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
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
Quantum-enhanced Bayesian inference offers a paradigm shift in the field of machine learning, addressing the fundamental limitations of classical Bayesian methods – namely, computational complexity and scalability – when dealing with high-dimensional data. This paper presents a novel quantum-enhanced Bayesian inference algorithm designed to drastically reduce these challenges. We explore the use of quantum annealing and quantum approximate optimization algorithms to efficiently navigate the complex search space of model parameters, leading to significantly improved accuracy and reduced computational costs. This work demonstrates the potential of quantum computing to revolutionize machine learning, particularly within domains characterized by high data complexity and demanding performance requirements. The core mechanism focuses on leveraging quantum phenomena – superposition and entanglement – to accelerate the exploration of parameter space and improve the convergence of inference algorithms. The investigation includes a detailed analysis of the algorithm's performance compared to classical methods, highlighting the benefits of quantum acceleration in specific machine learning tasks.
Quantum Bayesian Inference (QBI) presents a novel approach to statistical machine learning, utilizing the principles of quantum mechanics to enhance the accuracy and robustness of models, particularly when dealing with high-dimensional data and complex Bayesian frameworks. This paper introduces a quantum algorithm designed to efficiently estimate the posterior distribution of parameters in a Bayesian model through the application of quantum superposition and entanglement, aiming to overcome the limitations of classical methods. We explore the potential of this paradigm shift to deliver exponential speedups in inference tasks, offering a compelling path towards more accurate and reliable statistical machine learning algorithms.
This thesis explores the intersection of Bayesian inference and quantum computing, with a particular focus on developing and analyzing quantum approaches to probabilistic modeling. The motivation arises from the limitations of classical inference methods, which often become intractable when applied to high-dimensional distributions and complex Bayesian networks. By leveraging quantum algorithms, the work investigates how probabilistic reasoning can benefit from computational speedups, scalability, and more efficient handling of uncertainty.The implementation targets canonical benchmark problems—the Sprinkler Network and the Asia Network—where both classical and quantum Bayesian inference techniques are applied and compared. Using Qiskit, the thesis demonstrates how quantum circuits can encode probabilistic models through parameterized rotations and controlled operations, and how posterior distributions can be computed by sampling and amplitude amplification. Comparative experiments systematically evaluate the accuracy, variance, and scalability of quantum Bayesian inference against classical baselines, highlighting trade-offs between precision and shot counts while exploring the potential for quadratic speedups.The results show that although present-day hardware constraints, such as limited qubit counts and noise, restrict large-scale deployment, quantum implementations already display strong promise for complex probabilistic reasoning tasks. Importantly, the conclusions underscore the role of quantum Bayesian networks as a pathway toward practical quantum-enhanced machine learning.
This paper explores the synergistic combination of Bayesian inference and quantum computing for optimizing probabilistic graph models. Traditional Bayesian inference, particularly with complex graph structures, faces significant computational challenges. Quantum computing, leveraging its inherent parallelism, offers a promising avenue for accelerating these inference processes. We propose a framework that translates probabilistic graph models into quantum circuits, employing variational quantum algorithms such as Variational Quantum Eigensolver (VQE) or Quantum Approximate Optimization Algorithm (QAOA) to optimize the model parameters and expedite the inference. This approach aims to enhance both the accuracy and efficiency of Bayesian inference, addressing a critical bottleneck in various applications, including machine learning, statistical inference, and decision-making under uncertainty. The core claim of this research is the effective integration of Bayesian inference and quantum computing to accelerate the inference process. The underlying mechanism involves the transformation of probabilistic graph models into quantum circuits and utilizing quantum algorithms for optimization. This work represents a novel approach to tackling computationally intensive Bayesian inference problems, paving the way for more sophisticated and efficient probabilistic modeling. ---
Quantum Machine Learning represents a paradigm shift at the intersection of Quantum Computing and Machine Learning, leveraging quantum phenomena such as superposition, entanglement, and quantum parallelism to address the limitations of classical approaches in processing high-dimensional and large-scale datasets. This survey provides a comprehensive analysis of Quantum Machine Learning, detailing foundational concepts, algorithmic advancements, and their applications across domains such as healthcare, finance, and quantum chemistry. Key techniques, including Quantum Support Vector Machine, Quantum Neural Network, Quantum Decision Trees, and hybrid quantum-classical models, are explored with a focus on their theoretical foundations, computational benefits, and comparative performance against classical counterparts. While the potential for exponential speedups and enhanced efficiency is evident, the field faces significant challenges, including hardware constraints, noise, and limited qubit coherence in the current era of Noisy Intermediate-Scale Quantum devices. Emerging solutions, such as error mitigation techniques, hybrid frameworks, and advancements in quantum hardware, are discussed as critical enablers for scalable and fault-tolerant Quantum Machine Learning systems. By synthesizing state-of-the-art developments and identifying research gaps, this survey aims to provide a foundational resource for advancing Quantum Machine Learning toward practical, real-world applications in tackling computationally intensive problems.
Bayesian inference, a cornerstone of statistical modeling, often struggles with the complexities of high-dimensional data and non-Gaussian distributions commonly encountered in complex systems. This paper proposes a novel approach termed Quantum-Inspired Bayesian Inference (QIBI), leveraging concepts from quantum mechanics – specifically superposition and entanglement – to enhance the efficiency and accuracy of Bayesian inference. QIBI represents prior distributions as superposition states and employs entangled quantum-like circuits to perform marginalization and posterior calculation, effectively addressing the computational bottlenecks associated with traditional methods. We demonstrate the potential of this approach to significantly improve inference performance in scenarios where classical Bayesian methods face limitations. The core of this work lies in the conceptual mapping of Bayesian calculations onto a quantum-inspired framework, providing a new perspective on statistical inference. We define key mathematical formulations to illustrate the proposed methodology, including the superposition state representation of prior distributions and the entanglement-based circuit design for posterior calculation. This exploration aims to bridge the gap between statistical inference and quantum computing, opening avenues for tackling previously intractable problems.