In this paper, we will be discussing how a Hybrid Quantum/Classical algorithm enhanced with Game theory would impact the Finance world, particularly in the Portfolio Optimization Sector.For that purpose, we provide an overview of the current state of the Portfolio Optimization Sector, and an example of a Hybrid Classical/Quantum QAOA optimization algorithm capable of generating Higher Annual Expected returns in comparison to current classical models, while also taking into consideration factors such as the covariance between the assets in the portfolio, and the behavior of other investors of Investment funds using Game theory, and then compare it to current Classical Strategies.We also discuss the current limitations and problems that modern Quantum computers endure, and what impact a Quantum computer with less noise and more qubits may have in Industries such as Mutual funds, Hedge Funds, ETF, and more.
In this paper, we will be discussing how a Hybrid Quantum/Classical algorithm enhanced with Game theory would impact the Finance world, particularly in the Portfolio Optimization Sector.For that purpose, we provide an overview of the current state of the Portfolio Optimization Sector, and an example of a Hybrid Classical/Quantum QAOA optimization algorithm capable of generating Higher Annual Expected returns in comparison to current classical models, while also taking into consideration factors such as the covariance between the assets in the portfolio, and the behavior of other investors of Investment funds using Game theory, and then compare it to current Classical Strategies.We also discuss the current limitations and problems that modern Quantum computers endure, and what impact a Quantum computer with less noise and more qubits may have in Industries such as Mutual funds, Hedge Funds, ETF, and more.
This study explores the integration of quantum computing techniques, specifically the Quantum Approximate Optimization Algorithm (QAOA), with classical portfolio optimization frameworks through the Quadratic Unconstrained Binary Optimization (QUBO) approach. Using monthly turnover data from the National Stock Exchange of India (NSE), this paper demonstrates the construction of a QUBO matrix by encoding expected returns and covariance-based risk profiles. Binary asset inclusion constraints are introduced into portfolios and then optimised using both brute force enumeration and quantum inspired solvers. The analysis reveals those combinations including Index Futures and Index Options exhibit superior risk-adjusted performance (Sharpe Ratio≈0.286). The hybrid approach suggests the promise of quantum inspired models as means to improve financial decision making under uncertainty. The results also give a robust template for scalable asset selection models that operate within the constraints of quantum computing infrastructure.
Portfolio optimization is a fundamental problem in quantitative finance that seeks to maximize risk-adjusted returns while managing investment risk. With the advent of quantum computing, there is growing interest in applying quantum algorithms to solve complex optimization problems. This paper presents a comprehensive comparative study of quantum and classical approaches to portfolio optimization, specifically comparing the Quantum Approximate Optimization Algorithm (QAOA), Variational Quantum Eigensolver (VQE), and classical mean-variance optimization. We evaluate these methods on both real market data and synthetic datasets with varying correlation structures. Our experimental results show that while classical methods currently outperform quantum approaches on near-term quantum devices in terms of solution quality and computational efficiency, quantum algorithms demonstrate conceptual viability and promise for future applications as quantum hardware improves. The classical method achieves optimal Sharpe ratios of 1.2-1.8, while QAOA and VQE achieve 80-95% and 75-90% of classical performance respectively. This work provides insights into the current state and future potential of quantum computing for financial optimization.
Large-scale portfolio optimization is hard because investors must balance risk, return, diversification, and liquidity across many assets with complex constraints. Classical methods, such as quadratic programming or metaheuristics, often become slow or less effective as the number of assets and factors grows. In this project, I explore the use of the Quantum Approximate Optimization Algorithm (QAOA) as a hybrid quantum–classical approach to portfolio selection. The framework encodes portfolio decisions as qubits and represents financial objectives—such as mean–variance trade-offs or risk-adjusted return—inside a parameterized quantum circuit. Classical optimization is then used to tune the circuit parameters so that the quantum system converges toward low-risk, high-return portfolios. Multi-factor constraints, including sector limits, liquidity rules, ESG scores, and macroeconomic risk factors, are integrated into the Hamiltonian as penalty terms. A qualitative comparison with classical solvers (e.g., mixed-integer programming and simulated annealing) suggests that QAOA can scale more gracefully in high-dimensional settings and handle complex constraint structures. Overall, the project shows how quantum hybrid optimization could support future portfolio management, linking theoretical quantum algorithms with practical, sustainability-aware investment strategies.
Portfolio optimization (PO) plays a central role in finance, encompassing both resource allocation and risk management. While numerous algorithms have been developed for continuous-variable PO, the inclusion of large, indivisible assets such as real estate transforms the task into a combinatorial optimization problem, which is NP-hard for classical computers. This study explores using quantum-classical hybrid algorithms for multi-discretized portfolio optimization, addressing the needs of real-world applications. We propose a flexible theoretical model that can solve PO problems with various types of discrete assets and constraints, which is compatible with both quantum and classical computing paradigms. Then, we use the D-Wave quantum processor and classical solver to determine optimal investment strategies. Experimental results indicate that the hybrid quantum algorithm outperforms both classical computing methods and quantum annealing algorithms in terms of return and risk management. This research enhances quantum computing applications in finance and provides insights into future algorithm design.
The increasing complexity of financial markets has heightened the demand for advanced computational methods capable of optimizing portfolios under multi-dimensional constraints involving risk, return, diversification, and liquidity. Traditional optimization frameworks, such as mean-variance analysis and heuristic meta-optimization, are limited by their scalability and sensitivity to non-convex, high-dimensional data structures. This study explores the application of quantum algorithms to portfolio optimization, demonstrating how Quantum Approximate Optimization Algorithm (QAOA), Quantum Annealing, and Variational Quantum Eigensolver (VQE) can address computational bottlenecks inherent in classical approaches. Quantum computation offers the potential to encode complex financial systems as Hamiltonian functions, allowing parallel exploration of vast solution spaces through superposition and entanglement. This enables faster convergence toward optimal portfolio allocations while simultaneously accounting for multi-factor correlations and dynamic market conditions. The research further investigates the role of hybrid quantum–classical optimization pipelines, in which quantum solvers perform core optimization tasks while classical systems manage data preprocessing and constraint validation. Empirical modeling and simulation indicate that quantum-based approaches can outperform conventional methods in risk-adjusted return optimization, efficient frontier computation, and real-time portfolio rebalancing. By bridging the gap between quantum computing and financial engineering, this study contributes to the development of next-generation financial analytics systems, aligning with the broader goal of achieving more adaptive, transparent, and data-resilient financial decision-making.
Quantum computers are expected to surpass the computational capabilities of classical computers during this decade and have transformative impact on numerous industry sectors, particularly finance. In fact, finance is estimated to be the first industry sector to benefit from quantum computing, not only in the medium and long terms, but even in the short term. This survey paper presents a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modeling, optimization, and machine learning, describing how these solutions, adapted to work on a quantum computer, can potentially help to solve financial problems, such as derivative pricing, risk modeling, portfolio optimization, natural language processing, and fraud detection, more efficiently and accurately. We also discuss the feasibility of these algorithms on near-term quantum computers with various hardware implementations and demonstrate how they relate to a wide range of use cases in finance. We hope this article will not only serve as a reference for academic researchers and industry practitioners but also inspire new ideas for future research.