Multiclass Portfolio Optimization via Variational Quantum Eigensolver with Dicke State Ansatz

Abstract: Combinatorial optimization is a fundamental challenge in various domains, with portfolio optimization standing out as a key application in finance. Despite numerous quantum algorithmic approaches proposed for this problem, most overlook a critical feature of realistic portfolios: diversification. In this work, we introduce a novel quantum framework for multiclass portfolio optimization that explicitly incorporates diversification by leveraging multiple parametrized Dicke states, simultaneously initialized to encode the diversification constraints , as an ansatz of the Variational Quantum Eigensolver. A key strength of this ansatz is that it initializes the quantum system in a superposition of only feasible states, inherently satisfying the constraints. This significantly reduces the search space and eliminates the need for penalty terms. In addition, we also analyze the impact of different classical optimizers in this hybrid quantum-classical approach. Our findings demonstrate that, when combined with the CMA-ES optimizer, the Dicke state ansatz achieves superior performance in terms of convergence rate, approximation ratio, and measurement probability. These results underscore the potential of this method to solve practical, diversification-aware portfolio optimization problems relevant to the financial sector.