In a groundbreaking advancement at the intersection of finance and quantum computing, a team of researchers from Shanghai University and several quantum technology firms in Beijing has unveiled a novel approach to portfolio optimization (PO) that leverages quantum-classical hybrid algorithms. The study, recently published in Computational Economics, offers a powerful solution to the long-standing problem of optimizing investments in portfolios containing large, indivisible assets like real estate, NFTs, or private equity—categories that have long defied traditional methods.
The Problem: Complexity Beyond Classical Limits
Portfolio optimization has always been a cornerstone of financial strategy, aiming to balance risk and return under a web of real-world constraints. The classical Markowitz model, widely used for its elegance in handling continuous variables, struggles when faced with discrete and indivisible assets. These include high-value assets that cannot be fractionally owned or traded, transforming the problem into a combinatorial optimization challenge that is NP-hard—unsolvable within reasonable time frames by classical computers as asset complexity grows.
This complexity intensifies when portfolios include a mix of fungible continuous (e.g., stocks), fungible discrete (e.g., servers), and non-fungible (e.g., property) assets. Conventional algorithms falter in efficiently navigating the enormous solution spaces such problems entail.
The Breakthrough: Quantum-Classical Hybrid Annealing
To address this, the researchers proposed a flexible quantum-classical hybrid model that adapts the traditional PO problem into a Quadratic Unconstrained Binary Optimization (QUBO) format. By encoding discrete investment choices into binary variables, the model is rendered compatible with quantum hardware.
They implemented their approach using D-Wave’s superconducting quantum annealer. Unlike conventional quantum annealing, which is restricted by hardware qubit limitations, their Quantum-Classical Hybrid Annealing (QCHA) method decomposes the larger problem into manageable subproblems. Each subproblem is solved on the quantum processor, and the results are iteratively stitched together and refined through classical local search methods like Tabu Search or Steepest Descent.
Real-World Testing: Two Datasets, One Result
To evaluate the efficacy of the QCHA algorithm, the team tested it on two real-world datasets:
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Dataset 1: Included 10 publicly traded stocks from the Shanghai and Shenzhen exchanges over a four-month period.
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Dataset 2: Comprised 15 assets spanning stocks, mutual funds, and private equity funds over a shorter time window.
Using five key financial metrics—Net Asset Value (NAV), rate of return (RET), accumulated return (ACC), Sharpe ratio, and Sortino ratio—the researchers back-tested the performance of their algorithm. Across both datasets, QCHA outperformed all other tested methods, including classical solvers like Gurobi and simulated annealing, as well as pure quantum annealing.
Surpassing Classical Benchmarks
In Dataset-1, QCHA achieved a Sharpe ratio of 3.13, significantly higher than Gurobi (2.97) and classical alternatives. The QCHA solution also demonstrated high consistency, delivering robust returns while managing downside risk—a vital consideration for real-world investors.
In Dataset-2, which involved a more complex asset structure, QCHA once again proved its mettle. It maintained a Sortino ratio of 4.253—the highest among all algorithms tested—highlighting its superiority in managing downside volatility. Notably, the classical Gurobi solver edged out QCHA in accumulated returns, but the hybrid algorithm delivered more consistent risk-adjusted performance.
Qubit Scaling: Better Precision, Better Results
Another significant finding of the study was the impact of qubit scaling on performance. By increasing the number of qubits from 20 to 50 in Dataset-1 and up to 128 in Dataset-2, the researchers demonstrated a near-linear improvement in financial performance indicators. This reinforces the idea that as quantum hardware matures—with better gate fidelity and higher qubit counts—the potential for these algorithms to solve increasingly complex financial problems will only grow.
Real-World Constraints, Real-World Relevance
Perhaps most impressively, the model’s flexibility allowed for the inclusion of real-world constraints such as limits on the number of assets selected. Even with these constraints, the QCHA algorithm maintained strong performance, showcasing its adaptability and scalability. While classical algorithms suffered noticeable degradation when constraints were introduced, QCHA retained high-quality solutions with only marginal drops in return and risk metrics.
Implications for the Future of Finance
This research marks a critical step forward in integrating quantum computing into financial practice. The ability to handle multiple discrete variables with varying constraints opens doors to a more realistic and effective approach to investment strategy. With financial markets increasingly featuring complex asset types and evolving regulations, adaptable quantum algorithms could soon become indispensable.
As quantum hardware continues to advance, particularly in qubit coherence and gate fidelity, the authors suggest that larger and more dynamic portfolios could be optimized in real-time. Moreover, the integration of quantum algorithms with machine learning techniques could further enhance prediction accuracy and adaptability—leading to smarter, faster, and more profitable decision-making in global markets.
Final Thoughts
The collaboration between academia and industry showcased in this research underscores a growing convergence of finance, computer science, and quantum physics. By proving the feasibility and effectiveness of hybrid quantum-classical algorithms in solving real-world financial problems, the study not only addresses a long-standing computational hurdle but also paves the way for the future of algorithmic trading and asset management.