A Critical Review of "A Survey of Quantum Computing Algorithms for Mathematical Optimization: State-of-the-Art in Research & Exploration of Further Possibilities"
This review critically examines the preprint by Chakrabarti, Changdar, and Khanda (2026), which provides a comprehensive survey of quantum computing algorithms applied to mathematical optimization. The paper traces the evolution from foundational quantum mechanics to hybrid quantum-classical methods, while introducing novel contributions in quantum collaborative filtering and social network optimization. We contextualize the survey within the broader quantum computing literature, highlighting its pedagogical strengths in bridging theory and application. Key postulates, such as the role of superposition and entanglement in optimization, are evaluated alongside major findings, including simulations demonstrating practical feasibility on noisy intermediate-scale quantum (NISQ) hardware. Comparisons with contemporaneous works reveal the survey's unique emphasis on variational algorithms for machine learning tasks, though gaps in empirical validation persist. We conclude with directions for future research, advocating for scalable implementations and interdisciplinary integrations. This review underscores the paper's value as an accessible entry point for optimization researchers entering quantum paradigms. Also available on Academia.edu: https://www.academia.edu/attachments/131787157/download_file?s=portfolio
This review critically examines the preprint by Chakrabarti, Changdar, and Khanda (2026), which provides a comprehensive survey of quantum computing algorithms applied to mathematical optimization. The paper traces the evolution from foundational quantum mechanics to hybrid quantum-classical methods, while introducing novel contributions in quantum collaborative filtering and social network optimization. We contextualize the survey within the broader quantum computing literature, highlighting its pedagogical strengths in bridging theory and application. Key postulates, such as the role of superposition and entanglement in optimization, are evaluated alongside major findings, including simulations demonstrating practical feasibility on noisy intermediate-scale quantum (NISQ) hardware. Comparisons with contemporaneous works reveal the survey's unique emphasis on variational algorithms for machine learning tasks, though gaps in empirical validation persist. We conclude with directions for future research, advocating for scalable implementations and interdisciplinary integrations. This review underscores the paper's value as an accessible entry point for optimization researchers entering quantum paradigms. Also available on Academia.edu: https://www.academia.edu/attachments/131787157/download_file?s=portfolio
The intersection of quantum mechanics and mathematical optimization represents a fundamental reimagining of computational complexity, shifting the paradigm from deterministic Boolean logic to probabilistic unitary evolution within a complex Hilbert space. This report provides an exhaustive, critical analysis of the 2026 survey A Survey of Quantum Computing Algorithms for Mathematical Optimization: State-of-the-Art in Research & Exploration of Further Possibilities by Chakrabarti, Changdar, and Khanda. By contextualizing their findings within the rigorous frameworks of Hamiltonian mechanics and the geometry of time—specifically drawing upon the Anandan-Aharonov relation and the structured time geometry of Modgil—we elucidate the physical mechanisms that underpin quantum advantage. We rigorously examine the novel Quantum Collaborative Filtering (QCF) and Quantum Social Network (QSN) models proposed by the authors, deconstructing the specific Hamiltonians that drive their variational landscapes. Furthermore, we posit that the efficiency of these algorithms is governed by the geodesic curvature of the projective Hilbert space, where the "speed" of optimization is physically constrained by the energy Mamun, SM (2026) ………………………………………………….1 Hamiltonian Dynamics and the Geometry of Time: A Variational Framework for Quantum Mathematical Optimization uncertainty of the driving Hamiltonian. Also available on Academia.edu: https://www.academia.edu/attachments/131793645/download_file?s=portfolio
This paper presents a comprehensive review and systematic coverage of foundational quantum optimization algorithms-QAOA, Quantum Annealing, VQE, VQLS, and HHL-tracing their development all the way from Schrödinger's equation through gate-based quantum computing (Deutsch, Deutsch-Jozsa, Bernstein-Vazirani, QFT, Shor's, and Grover's algorithms) to hybrid quantum-classical approaches for NISQ-era hardware. We also present the transverse field Ising model's role in quantum annealing as well as practical hardware implementations with the Chimera, Pegasus, and Zephyr topologies of the D-Wave quantum annealer, addressing key challenges including barren plateaus, circuit trainability, and noise resilience. In the simulations section, quantum computing applications to collaborative filtering and social network optimization have been presented. We introduce two original contributions: (1) a quantum collaborative filtering model based on VQE principles that leverages quantum entanglement to represent user-item relationships, requiring logarithmically fewer parameters than classical embedding methods while accessing exponentially larger state spaces, and demonstrating test RMSE of 0.85 on synthetic data; and (2) a Quantum Social Network (QSN) framework modeling belief dynamics through superposition and entanglement, revealing emergent consensus and polarization phenomena validated via Qiskit simulations. By demonstrating that variational quantum algorithms can tackle real-world recommendation and network optimization problems on current hardware, we bridge theoretical quantum computing with practical machine learning applications and identify concrete pathways toward quantum advantage beyond traditional combinatorial optimization.
