In a new study, researchers from IBM and Vanguard explore how quantum computing can tackle one of the most computationally demanding problems in finance: constructing optimized portfolios under real-world constraints. The work, which leverages what’s known as a sampling-based variational quantum algorithm (VQA), shows that quantum-classical hybrid workflows have the potential to provide solutions on par with purely classical methods for complex financial optimization tasks — paving the way for future applications in asset management and beyond.
In practice, portfolio managers navigate a far more complex landscape than the Markowitz model approach. That landscape might involve discrete decisions such as whether to include a specific bond or not, nonlinear constraints such as constraints which may include interactions between assets held in the portfolio (e.g., risk), and multiple competing objectives such as cases where the goal is to both maximize return while also minimizing risks. As the number of candidate assets grows, often into the thousands, the optimization problem becomes exponentially harder.
In their work, the IBM-Vanguard team explored how sampling-based variational quantum algorithms may be able to address this challenge. These methods combine the strengths of quantum sampling with classical optimization and post-processing, enabling a new class of heuristics that can explore complex solution landscapes more efficiently than traditional methods.
In this study, the team used 109 qubits of the 133 available on an IBM Quantum Heron r1 processor, executing circuits with up to 4,200 gates. The quantum samples were then refined using a classical local search algorithm to further improve solution quality.
The researchers applied this method to a simplified bond exchange-traded fund (ETF) portfolio construction problem. The results were benchmarked against the classical optimization solver CPLEX, which is able to solve the problem to optimality at this scale.
Promising metrics were shown, including:
- An optimization gap within accepted industry standards after quantum sampling and local search
- Improved convergence at smaller problem scales when using more entangled quantum circuits
- Robust performance even in the presence of hardware noise, with sample quality improving over iterations
Importantly, the study found that the quantum-classical workflow consistently outperformed a purely classical local search approach, especially as problem size increased.
“This work highlights the growing potential of quantum optimization workflows. By combining quantum circuits that explore high-dimensional solution spaces with classical algorithms that refine and validate results, researchers can tackle problems that are too large or too complex for either quantum or classical methods alone.This approach is particularly promising for domains like finance, where optimization problems are often constrained, nonlinear, and sensitive to small changes in input data,” the authors and researchers wrote in a blog post.