  Pricing interest-rate financial derivatives is a major problem in finance, in
which it is crucial to accurately reproduce the time-evolution of interest
rates. Several stochastic dynamics have been proposed in the literature to
model either the instantaneous interest rate or the instantaneous forward rate.
A successful approach to model the latter is the celebrated Heath-Jarrow-Morton
framework, in which its dynamics is entirely specified by volatility factors.
On its multifactor version, this model considers several noisy components to
capture at best the dynamics of several time-maturing forward rates. However,
as no general analytical solution is available, there is a trade-off between
the number of noisy factors considered and the computational time to perform a
numerical simulation. Here, we employ the quantum principal component analysis
to reduce the number of noisy factors required to accurately simulate the time
evolution of several time-maturing forward rates. The principal components are
experimentally estimated with the $5$-qubit IBMQX2 quantum computer for
$2\times 2$ and $3\times 3$ cross-correlation matrices, which are based on
historical data for two and three time-maturing forward rates. This manuscript
is a first step towards the design of a general quantum algorithm to fully
simulate on quantum computers the Heath-Jarrow-Morton model for pricing
interest-rate financial derivatives. It shows indeed that practical
applications of quantum computers in finance will be achievable in the near
future.
