Quantum computing for finance

Quantum computers are expected to surpass the computational capabilities of classical computers and have a transformative impact on numerous industry sectors. We present a comprehensive summary of the state of the art of quantum computing for financial applications, with particular emphasis on stochastic modelling, optimization and machine learning. This Review is aimed at physicists, so it outlines the classical techniques used by the financial industry and discusses the potential advantages and limitations of quantum techniques. Finally, we look at the challenges that physicists could help tackle. Quantum computers are expected to surpass classical computers and transform industries. This Review focuses on quantum computing for financial applications and provides a summary for physicists on potential advantages and limitations of quantum techniques, as well as challenges that physicists could help tackle.