  Quantum computers are expected to have substantial impact on the finance
industry, as they will be able to solve certain problems considerably faster
than the best known classical algorithms. In this article we describe such
potential applications of quantum computing to finance, starting with the
state-of-the-art and focusing in particular on recent works by the QC Ware
team. We consider quantum speedups for Monte Carlo methods, portfolio
optimization, and machine learning. For each application we describe the extent
of quantum speedup possible and estimate the quantum resources required to
achieve a practical speedup. The near-term relevance of these quantum finance
algorithms varies widely across applications - some of them are heuristic
algorithms designed to be amenable to near-term prototype quantum computers,
while others are proven speedups which require larger-scale quantum computers
to implement. We also describe powerful ways to bring these speedups closer to
experimental feasibility - in particular describing lower depth algorithms for
Monte Carlo methods and quantum machine learning, as well as quantum annealing
heuristics for portfolio optimization. This article is targeted at financial
professionals and no particular background in quantum computation is assumed.
