This paper studies the application of quantum approximate optimization algorithm in portfolio optimization problem, and focuses on the real stock market, analyzes and quantifies the real data of ten stocks, compares the performance of quantum approximate optimization algorithm and classical algorithm in solving this problem, and also analyzes the effect of noise on the solution using quantum approximate optimization, showing the performance of quantum approximate optimization algorithm in the financial stock market and the The performance and application value of the quantum approximate optimization algorithm in the financial stock market are shown.
This paper studies the application of quantum approximate optimization algorithm in portfolio optimization problem, and focuses on the real stock market, analyzes and quantifies the real data of ten stocks, compares the performance of quantum approximate optimization algorithm and classical algorithm in solving this problem, and also analyzes the effect of noise on the solution using quantum approximate optimization, showing the performance of quantum approximate optimization algorithm in the financial stock market and the The performance and application value of the quantum approximate optimization algorithm in the financial stock market are shown.
Portfolio optimization, a core combinatorial optimization problem in quantitative finance, requires balancing return maximization and risk minimization within discrete asset sets. Classical algorithms often struggle with scalability and local optima traps when handling large-scale asset pools, limiting their practicality in dynamic markets. This study proposes a complete Quantum Approximate Optimization Algorithm (QAOA) workflow for portfolio optimization, from problem formalization to experimental validation. We first transform the portfolio optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) framework, then design a parameterized QAOA circuit with adjustable layers to balance expressiveness and noise resilience. We propose a methodology using Qiskit for quantum simulation and classical optimizers for parameter tuning, we propose implementing the algorithm on real-world S&P 500 stock data. We could also analyze the impact of quantum hardware noise and propose mitigation strategies, providing actionable insights for Noisy intermediate-scale quantum computing (NISQ)-era implementations. This work bridges quantum algorithm design with real-world financial applications, offering a theoretical framework for quantum-driven portfolio optimization.
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.
This research investigates the efficacy of quantum and classical algorithms in the context of portfolio optimization, focusing on a dataset comprising 20 equities from India's National Stock Exchange over a duration of three years. The study employs quantum methodologies such as the Quantum Approxi-mate Optimization Algorithm (QAOA), the Variational Quantum Eigensolver (VQE), and the Exact Minimum Eigen Solver, alongside conventional strategies including Mean-Variance Op-timization, Genetic Algorithms, and Simulated Annealing. The methodology for this study includes data preprocessing, issue designing, and performance evaluation based on metrics such as MSE, RMSE, and Mean Absolute Error. The results obtained show quantum algorithms exhibit better performance over the classical methods regarding prediction accuracy and risk-return profiles, especially the Exact Minimum Eigen hSolver and QAOA. The Exact Minimum Eigen Solver and QAOA had the lowest MSE values (0.006 and 0.005, respectively), whereas the best-performing classical technique, the Genetic Algorithm, had an MSE of 0.0105. These findings imply that quantum algorithms provide significant advantages in portfolio optimization problems, with the potential to revolutionize financial optimization tactics. The research can be further unfolded into avenues for future inquiry, including expansion of the choice of assets, alternative data sources integration, as well as hybrid quantum-classical models to efficiently enhance portfolio management strategies.
Previously only considered a frontier area of Physics, nowadays quantum computing is one of the fastest growing research field, precisely because of its technological applications in optimization problems, machine learning, information security and simulations. The goal of this article is to introduce the fundamentals of quantum computing, focusing on a promising quantum algorithm and its application to a financial market problem. More specifically, we discuss the portfolio optimization problem using the \textit{Quantum Approximate Optimization Algorithm} (QAOA). We not only describe the main concepts involved but also consider simple practical examples, involving financial assets available on the Brazilian stock exchange, with codes, both classic and quantum, freely available as a Jupyter Notebook. We also analyze in details the quality of the combinatorial portfolio optimization solutions through QAOA using SENAI/CIMATEC's ATOS QLM quantum simulator.
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.
Abstract This paper presents an improved Quantum Approximate Optimization Algorithm variant based on Conditional Value-at-Risk for addressing portfolio optimization problems. Portfolio optimization is a NP-hard combinatorial problem that aims to select an optimal set of assets and their quantities to balance risk against expected return. The proposed approach uses the QAOA to find the optimal asset combination that maximizes returns while minimizing risk, with a focus on the tail end of the loss distribution. An enhanced QAOA ansatz introduced that offers a balance between optimization quality and circuit depth, leading to faster convergence and higher probabilities of obtaining optimal solutions. Experiments are conducted using historical stock data from Nasdaq, optimizing portfolios with varying numbers of stocks. In the case of 16 stocks, our method achieves optimal cost values with merely 35 iterations, whereas the standard QAOA requires 700 iterations. Our method outperforms other approaches, particularly as the size of the problem increases.