Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing

• URL: http://arxiv.org/abs/2602.14827v1
• Date: Mon, 16 Feb 2026 15:19:15 GMT
• Title: Constrained Portfolio Optimization via Quantum Approximate Optimization Algorithm (QAOA) with XY-Mixers and Trotterized Initialization: A Hybrid Approach for Direct Indexing
• Abstract summary: This paper presents a constraint-preserving Quantum Approximate Algorithm (QAOA) formulation against Simulated Annealing (SA) and Hierarchical Risk Parity (HRP)<n>We show that our QAOA approach achieves a Sharpe Ratio of 1.81, significantly outperforming Simulated Annealing (1.31) and HRP (0.98)<n>Backtesting on a basket of 10 US equities over 2025 reveals that our QAOA approach achieves a Sharpe Ratio of 1.81, significantly outperforming Simulated Annealing (1.31) and HRP (0.98)
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Portfolio optimization under strict cardinality constraints is a combinatorial challenge that defies classical convex optimization techniques, particularly in the context of "Direct Indexing" and ESG-constrained mandates. In the Noisy Intermediate-Scale Quantum (NISQ) era, the Quantum Approximate Optimization Algorithm (QAOA) offers a promising hybrid approach. However, standard QAOA implementations utilizing transverse field mixers often fail to strictly enforce hard constraints, necessitating soft penalties that distort the energy landscape. This paper presents a comprehensive analysis of a constraint-preserving QAOA formulation against Simulated Annealing (SA) and Hierarchical Risk Parity (HRP). We implement a specific QAOA ansatz utilizing a Dicke state initialization and an XY-mixer Hamiltonian that strictly preserves the Hamming weight of the solution, ensuring only valid portfolios of size K are explored. Furthermore, we introduce a Trotterized parameter initialization schedule inspired by adiabatic quantum computing to mitigate the "Barren Plateau" problem. Backtesting on a basket of 10 US equities over 2025 reveals that our QAOA approach achieves a Sharpe Ratio of 1.81, significantly outperforming Simulated Annealing (1.31) and HRP (0.98). We further analyze the operational implications of the algorithm's high turnover (76.8%), discussing the trade-offs between theoretical optimality and implementation costs in institutional settings.

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