching)
13.3.3 Stochastic/Online PCA Branch (Single-Pass Updates)
13.3.4 Proposed Method: Sketch-Then-Refine Hybrid (SRH)
13.3.5 Distributed Coordination and Serving
13.3.6 Operational Knobs and Defaults
13.4 Applications of Hybrid Swarm Intelligence
13.4.1 Randomized PCA Batch Acceleration at Scale
13.5 Experimental Results and Performance Analysis
13.6 Conclusion
References
14. Distributed and Incremental PCA for Real-Time Applications
Barakkath Nisha U., Yasir Abdullah R., Palani S., Ramprasath J. and Sivaganesan D.
14.1 Introduction
14.1.1 Why Distributed and Incremental
14.1.2 Limits of Classical PCA in Real-Time Pipelines
14.1.3 Our Perspective and Contributions
14.1.4 Reader’s Guide
14.2 Background and Related Work
14.2.1 Classical PCA and Scaling Limits
14.2.2 Distributed PCA: Sketches, Fusion, and Coordination
14.2.3 Incremental (Online) PCA: Single-Pass Subspace Tracking
14.2.4 Numerical Hygiene and Privacy in Production
14.2.5 Data Quality at Ingest: Anomaly-Aware Gates
14.2.6 Domain Evidence from IoT, WSN, and Edge Analytics
14.2.7 What the 2024–2025 Evidence Adds
14.2.8 Synthesis and Gaps
14.3 Framework of Randomized and Stochastic Algorithms
14.3.1 System Architecture
14.3.2 Local Incremental Update at the Worker
14.3.3 Coordinator Side Fusion and Serving
14.3.4 Anomaly-Aware Ingest
14.3.5 Monitoring and Control Loops
14.3.6 Privacy, Robustness, and Fault Tolerance
14.3.7 Operational Defaults and Small Recipes
14.4 Experimental Results and Performance Analysis
14.5 Conclusion
Bibliography
15. Quantum Palimpsests: Eigenvector Erasure and the Rebirth of Latent Space in Holographic Mnemonic Sanctuaries
Shanmugha Priya R. K., Praveena R., B. Saritha, R. Radhika and Prithivirajan P. T.
15.1 Introduction
15.2 Related Work
15.2.1 Quantum Holonomy and Non-Abelian Encodings
15.2.2 Quantum Annealing and Eigenvalue Adaptation
15.2.3 LiDAR Point Clouds and Quantum Compression
15.2.4 Topological Measures via Sheaf Theory
15.2.5 Quantum Discord and Non-Classical Correlations
15.2.6 Applications in Astrobiology and Biosignature Mapping
15.2.7 Cosmological Eigenmapping and Quantum Sensing
15.3 Proposed Work
15.3.1 Introduction to the Adaptive Quantum Geometric Manifold (AQGM)
15.3.2 Integration of Non-Abelian Gauge Theories
15.3.3 Application to LiDAR Point Cloud Compression
15.4 Experimental Setup and Results
15.4.1 Environment Configuration
15.4.2 Dataset Specifications
15.4.3 Evaluation Metrics
15.4.4 Performance Results
15.4.5 Comparative Analysis
15.5 Ablation Study
15.5.1 Experimental Setup
15.5.2 Comparative Results
15.5.3 Insights
15.5.4 Mathematical Drop in TDL
15.6 Conclusion and Future Work
15.6.1 Future Work
References
Index
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