Quantum Algorithm Boosts Portfolio Returns with Constraints
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Portfolio optimisation with strict cardinality constraints presents a significant combinatorial challenge for classical methods, especially within the growing field of Direct Indexing and increasingly common ESG-constrained investment mandates. Javier Mancilla from SquareOne Capital, Theodoros D. Bouloumis from Aristotle University of Thessaloniki, and Frederic Goguikian, also from SquareOne Capital, demonstrate a novel hybrid approach utilising the Quantum Approximate Optimisation Algorithm (QAOA) to address this problem. Their research, conducted in collaboration between SquareOne Capital and Aristotle University of Thessaloniki, details a constraint-preserving QAOA formulation employing a Dicke state initialisation and XY-mixer Hamiltonian, ensuring the algorithm explores only portfolios of a defined size. This innovative method, coupled with a new Trotterized parameter initialisation schedule designed to combat the ‘Barren Plateau’ problem, achieves a Sharpe Ratio of 1.81 during backtesting on US equities, substantially exceeding the performance of both Simulated Annealing and Hierarchical Risk Parity, and offering a potentially transformative tool for institutional investors. Scientists are applying the power of quantum computing to a persistent problem in finance: building better investment portfolios with specific criteria. The challenge of balancing risk and reward, particularly when ethical or practical limits are imposed, has traditionally defied conventional methods. This novel hybrid approach offers a potential route to genuinely optimised solutions, even with today’s limited quantum hardware.
Scientists have developed a quantum algorithm that significantly outperforms traditional methods for optimising investment portfolios with strict limitations on the number of assets selected. Furthermore, the researchers addressed the practical implications of implementing this algorithm, acknowledging a relatively high portfolio turnover rate of 76.8. This turnover, while indicative of potentially optimal allocations, necessitates a careful consideration of transaction costs and operational feasibility within institutional investment settings.
The team also introduced a novel parameter initialisation schedule, inspired by adiabatic quantum computing, to mitigate the “Barren Plateau” problem, a common obstacle in quantum optimisation that hinders the algorithm’s ability to converge on optimal solutions. Furthermore, a novel Trotterized parameter initialisation schedule, inspired by adiabatic principles, was employed to mitigate the Barren Plateau problem, a common obstacle in quantum circuit optimisation. However, the algorithm’s operational implications were also carefully considered, with analysis revealing a relatively high portfolio turnover rate of 76.8% per cycle. Unlike conventional QAOA implementations that rely on transverse field mixers and introduce soft penalties for constraints, this research utilizes an XY-mixer Hamiltonian coupled with Dicke state initialisation. This innovative combination strictly enforces the Hamming weight, effectively limiting the solution space to only valid portfolios containing precisely K assets, thereby avoiding distortion of the energy landscape. The choice of an XY-mixer, which preserves the total magnetization of the system, is crucial for maintaining constraint satisfaction throughout the quantum evolution. To further enhance performance and address the “Barren Plateau” problem, a common obstacle in quantum optimisation where gradients vanish, a Trotterized parameter initialisation schedule was implemented. Inspired by adiabatic quantum computation, this schedule carefully sets the initial values of the QAOA parameters, guiding the optimisation process towards more promising regions of the solution space. This initialisation leverages insights from slowly varying Hamiltonians to improve the likelihood of finding optimal or near-optimal solutions. The entire quantum circuit was constructed and simulated using established quantum computing frameworks, allowing for rigorous testing and analysis of the algorithm’s capabilities. The selection of these baselines provides a comprehensive comparison against both widely used and more recent classical methods for portfolio construction, highlighting the potential advantages of the quantum approach. A rigorous backtesting procedure, spanning a 2025 period, was then used to evaluate the algorithms’ performance on a basket of 10 US equities. Quantum algorithms optimise portfolio construction with embedded cardinality constraints The relentless pursuit of better portfolio construction isn’t about chasing higher returns; it’s about navigating increasingly complex constraints. For years, institutional investors have grappled with the tension between optimising for profit and adhering to strict rules, whether those relate to the number of holdings, ethical considerations, or regulatory demands. Classical methods often struggle with these ‘cardinality constraints’, forcing compromises or computationally expensive workarounds. This new work offers a compelling demonstration that quantum-inspired algorithms, specifically a carefully constructed variant of QAOA, can genuinely improve performance within these limitations. The resulting portfolio demonstrably outperformed benchmarks, suggesting a pathway towards genuinely useful quantum advantage in finance. However, a Sharpe Ratio, while impressive, only tells part of the story. The reported high turnover rate raises a critical question: is the theoretical optimality worth the associated transaction costs and market impact. Furthermore, the backtesting period, while reasonable, needs to be extended to encompass diverse market conditions. Future work should explore how this algorithm performs during periods of volatility and stress. Crucially, translating this success to actual quantum hardware remains a significant hurdle, demanding robust error mitigation strategies and a deeper understanding of how noise affects constraint preservation. The next step isn’t simply scaling up the computation, but refining the algorithm to be resilient and practical. 👉 More information 🗞 Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing 🧠 ArXiv: https://arxiv.org/abs/2602.14827 Tags: