Achieving High-Quality Portfolio Optimization with the Variational Quantum Eigensolver

Abstract: Portfolio optimization is a fundamental problem in finance that aims to determine the optimal allocation of assets within a portfolio to maximize returns while minimizing risk. It can be formulated as a Quadratic Unconstrained Binary Optimization (QUBO) problem, which is NP-hard. Quantum computing offers the potential to solve such problems more efficiently than classical methods. In this work, we employ the Variational Quantum Eigensolver (VQE) to address the portfolio optimization problem. To increase the likelihood of converging to high-quality solutions, we propose using the Weighted Conditional Value-at-Risk (WCVaR) as the cost function and the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) as the optimizer. Our experiments are conducted using the classical simulations on the Wuyue QuantumAI platform. The results demonstrate that the combination of WCVaR and CMA-ES leads to improved performance in solving the portfolio optimization problem.