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arXiv:2407.19857 · IEEE International Conference on Quantum Computing and Engineering (QCE)

PO-QA: A Framework for Portfolio Optimization using Quantum Algorithms

Kamila Zaman, Alberto Marchisio, Muhammad Kashif, Muhammad Shafique

Published Sep 15, 2024• 12 citations
arXivHTMLPDF

Abstract

Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) infrastructure. Utilizing QC's applicable strengths to the finance industry's problems, such as PO, allows us to solve these problems using quantum-based algorithms such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). While the Quantum potential for finance is highly impactful, the architecture and composition of the quantum circuits have not yet been properly defined as robust financial frameworks/algorithms as state of the art in present literature for research and design development purposes. In this work, we propose a novel scalable framework, denoted PO-QA, to systematically investigate the variation of quantum parameters (such as rotation blocks, repetitions, and entanglement types) to observe their subtle effect on the overall performance. In our paper, the performance is measured and dictated by convergence to similar ground-state energy values for resultant optimal solutions by each algorithm variation set for QAOA and VQE to the exact eigensolver (classical solution). Our results provide effective insights into comprehending PO from the lens of Quantum Machine Learning in terms of convergence to the classical solution, which is used as a benchmark. This study paves the way for identifying efficient configurations of quantum circuits for solving PO and unveiling their inherent inter-relationships.

DOI
10.1109/qce60285.2024.00166

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Portfolio Optimization (PO) is a financial problem aiming to maximize the net gains while minimizing the risks in a given investment portfolio. The novelty of Quantum algorithms lies in their acclaimed potential and capability to solve complex problems given the underlying Quantum Computing (QC) infrastructure. Utilizing QC's applicable strengths to the finance industry's problems, such as PO, allows us to solve these problems using quantum-based algorithms such as Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA). While the Quantum potential for finance is highly impactful, the architecture and composition of the quantum circuits have not yet been properly defined as robust financial frameworks/algorithms as state of the art in present literature for research and design development purposes. In this work, we propose a novel scalable framework, denoted PO-QA, to systematically investigate the variation of quantum parameters (such as rotation blocks, repetitions, and entanglement types) to observe their subtle effect on the overall performance. In our paper, the performance is measured and dictated by convergence to similar ground-state energy values for resultant optimal solutions by each algorithm variation set for QAOA and VQE to the exact eigensolver (classical solution). Our results provide effective insights into comprehending PO from the lens of Quantum Machine Learning in terms of convergence to the classical solution, which is used as a benchmark. This study paves the way for identifying efficient configurations of quantum circuits for solving PO and unveiling their inherent inter-relationships.
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.
Quantum algorithms have gained increasing attention for addressing complex combinatorial problems in finance, notably portfolio optimization. This study systematically benchmarks two prominent variational quantum approaches, Variational Quantum Eigensolver (VQE) and Quantum Approximate Optimization Algorithm (QAOA), under diverse experimental settings, including different asset universes, ansatz architectures, and circuit depths. Although both methods demonstrate effective cost function minimization, the resulting portfolios often violate essential financial criteria, such as adequate diversification and realistic risk exposure. To bridge the gap between computational optimization and practical viability, we introduce an Expert Analysis Evaluation framework in which financial professionals assess the economic soundness and the market feasibility of quantum-optimized portfolios. Our results highlight a critical disparity between algorithmic performance and financial applicability, emphasizing the necessity of incorporating expert judgment into quantum-assisted decision-making pipelines.
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.
Quantum Computing is a dynamic field which has evolved since its inception around 3 decades back, to the development of various powerful algorithms including Quantum Approximate Optimization Algorithm (QAOA) and Variational Quantum Eigensolver (VQE) to name a few. Today's quantum computers are not as powerful as the current breed of supercomputers. However, the existing breed of NISQ (Noisy Intermediate Scale Quantum) quantum computers have a significant potential to provide faster solutions to problems in various domains which are not just relevant for the present but also for the future such as Quantum Machine Learning in the Fintech domain. Portfolio Optimization (PO) is one such problem in research and the financial services industry at large. In principle, Quantum Computing, makes it possible to arrive at an optimal portfolio composition for a high return and low risk investment much faster than any existing supercomputer today. This review paper examines literature on classical and quantum machine learning approaches for Mutual Fund PO, analyzing 44 papers from 2003 to 2023. PO being a vast topic, we limit our scope to Mutual Funds and its driver that is the equity markets. We provide an overview to the types of problems, preferred approaches, their benchmarks, deduced conclusions, and research gaps as a comprehensive survey for diverse readers.
A quantum approach for portfolio optimization involves using quantum computing to solve complex optimization problems related to portfolio selection. The approach involves constructing a mathematical model of the portfolio optimization problem using various algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) or the Variational Quantum Eigensolver (VQE). This approach has the potential to provide more accurate and efficient solutions than classical approaches, particularly for large and complex portfolio optimization problems. Moreover, this paper also dives into discussing and comparing the results obtained from both these approaches. Our work is under the assumptions required for the proposed formulation deriving meaningful considerations about the solution quality found, measured as the value of Sharpe Ratio.
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.