Quantum computing has transitioned from a largely theoretical construct into a rapidly evolving technological paradigm with significant implications for computational finance and financial data science. This article presents a comprehensive and integrative research synthesis examining the convergence of quantum algorithms, quantum machine learning, and probabilistic modeling techniques—particularly determinantal point processes—in the context of financial optimization, risk management, asset pricing, and data-driven decision-making. Drawing exclusively from a curated body of foundational and contemporary literature, the study explores how quantum computational advantages may address long-standing computational bottlenecks in finance, including high-dimensional optimization, stochastic simulation, portfolio construction, and time-series forecasting under uncertainty.

The article begins by situating quantum finance within the broader evolution of financial computation, emphasizing the limitations of classical Monte Carlo methods, convex optimization frameworks, and deep learning architectures when confronted with combinatorial complexity and structural constraints inherent in modern financial systems. It then provides an extensive theoretical elaboration of quantum algorithms relevant to finance, including amplitude estimation, quantum portfolio optimization, stochastic optimal stopping, and martingale-based asset pricing in incomplete markets. Particular attention is devoted to algorithmic primitives such as low-depth amplitude estimation and near-term implementations on noisy intermediate-scale quantum hardware, highlighting their feasibility and constraints.

A substantial portion of the article is dedicated to quantum machine learning models and their classical counterparts, examining parameterized quantum circuits, quantum-enhanced feature spaces, Bayesian quantum neural networks, and subspace-based learning. These models are critically compared with established classical approaches such as random forests, orthogonal neural networks, and tree-based ensembles, especially in the context of tabular financial data. The discussion is further enriched by an in-depth theoretical treatment of determinantal point processes as a unifying probabilistic framework for diversity-aware sampling, feature selection, and data imputation, including their classical and emerging quantum formulations.

By synthesizing insights across quantum algorithms, machine learning theory, and financial engineering, this article articulates both the transformative potential and the unresolved challenges of quantum finance. It concludes with a forward-looking discussion on scalability, hardware constraints, hybrid quantum-classical workflows, and the epistemic implications of adopting quantum models in financial decision-making. The work aims to serve as a foundational reference for researchers and practitioners seeking a deep theoretical understanding of quantum computational finance as an emerging interdisciplinary field.