Portfolio optimization based on quantum linear algorithm

Abstract The rapid development of quantum computation has brought new possibilities to many fields. Especially in finance, quantum computing offers significant advantages. Recently, the portfolio optimization problem has been solved by a quantum algorithm with a mean-variance model with sparse data. However, the mean-variance model does not match the practice, and furthermore, the data is mostly dense. To fill the gap, we propose the Quantum-Enhanced Portfolio Optimization based on the mean-semi-variance model, where the mean-semi-variance model incorporates an optimized risk definition. The algorithm also effectively reduces the time complexity of solving high-dimensional linear systems and achieves sparsity independence.