  Financial derivatives are contracts that can have a complex payoff dependent
upon underlying benchmark assets. In this work, we present a quantum algorithm
for the Monte Carlo pricing of financial derivatives. We show how the relevant
probability distributions can be prepared in quantum superposition, the payoff
functions can be implemented via quantum circuits, and the price of financial
derivatives can be extracted via quantum measurements. We show how the
amplitude estimation algorithm can be applied to achieve a quadratic quantum
speedup in the number of steps required to obtain an estimate for the price
with high confidence. This work provides a starting point for further research
at the interface of quantum computing and finance.
