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arXiv:2410.05932

Quantum-Inspired Portfolio Optimization In The QUBO Framework

Lu, Ying-Chang, Chao‐Ming Fu, Lien-Po Yu, Yen-Jui Chang, Chang, Ching-Ray

Published Oct 8, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2410.05932

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The relentless quest for optimized financial portfolios has led to the exploration of advanced computational techniques capable of navigating financial markets’ complex and dynamic landscape. This dissertation presents a solution for portfolio optimization by harnessing the synergistic potential of quantum computing and machine learning. We propose a hybrid framework that integrates quantum algorithms’ optimization capabilities with machine learning’s predictive accuracy to address the multifaceted challenges of portfolio management. The study begins with a comprehensive review of traditional and contemporary portfolio optimization methods and an in-depth analysis of quantum computing principles relevant to optimization problems. Next, we examine machine learning models commonly used for forecasting financial time series, which serve as critical inputs for the quantum optimization process. The proposed solution is evaluated through simulations and real-world financial data to demonstrate its efficacy in achieving optimized asset allocations with enhanced risk-adjusted returns. This research contributes to the theoretical advancement of financial optimization techniques and provides practical insights for investors and portfolio managers seeking to leverage emerging technologies for strategic decision-making.
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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.
This study explores the integration of quantum computing techniques, specifically the Quantum Approximate Optimization Algorithm (QAOA), with classical portfolio optimization frameworks through the Quadratic Unconstrained Binary Optimization (QUBO) approach. Using monthly turnover data from the National Stock Exchange of India (NSE), this paper demonstrates the construction of a QUBO matrix by encoding expected returns and covariance-based risk profiles. Binary asset inclusion constraints are introduced into portfolios and then optimised using both brute force enumeration and quantum inspired solvers. The analysis reveals those combinations including Index Futures and Index Options exhibit superior risk-adjusted performance (Sharpe Ratio≈0.286\approx 0.286≈0.286). The hybrid approach suggests the promise of quantum inspired models as means to improve financial decision making under uncertainty. The results also give a robust template for scalable asset selection models that operate within the constraints of quantum computing infrastructure.
Quantum finance represents a pivotal and cutting-edge application domain within the burgeoning field of quantum computing. In this work, we propose a two-step quantum approximate optimization algorithm (two-step QAOA) for portfolio optimization and risk assessment. The algorithm initiates by formulating the stock selection problem as a quadratic unconstrained binary optimization (QUBO) problem and employs a classical-quantum hybrid method to find the ground state of the Hamiltonian. We then introduce an energy-based characteristic indicator U∈[0,1), which quantitatively evaluates portfolio performance under customizable investment preferences, effectively capturing the trade-off between expected return and risk. The number of qubits required scales with the number of stocks N in the pool, and the number of Hamiltonian terms is O(N2). Numerical simulations show that the algorithm provides consistent and reasonable assessment results on both training and test datasets under different investment preferences (aggressive or conservative), validating the capability of the characteristic indicator to extract intrinsic information from the portfolios. Additionally, by incorporating warm-starting and digitized counterdiabatic techniques, the algorithm achieves improved scalability and faster convergence. Our work presents a flexible and practical algorithmic framework for applying quantum computing in the financial domain.
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.