In portfolio theory, the investment portfolio optimization problem is one of those problems whose complexity grows exponentially with the number of assets. By backtesting classical and quantum computing algorithms, we can get a sense of how these algorithms might perform in the real world. This work establishes a methodology for backtesting classical and quantum algorithms in equivalent conditions, and uses it to explore four quantum and three classical computing algorithms for portfolio optimization and compares the results. Running 10 000 experiments on equivalent conditions we find that quantum can match or slightly outperform classical results, showing a better escalability trend. To the best of our knowledge, this is the first work that performs a systematic backtesting comparison of classical and quantum portfolio optimization algorithms. In this work, we also analyze in more detail the variational quantum eigensolver algorithm, applied to solve the portfolio optimization problem, running on simulators and real quantum computers from IBM. The benefits and drawbacks of backtesting are discussed, as well as some of the challenges involved in using real quantum computers of more than 100 qubits. Results show quantum algorithms can be competitive with classical ones, with the advantage of being able to handle a large number of assets in a reasonable time on a future larger quantum computer.
In portfolio theory, the investment portfolio optimization problem is one of those problems whose complexity grows exponentially with the number of assets. By backtesting classical and quantum computing algorithms, we can get a sense of how these algorithms might perform in the real world. This work establishes a methodology for backtesting classical and quantum algorithms in equivalent conditions, and uses it to explore four quantum and three classical computing algorithms for portfolio optimization and compares the results. Running 10 000 experiments on equivalent conditions we find that quantum can match or slightly outperform classical results, showing a better escalability trend. To the best of our knowledge, this is the first work that performs a systematic backtesting comparison of classical and quantum portfolio optimization algorithms. In this work, we also analyze in more detail the variational quantum eigensolver algorithm, applied to solve the portfolio optimization problem, running on simulators and real quantum computers from IBM. The benefits and drawbacks of backtesting are discussed, as well as some of the challenges involved in using real quantum computers of more than 100 qubits. Results show quantum algorithms can be competitive with classical ones, with the advantage of being able to handle a large number of assets in a reasonable time on a future larger quantum computer.
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.
The possibility of adopting quantum computing in the field of financial services can bring a new breakthrough in portfolio management since the optimization of this method requires large numbers for the solution that exceed the capabilities of classical computing algorithms. This study focuses on using a hybrid quantum-classical computational method known as the Variational Quantum Eigensolver (VQE) in optimizing portfolio selection. The VQE aims at finding the best allocation of the portfolio; the best weights that correspond to minimum risk and maximum return as predicted by the modern portfolio theory. The study assesses the suitability and speed of VQE in solving matters involving portfolio management tasks such as handling vast data and nonlinear constraints which are hard to solve through other optimization methods. Thus, under the theoretical framework of quantum computing, the study seeks to address some of the following challenges: computational time and scalability in portfolio optimization. The VQE algorithm work on different portfolio configurations; their performance in comparison with classical techniques; special attention is paid to the rate of convergence and the achievement of the optimal solution. Based on the results of this work we can conclude that there is a considerable literature on quantum finance and that this field can benefit from utilization of quantum algorithms as a tool to improve decision-making in the financial market. That is why the study proves that quantum optimization techniques, to wit VQE, can provide better solutions when it comes to portfolio management within the sphere of finance.
In finance, portfolio optimization aims at finding optimal investments maximizing a trade-off between return and risks, given some constraints. Classical formulations of this quadratic optimization problem have exact or heuristic solutions, but the complexity scales up as the market dimension increases. Recently, researchers are evaluating the possibility of facing the complexity scaling issue by employing quantum computing. In this paper, the problem is solved using the Variational Quantum Eigensolver (VQE), which in principle is very efficient. The main outcome of this work consists of the definition of the best hyperparameters to set, in order to perform Portfolio Optimization by VQE on real quantum computers. In particular, a quite general formulation of the constrained quadratic problem is considered, which is translated into Quadratic Unconstrained Binary Optimization by the binary encoding of variables and by including constraints in the objective function. This is converted into a set of quantum operators (Ising Hamiltonian), whose minimum eigenvalue is found by VQE and corresponds to the optimal solution. In this work, different hyperparameters of the procedure are analyzed, including different ansatzes and optimization methods by means of experiments on both simulators and real quantum computers. Experiments show that there is a strong dependence of solutions quality on the sufficiently sized quantum computer and correct hyperparameters, and with the best choices, the quantum algorithm run on real quantum devices reaches solutions very close to the exact one, with a strong convergence rate towards the classical solution, even without error-mitigation techniques. Moreover, results obtained on different real quantum devices, for a small-sized example, show the relation between the quality of the solution and the dimension of the quantum processor. Evidences allow concluding which are the best ways to solve real Portfolio Optimization problems by VQE on quantum devices, and confirm the possibility to solve them with higher efficiency, with respect to existing methods, as soon as the size of quantum hardware will be sufficiently high.
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.
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.
Recently, several researchers proposed portfolio optimization as a potential use case for quantum optimization. However, the literature is lacking an extensive benchmark quantifying the potential of quantum computers for portfolio optimization. In this work, we contribute to closing this gap. We provide a computational study, comparing quantum approaches against state-of-the-art classical methods on a meaningful, real-world instance set. In particular, we compare quantum annealing and the quantum approximate optimization algorithm against classical mixed-integer programming, simulated annealing, steepest descent local search, tabu search and a problem-tailored heuristic. We consider a variance-minimizing variant of portfolio optimization which we show to be more difficult to solve for classical optimizers than return-maximizing or multi-objective formulations. Our benchmark data set comprises 270 instances with up to 1,000 assets from actual stock data. Due to hardware limitation, quantum methods could only be tested for instances with at most 30 assets. The results show that all instances can be solved to proven optimality by mixed-integer programming in the order of seconds. Moreover, the problem-tailored heuristic consistently outperforms quantum approaches in terms of solution quality for fixed runtime. Thus, we conclude that there is only very limited room for a potential quantum advantage for the considered variant of portfolio optimization.