The exponential growth of high-dimensional data in domains such as computer vision, genomics, and natural language processing has made similarity search a foundational yet challenging operation, primarily due to the "curse of dimensionality" that forces classical systems into computationally prohibitive exhaustive searches. This comprehensive report examines the transformative potential of integrating quantum computing to circumvent these classical bottlenecks. Quantum similarity search utilizes superposition and entanglement to evaluate exponential state spaces, promising quadratic speedups over classical algorithms. The analysis details the transition from classical indexing innovations like memory vectors to modalities of quantum data encoding, notably Amplitude Encoding and the Quantum Pixel Mamun, SM (2026) ……………………………………1 Quantum Similarity Search: Bridging Classical and Quantum Paradigms in High-Dimensional Data Retrieval Representation (QPIXL). It critically assesses vanguard quantum algorithms, particularly the Amplitude Estimation-based Quantum Inner Product (AE-QIP)—which provides a deterministic quadratic speedup over the prohibitive SWAP test—and Quantum Unsupervised Similarity Learning (QUSL), which uses evolutionary algorithms to optimize quantum circuits for complex tasks like image retrieval. Also available on Academia.edu: https://www.academia.edu/attachments/132047821/download_file?s=portfolio
The exponential growth of high-dimensional data in domains such as computer vision, genomics, and natural language processing has made similarity search a foundational yet challenging operation, primarily due to the "curse of dimensionality" that forces classical systems into computationally prohibitive exhaustive searches. This comprehensive report examines the transformative potential of integrating quantum computing to circumvent these classical bottlenecks. Quantum similarity search utilizes superposition and entanglement to evaluate exponential state spaces, promising quadratic speedups over classical algorithms. The analysis details the transition from classical indexing innovations like memory vectors to modalities of quantum data encoding, notably Amplitude Encoding and the Quantum Pixel Mamun, SM (2026) ……………………………………1 Quantum Similarity Search: Bridging Classical and Quantum Paradigms in High-Dimensional Data Retrieval Representation (QPIXL). It critically assesses vanguard quantum algorithms, particularly the Amplitude Estimation-based Quantum Inner Product (AE-QIP)—which provides a deterministic quadratic speedup over the prohibitive SWAP test—and Quantum Unsupervised Similarity Learning (QUSL), which uses evolutionary algorithms to optimize quantum circuits for complex tasks like image retrieval. Also available on Academia.edu: https://www.academia.edu/attachments/132047821/download_file?s=portfolio
The escalating global demand for data storage, projected to reach 1024 bits by 2040, is rapidly outpacing the capacity of classical silicon-based memory, exposing an infrastructural crisis. Synthetic Deoxyribonucleic Acid (DNA) is the premier ultra-high-density archival candidate, offering 1018 bits per cubic centimeter, but its enterprise-scale adoption is severely limited by biochemical (imperfect synthesis, PCR biases) and computational bottlenecks (intractable encoding combinatorics, the Data Loading Problem) inherent to classical architectures. This report details how the strategic integration of Quantum-AI hybrid algorithms—specifically Variational Quantum Eigensolvers (VQE), Quantum Neural Networks (QNNs), and Artificial General Intelligence (AGI) orchestration—provides the necessary computational leverage to overcome these historic limitations. Hybrid frameworks like Quantum-DNA Image Compression (Q-DIC) utilize NISQ-compatible VQEs to enforce hardware Mamun, SM (2026) …………………………….1 Quantum-AI Hybrid Algorithms: Bridging Classical Intelligence, Quantum Acceleration, and Biological Data Storage (Vol-II) K S C synthesis constraints and achieve significant compression, while the 2026 breakthrough of Quantum Oracle Sketching bypasses the need for Quantum Random Access Memory (QRAM) by processing petabyte-scale data streams "on the fly". Also available on Academia.edu: https://www.academia.edu/attachments/132470386/download_file?s=portfolio
Quantum-AI hybrid algorithms represent the most practical near-term pathway for leveraging quantum computing's probabilistic power alongside classical AI's scalability and optimization strengths. In the noisy intermediate-scale quantum (NISQ) era, these hybrids—primarily variational quantum algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA)—delegate hard subproblems (e.g., high-dimensional sampling, optimization under quantum constraints, or feature extraction in entangled spaces) to quantum processors while classical optimizers or neural networks handle parameter tuning, error mitigation, and large-scale data processing (Ferguson et al., 2026; Acampora, 2026). This exploration builds on the 2025 NSF AI+MPS community paper by integrating accelerated timelines: mass deployment of utility-scale quantum computing by August 2027 and AGI substantially before 2030. Hybrid approaches become critical enablers for MPS grand challenges in Mamun, SM (2026)…………………………………………1 Quantum-AI Hybrid Algorithms: Bridging Classical Intelligence, Quantum Acceleration, and Scientific Discovery in the MPS Domains (Vol-I) chemistry (molecular ground states), materials (inverse design), physics (many-body simulation), and astronomy (anomaly detection under uncertainty). Also available on Academia.edu: https://www.academia.edu/attachments/132469868/download_file?s=portfolio
Retrieval-Augmented Generation (RAG) systems rely on high-dimensional vector similarity search to retrieve relevant documents for large language models. However, classical nearest-neighbor methods face scalability limits dueto the "curse of dimensionality" and the computational cost of comparing massive vector sets.The authors propose a hybrid quantum-classical pipeline that leverages quantum computing for similarity evaluation.Experimental results on synthetic data demonstrate that the swap-test similarity estimates closely match classical dot products, and that clustering dramatically reduces search overhead.The present studies show the feasibility of quantum-enhanced retrieval: the quantum similarity scores approximate classical results within statistical error.We discuss accuracy, runtime trade-offs, and the challenges of state preparation in the Noisy Intermediate-Scale Quantum (NISQ) era.
