This paper investigates the experimental performance of a discrete portfolio optimization problem relevant to the financial services industry on the gate-model of quantum computing. We implement and evaluate a portfolio rebalancing use case on an idealized simulator of a gate-model quantum computer. The characteristics of this exemplar application include trading in discrete lots, non-linear trading costs, and the investment constraint. We design a novel problem encoding and hard constraint mixers for the Quantum Alternating Operator Ansatz, and compare to its predecessor the Quantum Approximate Optimization Algorithm. Experimental analysis demonstrates the potential tractability of this application on Noisy Intermediate-Scale Quantum (NISQ) hardware, identifying portfolios within 5% of the optimal adjusted returns and with the optimal risk for a small eight-stock portfolio.
This paper investigates the experimental performance of a discrete portfolio optimization problem relevant to the financial services industry on the gate-model of quantum computing. We implement and evaluate a portfolio rebalancing use case on an idealized simulator of a gate-model quantum computer. The characteristics of this exemplar application include trading in discrete lots, non-linear trading costs, and the investment constraint. We design a novel problem encoding and hard constraint mixers for the Quantum Alternating Operator Ansatz, and compare to its predecessor the Quantum Approximate Optimization Algorithm. Experimental analysis demonstrates the potential tractability of this application on Noisy Intermediate-Scale Quantum (NISQ) hardware, identifying portfolios within 5% of the optimal adjusted returns and with the optimal risk for a small eight-stock portfolio.
Portfolio optimization, a core combinatorial optimization problem in quantitative finance, requires balancing return maximization and risk minimization within discrete asset sets. Classical algorithms often struggle with scalability and local optima traps when handling large-scale asset pools, limiting their practicality in dynamic markets. This study proposes a complete Quantum Approximate Optimization Algorithm (QAOA) workflow for portfolio optimization, from problem formalization to experimental validation. We first transform the portfolio optimization problem into a Quadratic Unconstrained Binary Optimization (QUBO) framework, then design a parameterized QAOA circuit with adjustable layers to balance expressiveness and noise resilience. We propose a methodology using Qiskit for quantum simulation and classical optimizers for parameter tuning, we propose implementing the algorithm on real-world S&P 500 stock data. We could also analyze the impact of quantum hardware noise and propose mitigation strategies, providing actionable insights for Noisy intermediate-scale quantum computing (NISQ)-era implementations. This work bridges quantum algorithm design with real-world financial applications, offering a theoretical framework for quantum-driven portfolio optimization.
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.
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.
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 an essential use case in Finance, but its computational complexity forces financial institutions to resort to approximated solutions, which are still time consuming. Thus, the scientific community is looking at how Quantum Computing can be used for efficient and accurate portfolio optimization.
Portfolio optimization can be formulated as a quadratic program, with the cost function enforcing risk minimization for a targeted return. Of particular interest is the mean-variance portfolio optimization problem.
Using the method of Lagrange multipliers, the program can be converted into a system of linear equations and potentially benefit from the exponential speedup provided by the HHL quantum algorithm. However, multiple components in HHL are unsuitable for execution on Noisy Intermediate Scale Quantum (NISQ) hardware.
This paper introduces NISQ-HHL, the first hybrid formulation of HHL suitable for the end-to-end execution of small-scale portfolio-optimization problems on NISQ devices. NISQ-HHL extends the hybrid HHL variant with newly available quantum-hardware features: mid-circuit measurement, Quantum Conditional Logic (QCL), and qubit reset and reuse. To best of our knowledge, NISQ-HHL is the first algorithm incorporating a QCL-enhanced version of Phase Estimation that was executed on real hardware. In addition, NISQ-HHL includes a novel method for choosing the optimal evolution time for the Hamiltonian simulation. Although this paper focuses on portfolio optimization, the techniques it proposes to make HHL more scalable are generally applicable to any problem that can be solved via HHL in the NISQ era.
We empirically demonstrate the effectiveness of NISQ-HHL by presenting the experimental results we obtained on a real quantum device, the trapped-ion Honeywell System Model H1.
Portfolio optimization under conditions of risk and market uncertainty remains a foundational challenge in financial economics and investment management. Classical optimization frameworks, including mean–variance models and stochastic programming approaches, often struggle with high-dimensional asset universes, nonlinear correlations, and dynamic market regimes. This paper examines quantum computing approaches to portfolio optimization under risk and market uncertainty, focusing on hybrid quantum–classical algorithms designed to enhance combinatorial optimization and probabilistic modeling. By integrating quantum annealing, variational quantum circuits, and quantum-enhanced sampling techniques with classical financial analytics, the study evaluates their potential to improve computational efficiency and scenario sensitivity. The analysis considers both theoretical advantages and practical limitations within the Noisy Intermediate-Scale Quantum (NISQ) era. The findings suggest that quantum-assisted optimization may complement traditional portfolio models by expanding feasible solution spaces and improving robustness under uncertainty, thereby contributing to more adaptive and resilient investment strategies.