Abstract Portfolio optimization plays a central role in finance to obtain optimal portfolio allocationsthat aim to achieve certain investment goals. Over the years, many works have investigateddifferent variants of portfolio optimization. Portfolio optimization also provides a rich area tostudy the application of quantum computers to obtain advantages over classical computers.In this work, we give a sampling version of an existing classical online portfolio optimizationalgorithm by Helmbold et al., for which we in turn develop a quantum version. The quantumadvantage is achieved by using techniques such as quantum state preparation, inner productestimation and multi-sampling. Our quantum algorithm provides a quadratic speedup inthe time complexity, in terms of n, where n is the number of assets in the portfolio. Thetransaction cost of both of our classical and quantum algorithms is independent of n whichis especially useful for practical applications with a large number of assets.
Abstract Portfolio optimization plays a central role in finance to obtain optimal portfolio allocationsthat aim to achieve certain investment goals. Over the years, many works have investigateddifferent variants of portfolio optimization. Portfolio optimization also provides a rich area tostudy the application of quantum computers to obtain advantages over classical computers.In this work, we give a sampling version of an existing classical online portfolio optimizationalgorithm by Helmbold et al., for which we in turn develop a quantum version. The quantumadvantage is achieved by using techniques such as quantum state preparation, inner productestimation and multi-sampling. Our quantum algorithm provides a quadratic speedup inthe time complexity, in terms of n, where n is the number of assets in the portfolio. Thetransaction cost of both of our classical and quantum algorithms is independent of n whichis especially useful for practical applications with a large number of assets.
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.
Quantum Computing for Portfolio Optimization explores the application of quantum algorithms to enhance asset allocation, risk management, and investment decision-making. By leveraging quantum computing techniques, the approach can process complex financial datasets, identify optimal portfolio structures, and improve computational efficiency beyond classical methods. This emerging field has the potential to transform quantitative finance, enabling faster, more accurate, and adaptive portfolio optimization strategies.
Abstract We present a detailed study of portfolio optimization using different versions of the quantum approximate optimization algorithm (QAOA). For a given list of assets, the portfolio optimization problem is formulated as quadratic binary optimization constrained on the number of assets contained in the portfolio. QAOA has been suggested as a possible candidate for solving this problem (and similar combinatorial optimization problems) more efficiently than classical computers in the case of a sufficiently large number of assets. However, the practical implementation of this algorithm requires a careful consideration of several technical issues, not all of which are discussed in the present literature. The present article intends to fill this gap and thereby provides the reader with a useful guide for applying QAOA to the portfolio optimization problem (and similar problems). In particular, we will discuss several possible choices of the variational form and of different classical algorithms for finding the corresponding optimized parameters. Viewing at the application of QAOA on error-prone NISQ hardware, we also analyse the influence of statistical sampling errors (due to a finite number of shots) and gate and readout errors (due to imperfect quantum hardware). Finally, we define a criterion for distinguishing between ‘easy’ and ‘hard’ instances of the portfolio optimization problem.
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.
A quantum-inspired optimization approach is proposed to study the portfolio optimization aimed at selecting an optimal mix of assets based on the risk-return trade-off to achieve the desired goal in investment. By integrating conventional approaches with quantum-inspired methods for penalty coefficient estimation, this approach enables faster and accurate solutions to portfolio optimization which is validated through experiments using a real-world dataset of quarterly financial data spanning over ten-year period. In addition, the proposed preprocessing method of two-stage search further enhances the effectiveness of our approach, showing the ability to improve computational efficiency while maintaining solution accuracy through appropriate setting of parameters. This research contributes to the growing body of literature on quantum-inspired techniques in finance, demonstrating its potential as a useful tool for asset allocation and portfolio management.
Portfolio optimization is a critical problem in the field of finance, and quantum computing offers a new approach to address this problem. The author explains the development process of the quantum computing model, including quantum bits, quantum entanglement, quantum gates, quantum circuits, while specifically focusing on quantum state preparation, problem coding, quantum gate operation and quantum measurement in the design of quantum algorithms. Furthermore, the author also introduces the mathematical model of portfolio optimization, including expected return, risk analysis, and mathematical constraints, and illustrates the performance evaluation results of quantum algorithms in portfolio optimization from the perspective of speed and optimization accuracy. With respect to traditional methods, quantum algorithms offer both speed and optimization accuracy advantages, and the optimization accuracy reaches 100%, which illustrates that the quantum algorithm has shown good performance in asset portfolio optimization.