The pursuit of massive foundation models is hindered by the limitations of Maximum Likelihood Estimation (MLE), which struggles with uncertainty quantification and out-of-distribution generalization. The Bayesian framework resolves these deficiencies but is crippled by the "marginalisation bottleneck"—the computational intractability of integrating over high-dimensional parameter spaces. Classical approximations like MCMC and Variational Inference (VI) are fundamentally limited by slow mixing times or sub-optimal local minima. Quantum computing offers a paradigm-shifting resolution, leveraging superposition and entanglement to execute high-dimensional integrals with theoretical exponential speedups by mapping statistical probabilities to quantum amplitude vectors. This review systematically details foundational quantum mapping and state-of-the-art Mamun, SM (2026) ………………………………….1 Quantum Computing for Bayesian Inference: Algorithms, Speedups, Challenges, and Synergies with Scalable Machine Learning (Vol-III) K S C algorithms, including Quantum Bayesian Computation (QBC), Quantum Annealing Variational Bayes (QAVB), and Quantum Gaussian Processes (Q-GPs). A key insight is the deep synergy where inherent quantum noise (decoherence) functionally serves as a native Bayesian regularizer, analogous to classical dropout. Also available on Academia.edu: https://www.academia.edu/attachments/132601227/download_file?s=portfolio
This paper provides a rigorous academic review of the seminal work by Mamun and Grok xAI (2025) on advancing quantum matrix computations through the integration of geometric mean subroutines and Chebyshev-accelerated chain multiplications for nonlinear and iterative challenges in machine learning and quantum information. Following a thorough summary of its salient contributions, we compare and contrast the approach with contemporary research in quantum genetic algorithms (QGAs), variational quantum eigensolvers (VQEs), and tensor network methods. Strengths in polylogarithmic complexity and hybrid fault-tolerance are highlighted, alongside limitations in NISQ-era decoherence. Extending the framework, we propose novel integrations with fractal-recursive ontologies for non-integer dimensional simulations, the Principle of Co-Adaptation for bivariational dynamics in adaptive quantum circuits, and Souriau's axiomatic geometric model for positive-type state representations in high-dimensional entanglement. These extensions unify quadratic tensor structures with emergent fractal geometries, enabling scalable applications in quantum gravity simulations and autopoietic cognitive systems. Implications for post-quantum cryptography and geopolitical quantum strategies are discussed, advocating for interdisciplinary policies to harness transformative potential while mitigating risks. Also available on Academia.edu: https://www.academia.edu/attachments/131744773/download_file?s=portfolio
Quantum computing has emerged as a transformative paradigm for tackling complex matrix operations that underpin applications in machine learning and quantum information. In this paper, we synthesize recent advancements in quantum computing by integrating the quantum subroutines for matrix geometric means from Liu et al. (2025), which enable efficient solutions to nonlinear matrix equations like algebraic Riccati equations, with the Chebyshev-accelerated quantum matrix multiplication framework from Li et al. (2025), offering quadratic speedups for iterative chain operations on complex matrices. Through detailed reviews of each approach, we highlight shared primitives such as block-encoding, quantum singular value transformation, Hermitianization, and polynomial approximations, demonstrating their complementarity in constructing hybrid algorithms for nonlinear iterative problems. These hybrids achieve polylogarithmic complexities in matrix dimensions while optimizing precision and conditioning dependencies, exemplified in frameworks for Riccati iterations and kernel enhancements. Applications are explored in machine learning, including geometric mean metric learning for anomaly detection in classical and quantum data, and in quantum information, such as optimal fidelity and Rényi entropy estimation with accelerated power computations for error correction. Also available on Academia.edu: https://www.academia.edu/attachments/125700844/download_file?s=portfolio