Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems to enable solving large-scale optimization problems efficiently on the available hardware. The existing work uses a method called Large System Sampling Approximation (LSSA) that involves dividing the large problem into several smaller problems and then combining the multiple solutions to approximate the solution to the original problem. This paper introduces a novel technique to modify the sampling step of LSSA. We divide the portfolio optimization problem into sub-systems of smaller sizes by selecting a diverse set of assets that act as representatives of the entire market and capture the highest correlations among assets. We conduct tests on real-world stock data from the Indian stock market on up to 64 assets. Our experimentation shows that the hybrid approach performs at par with the traditional classical optimization methods with a good approximation ratio. We also demonstrate the effectiveness of our approach on a range of portfolio optimization problems of different sizes. We present the effects of different parameters on the proposed method and compare its performance with the earlier work. Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios in the near future.
Portfolio optimization is one of the most studied problems for demonstrating the near-term applications of quantum computing. However, large-scale problems cannot be solved on today's quantum hardware. In this work, we extend upon a study to use the best of both quantum annealing and gate-based quantum computing systems to enable solving large-scale optimization problems efficiently on the available hardware. The existing work uses a method called Large System Sampling Approximation (LSSA) that involves dividing the large problem into several smaller problems and then combining the multiple solutions to approximate the solution to the original problem. This paper introduces a novel technique to modify the sampling step of LSSA. We divide the portfolio optimization problem into sub-systems of smaller sizes by selecting a diverse set of assets that act as representatives of the entire market and capture the highest correlations among assets. We conduct tests on real-world stock data from the Indian stock market on up to 64 assets. Our experimentation shows that the hybrid approach performs at par with the traditional classical optimization methods with a good approximation ratio. We also demonstrate the effectiveness of our approach on a range of portfolio optimization problems of different sizes. We present the effects of different parameters on the proposed method and compare its performance with the earlier work. Our findings suggest that hybrid annealer-gate quantum computing can be a valuable tool for portfolio managers seeking to optimize their investment portfolios in the near future.
Portfolio optimization is a well-established problem in the field of finance and has recently gained attention in the context of quantum computing. The hardware limitations of quantum computers prevent the direct application of quantum algorithms to large-scale problems. We propose a novel two-stage approach that combines the strengths of both quantum annealing and gate-based quantum computing to efficiently solve large-scale portfolio optimization problems. Building upon the existing Large System Sampling Approximation (LSSA) approach, our work introduces a novel modification to the decomposition and aggregation steps of LSSA. We divide the problem into sub-problems of smaller sizes by solving the Maximum Independent Set (MIS) of the market graph and use a Parameterized Quantum Circuit (PQC) to aggregate the sub-problem solutions. We conduct extensive experiments on real-world data from the US stock market on up to 128 assets on simulators. Our results demonstrate that the proposed approach performs better with the same hardware resources. The outcomes of our research suggest that hybrid annealer-gate quantum computing can provide a practical and scalable solution to large-scale portfolio optimization problems, bridging the gap between theoretical advancements in quantum computing and real-world applications in finance.
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.
Abstract One of the major problems of quantum computing applications is that the required number of qubits to solve a practical problem is much larger than that of today's quantum hardware. In this work, we introduce the large-system sampling approximation (LSSA) algorithm to solve Ising problems with sizes up to Ngb2Ngb by an Ngb-qubit gate-based quantum computer, and problems with sizes up to Nan2Ngb by a hybrid computational architecture of an Nan-qubit quantum annealer and an Ngb-qubit gate-based quantum computer. By dividing the full-system problem into smaller subsystem problems, the LSSA algorithm then solves the subsystem problems by either gate-based quantum computers or quantum annealers, and optimizes the amplitude contributions of the solutions of the different subsystems with the full-problem Hamiltonian by the variational quantum eigensolver (VQE) on a gate-based quantum computer to determine the approximated ground-state configuration. LSSA has polynomial time complexity and can be further extended to a deeper level of approximation with computational overhead that grows linearly with the problem size. The effects of different subsystem sizes, numbers of subsystems, and full problem sizes on the performance of LSSA are investigated on both simulators and real hardware. The completely new computational concept of the hybrid gate-based and annealing quantum computing architecture opens a promising possibility to investigate large-size Ising problems and combinatorial optimization problems, making practical applications by quantum computing possible in the near future.
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.
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.
Recently, several researchers proposed portfolio optimization as a potential use case for quantum optimization. However, the literature is lacking an extensive benchmark quantifying the potential of quantum computers for portfolio optimization. In this work, we contribute to closing this gap. We provide a computational study, comparing quantum approaches against state-of-the-art classical methods on a meaningful, real-world instance set. In particular, we compare quantum annealing and the quantum approximate optimization algorithm against classical mixed-integer programming, simulated annealing, steepest descent local search, tabu search and a problem-tailored heuristic. We consider a variance-minimizing variant of portfolio optimization which we show to be more difficult to solve for classical optimizers than return-maximizing or multi-objective formulations. Our benchmark data set comprises 270 instances with up to 1,000 assets from actual stock data. Due to hardware limitation, quantum methods could only be tested for instances with at most 30 assets. The results show that all instances can be solved to proven optimality by mixed-integer programming in the order of seconds. Moreover, the problem-tailored heuristic consistently outperforms quantum approaches in terms of solution quality for fixed runtime. Thus, we conclude that there is only very limited room for a potential quantum advantage for the considered variant of portfolio optimization.