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Journal of Management Science and Engineering

Application of quantum computing in discrete portfolio optimization

Justus Shunza, Mary Akinyemi, Chika Yinka-Banjo

Published May 22, 2023• 10 citations
Publisher

Abstract

This article proposes a new, more efficient quantum algorithm for portfolio optimization and uses quantum combinatorial optimization (QCO) techniques. The recent construction developed in 2021 has sparked the field of financial portfolio optimization through the Quantum Walk Optimization Algorithm (QWOA). We study the complexity and efficiency of quantum optimization algorithms with a special interest in QWOA. The objective is to minimize the risk of investing by having a good combination of assets in the portfolio. We also focus on reducing the number of iterations yet attaining a high-quality resolution through contraction of the solution space that eases computations. We extend QWOA’s idea by constructing a newly outperforming scheme known as ’Quantum Mix Optimization Algorithm (QMOA)’. QMOA algorithm codes are provided for the implementation and simulation of numerical results. In addition, QMOA’s efficiency (better than the existing QCO algorithms) is discussed. For instance, the least QWOA number of computations required to execute the initial state equation is p > 2 while this value is p ≥ 2 in the proposed QMOA.

DOI
10.1016/j.jmse.2023.02.001

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This article proposes a new, more efficient quantum algorithm for portfolio optimization and uses quantum combinatorial optimization (QCO) techniques. The recent construction developed in 2021 has sparked the field of financial portfolio optimization through the Quantum Walk Optimization Algorithm (QWOA). We study the complexity and efficiency of quantum optimization algorithms with a special interest in QWOA. The objective is to minimize the risk of investing by having a good combination of assets in the portfolio. We also focus on reducing the number of iterations yet attaining a high-quality resolution through contraction of the solution space that eases computations. We extend QWOA’s idea by constructing a newly outperforming scheme known as ’Quantum Mix Optimization Algorithm (QMOA)’. QMOA algorithm codes are provided for the implementation and simulation of numerical results. In addition, QMOA’s efficiency (better than the existing QCO algorithms) is discussed. For instance, the least QWOA number of computations required to execute the initial state equation is p > 2 while this value is p ≥ 2 in the proposed QMOA.
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.
This paper proposes a highly efficient quantum algorithm for portfolio optimisation targeted at near-term noisy intermediate-scale quantum computers. Recent work by Hodson et al. (2019) explored potential application of hybrid quantum-classical algorithms to the problem of financial portfolio rebalancing. In particular, they deal with the portfolio optimisation problem using the Quantum Approximate Optimisation Algorithm and the Quantum Alternating Operator Ansatz. In this paper, we demonstrate substantially better performance using a newly developed Quantum Walk Optimisation Algorithm in finding high-quality solutions to the portfolio optimisation problem.
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.
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.
Portfolio optimization is a primary component of the decision-making process in finance, aiming to tactfully allocate assets to achieve optimal returns while considering various constraints. Herein, we proposed a method that uses the knapsack-based portfolio optimization problem and incorporates the quantum computing capabilities of the quantum walk mixer with the quantum approximate optimization algorithm (QAOA) to address the challenges presented by the NP-hard problem. Additionally, we present the sequential procedure of our suggested approach and demonstrate empirical proof to illustrate the effectiveness of the proposed method in finding the optimal asset allocations across various constraints and asset choices. Moreover, we discuss the effectiveness of the QAOA components in relation to our proposed method. Consequently, our study successfully achieves the approximate ratio of the portfolio optimization technique using a circuit layer ofp⩾3p\geqslant 3p⩾3, compared to the classical best-known solution of the knapsack problem. Our proposed methods potentially contribute to the growing field of quantum finance by offering insights into the potential benefits of employing quantum algorithms for complex optimization tasks in financial portfolio management.
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.