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, grounded in the principles of superposition and entanglement, has emerged as a revolutionary paradigm with the potential to outperform classical systems in specific computational tasks. This paper presents a comprehensive survey of the foundational concepts, algorithmic developments, hardware architectures, and programming ecosystems in quantum computing. We analyze the current progress in key application areas such as cryptography, machine learning, optimization, and quantum chemistry. Furthermore, we review recent advances between 2023 and 2025, including developments in fault-tolerant architectures and quantum error correction. The paper also discusses the significant technical challenges that hinder large-scale practical deployment, including qubit scalability, decoherence, and programming limitations. By synthesizing literature across disciplines, this review aims to provide a holistic understanding of the quantum computing landscape and outline critical directions for future research and integration with classical systems.
Quantum computing offers a fundamentally new paradigm for solving complex optimisation and learning tasks by exploiting superposition, entanglement, and other quantum phenomena. Over the past decade, research has increasingly focused on quantum-enhanced approaches to optimisation and machine learning (ML), showing the potential to outperform classical methods in specific settings (Zaman, 2023; Peral-García, 2024). This paper presents a comprehensive review of quantum algorithms for optimisation (e.g., the Quantum Approximate Optimization Algorithm and quantum annealing) and quantum machine learning frameworks (such as quantum support vector machines and quantum neural networks), analysing their theoretical underpinnings, implementation status, and applicability to real-world tasks. Key challenges including hardware noise, limited qubit counts, and algorithmic scalability are examined (Chen, 2024). We also explore hybrid quantum-classical architectures as a near-term route to quantum advantage and propose future research directions aimed at bridging the current gap between quantum algorithm theory and large-scale deployment. Through this synthesis, we aim to provide both academic and practitioner audiences with a clear roadmap for leveraging quantum algorithms in optimisation and ML workflows
In recent years, the intersection of quantum computing and machine learning has emerged as a promising frontier for addressing complex optimization problems that are computationally intractable for classical approaches. This paper presents a comprehensive review and analysis of quantum machine learning (QML) algorithms tailored for complex optimization tasks. We explore the theoretical foundations of quantum-enhanced algorithms, including quantum annealing, variational quantum eigensolvers, and quantum neural networks, highlighting their potential advantages over classical methods in terms of convergence speed and solution accuracy. The paper further investigates practical implementations and hybrid quantum-classical strategies that leverage quantum resources to tackle large-scale optimization problems in diverse fields such as combinatorial optimization, financial modeling, and structural design. We also discuss current challenges and limitations, including hardware constraints and algorithmic scalability, and propose future research directions to bridge the gap between theoretical potential and practical application. Our findings suggest that while QML holds substantial promise, significant advancements are required to fully realize its capabilities in solving complex optimization problems. DOI: https://doi.org/10.17762/ijisae.v12i4.6663