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arXiv:2512.22001

Variational Quantum Eigensolver for Real-World Finance: Scalable Solutions for Dynamic Portfolio Optimization Problems

Irene De León, Danel Arias, Manuel Martín-Cordero, María Esperanza Molina, Pablo Serrano, Senaida Hernández-Santana, Miguel Ángel Jiménez Herrera, Joana Fraxanet, Ginés Carrascal, Escolástico Sánchez, Inmaculada Posadillo, Álvaro Nodar

quant-phq-fin.CPq-fin.PMSubmitted Dec 26, 2025• Announced Dec 29, 2025• 0 citations
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Abstract

We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications.

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We present a scalable, hardware-aware methodology for extending the Variational Quantum Eigensolver (VQE) to large, realistic Dynamic Portfolio Optimization (DPO) problems. Building on the scaling strategy from our previous work, where we tailored a VQE workflow to both the DPO formulation and the target QPU, we now put forward two significant advances. The first is the implementation of the Ising Sample-based Quantum Configuration Recovery (ISQR) routine, which improves solution quality in Quadratic Unconstrained Binary Optimization problems. The second is the use of the VQE Constrained method to decompose the optimization task, enabling us to handle DPO instances with more variables than the available qubits on current hardware. These advances, which are broadly applicable to other optimization problems, allow us to address a portfolio with a size relevant to the financial industry, consisting of up to 38 assets and covering the full Spanish stock index (IBEX 35). Our results, obtained on a real Quantum Processing Unit (IBM Fez), show that this tailored workflow achieves financial performance on par with classical methods while delivering a broader set of high-quality investment strategies, demonstrating a viable path towards obtaining practical advantage from quantum optimization in real financial applications.
In finance, portfolio optimization aims at finding optimal investments maximizing a trade-off between return and risks, given some constraints. Classical formulations of this quadratic optimization problem have exact or heuristic solutions, but the complexity scales up as the market dimension increases. Recently, researchers are evaluating the possibility of facing the complexity scaling issue by employing quantum computing. In this paper, the problem is solved using the Variational Quantum Eigensolver (VQE), which in principle is very efficient. The main outcome of this work consists of the definition of the best hyperparameters to set, in order to perform Portfolio Optimization by VQE on real quantum computers. In particular, a quite general formulation of the constrained quadratic problem is considered, which is translated into Quadratic Unconstrained Binary Optimization by the binary encoding of variables and by including constraints in the objective function. This is converted into a set of quantum operators (Ising Hamiltonian), whose minimum eigenvalue is found by VQE and corresponds to the optimal solution. In this work, different hyperparameters of the procedure are analyzed, including different ansatzes and optimization methods by means of experiments on both simulators and real quantum computers. Experiments show that there is a strong dependence of solutions quality on the sufficiently sized quantum computer and correct hyperparameters, and with the best choices, the quantum algorithm run on real quantum devices reaches solutions very close to the exact one, with a strong convergence rate towards the classical solution, even without error-mitigation techniques. Moreover, results obtained on different real quantum devices, for a small-sized example, show the relation between the quality of the solution and the dimension of the quantum processor. Evidences allow concluding which are the best ways to solve real Portfolio Optimization problems by VQE on quantum devices, and confirm the possibility to solve them with higher efficiency, with respect to existing methods, as soon as the size of quantum hardware will be sufficiently high.
Portfolio optimization is a cornerstone of financial decision-making, traditionally relying on classical algorithms to balance risk and return. Recent advances in quantum computing offer a promising alternative, leveraging quantum algorithms to efficiently explore complex solution spaces and potentially outperform classical methods in high-dimensional settings. However, conventional quantum approaches typically assume a one-to-one correspondence between qubits and variables (e.g. financial assets), which severely limits the applicability of gate-based quantum systems due to current hardware constraints. As a result, only quantum annealing-like methods have been used in realistic scenarios. In this work, we show how a gate-based variational quantum algorithm can be applied to a real-world portfolio optimization problem by assigning multiple variables per qubit. Specifically, we address a problem involving over 250 variables, where the market graph representing a real stock market is iteratively partitioned into sub-portfolios of highly correlated assets. This approach enables improved scalability compared to traditional variational methods and opens new possibilities for quantum-enhanced financial applications.
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.
Loan portfolio optimization (LPO) seeks portfolios that minimize credit risk while satisfying practical selection constraints. Accounting for portfolio-level risk requires modeling not only expected losses but also loss variability and borrower-default correlations, leading to a large-scale combinatorial optimization problem whose complexity grows rapidly with portfolio size. In this work, we formulate LPO as a Quadratic Constrained Binary Optimization (QCBO) problem that jointly captures expected and unexpected losses and transform the resulting formulation into a Quadratic Unconstrained Binary Optimization (QUBO) model suitable for variational quantum optimization. To address the limited qubit resources of current quantum hardware, we employ Pauli Correlation Encoding (PCE), which enables a large number of portfolio-selection variables to be represented using comparatively few qubits. The proposed framework is evaluated on a real-world microfinance dataset comprising 2012 borrowers. For problem instances with up to 1000 portfolio-selection variables, we benchmark classical simulations of a variational quantum algorithm (VQA) against Google OR-Tools under matched time budgets, obtaining feasible portfolios with an objective-value gap of about 40% across all sizes. We further implement the framework on superconducting quantum hardware for instances containing up to 1500 variables. Across these instances, the experimentally obtained objective values are within 10% of the corresponding simulation results. These findings demonstrate the feasibility of applying PCE-based variational quantum optimization to large-scale loan portfolio optimization under current quantum hardware limitations.
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.
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.