  Quantum computers are expected to surpass the computational capabilities of
classical computers during this decade and have transformative impact on
numerous industry sectors, particularly finance. In fact, finance is estimated
to be the first industry sector to benefit from quantum computing, not only in
the medium and long terms, but even in the short term. This survey paper
presents a comprehensive summary of the state of the art of quantum computing
for financial applications, with particular emphasis on stochastic modeling,
optimization, and machine learning, describing how these solutions, adapted to
work on a quantum computer, can potentially help to solve financial problems,
such as derivative pricing, risk modeling, portfolio optimization, natural
language processing, and fraud detection, more efficiently and accurately. We
also discuss the feasibility of these algorithms on near-term quantum computers
with various hardware implementations and demonstrate how they relate to a wide
range of use cases in finance. We hope this article will not only serve as a
reference for academic researchers and industry practitioners but also inspire
new ideas for future research.
