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Genetic and Evolutionary Computation Conference Companion (GECCO Companion)

Quantum Annealing for Bi-objective Weighted Portfolio Optimization in Real-world Financial Markets

Shu–Yu Kuo, Kun-Lin Lee, Yao–Hsin Chou, Jyun–Yi Shen, Sy‐Yen Kuo

Published Jul 14, 2025• 1 citation
Publisher

Abstract

Quantum computing, leveraging principles such as superposition and entanglement, has shown remarkable potential in solving complex optimization problems. Quantum annealing (QA) is particularly effective for combinatorial optimization and has gained increasing attention in financial applications. However, financial decision-making problems typically involve conflicting objectives, such as the trade-off between minimizing risk and maximizing returns, posing challenges for current QA approaches in efficiently encoding multi-objective problems and constraints. To address this gap, we propose the first quantum annealing framework for bi-objective weighted portfolio optimization based on the trend ratio model, integrating D-Wave's latest constrained quadratic model (CQM) hybrid solver. Our approach offers flexibility to accommodate diverse investor preferences. Experimental evaluations using real-world U.S. stock market data demonstrate the effectiveness of our method, showing higher-quality solutions and faster runtimes compared to classical multi-objective optimization algorithms. These promising results highlight the significant potential of quantum computing in practical financial optimization scenarios.

DOI
10.1145/3712255.3734282

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Quantum finance has emerged as a key research area as interest grows in leveraging quantum computing for solving complex optimization problems in financial technology. Quantum annealing (QA), which leverages quantum tunneling effects, presents a promising method for tackling portfolio optimization challenges that primarily involve balancing risk and return. Traditional single-solution optimization approaches often fail to accommodate diverse investor preferences regarding risk tolerance and expected returns. To bridge this gap, we propose a novel bi-objective weighted portfolio optimization framework based on the trend ratio (TR) model. Our approach integrates D-Wave's advanced constrained quadratic model (CQM) hybrid solver with QA and employs scalarization-based non-dominated analysis, enabling multiple runs with different weights between risk and return to effectively achieve bi-objective optimization. This flexible strategy generates a diverse set of high-quality solutions tailored to different investor profiles. In our experiments, we investigate the interaction between two well-known international stock indices, DJI and Nikkei, to gain insights into cross-market dynamics and enhance portfolio diversification. Experimental results show that the proposed approach consistently demonstrates strong potential compared to conventional multi-objective optimization algorithms, delivering solutions with improved quality and computational efficiency. These findings highlight the potential of quantum computing in advancing financial decision-making and portfolio optimization.
Quantum annealing (QA) represents a promising optimization technique to achieve both quantum and classical advantages and address real-world applications such as quantum finance, enabled by the rapid advancements in quantum computing (QC) in recent years. This study represents the first attempt to explore a novel weighted portfolio optimization model based on a new assessment strategy, trend ratio (TR), and extends its application to international stock markets, including DJIA, TSX, CAC, and FTSE. It utilizes the D-Wave Advantage quantum system and a hybrid solver to demonstrate its effectiveness and efficiency in solving enterprise-scale financial problems. Experimental findings demonstrate that QA outperforms both classical and state-of-the-art quantum-inspired optimization techniques in evaluating returns and risks, including metrics such as daily profit factor (DPF), maximum drawdown (MDD), and TR. Furthermore, QA exhibits outstanding search capabilities, facilitating rapid identification of high-performance portfolios within a remarkably short timeframe. Statistical tests are adopted to prove that QA significantly improves solution quality while requiring less computational cost.
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Quantum annealing has emerged as a promising computational paradigm for solving large-scale combinatorial optimization problems that are intractable for classical algorithms. Financial portfolio optimization, which involves balancing expected returns against risk under multiple practical constraints, represents one of the most challenging optimization tasks in quantitative finance. Traditional approaches based on mean-variance theory, heuristic meta-optimization, and classical quadratic programming often struggle to scale efficiently as the dimensionality of assets and constraints increases. This study explores the application of quantum annealing techniques to financial portfolio optimization by formulating the problem as a quadratic unconstrained binary optimization model suitable for quantum hardware. The paper provides a systematic mapping of portfolio objectives and constraints into the Ising Hamiltonian framework and analyzes how quantum tunneling and probabilistic state transitions can enhance convergence toward near-global optima. Comparative insights between classical solvers and quantum annealing-based approaches are discussed in terms of solution quality, computational efficiency, and scalability. Furthermore, the study highlights current hardware limitations, embedding challenges, and noise effects that influence optimization performance. The findings indicate that quantum annealing offers substantial potential for accelerating portfolio optimization in high-dimensional financial systems, particularly in scenarios involving complex constraints and dynamic market conditions, thereby establishing a foundation for future quantum-driven financial decision-support systems.
Hybrid quantum computing (QC) combines classical and quantum resources to tackle challenging optimization problems, leveraging the strengths of both within the current constraints of quantum computers, which are limited in size and power. Therefore, we explore the efficacy of a hybrid quantum annealing (QA) search algorithm in improving portfolio optimization. This study pioneers the application of the trend ratio (TR) to a quantum annealing computer, converting it into a constrained quadratic model with a flexible presentation. The TR serves as a promising indicator in portfolio evaluation, considering the great balance between expected returns and risks. Utilizing D- Wave's hybrid solver, we present a thorough analysis and discussion of the proposed model realized in the QA structure. The experimental results demonstrate that our model can discover solutions of comparable quality in a significantly shorter amount of time than an exhaustive search. When extending the search space to sizes challenging for exhaustive search, we conducted experiments comparing our approach with state-of-the-art quantum-inspired artificial intelligence (AI) algorithms. The results show that our method not only constructs higher-quality solutions but also requires the least computation time. The hybrid quantum-classical AI represents a forward-looking technology paradigm poised to revolutionize problem-solving methods.
ABSTRACT Hybrid quantum‐classical optimization has emerged as a promising direction for addressing financial decision problems under current quantum hardware constraints. In this work we present a practical end‐to‐end portfolio optimization pipeline that combines (i) a continuous mean‐variance and Sharpe‐ratio formulation, (ii) a QUBO/CQM‐based discrete asset selection stage solved using D‐Wave's hybrid quantum annealing solver, (iii) classical convex optimization for computing optimal asset weights, and (iv) a quarterly rebalancing mechanism. Rather than claiming quantum advantage, our goal is to evaluate the feasibility and integration of these components within a deployable financial workflow. We empirically compare our hybrid pipeline against a fund manager in real time and indexes used in Indian stock market. The results indicate that the proposed framework can construct diversified portfolios and achieve competitive returns. We also report computational considerations and scalability observations drawn from the hybrid solver behavior. While the experiments are limited to moderate sized portfolios dictated by current annealing hardware and QUBO embedding constraints, the study illustrates how quantum assisted selection and classical allocation can be combined coherently in a real‐world setting. This work emphasizes methodological reproducibility and practical applicability, and aims to serve as a step toward larger‐scale financial optimization workflows as quantum annealers continue to mature.