  Random numbers are a fundamental and useful resource in science and
engineering with important applications in simulation, machine learning and
cyber-security. Quantum systems can produce true random numbers because of the
inherent randomness at the core of quantum mechanics. As a consequence, quantum
random number generators are an efficient method to generate random numbers on
a large scale. We study in this paper the applications of a viable source of
unbiased quantum random numbers (QRNs) whose statistical properties can be
arbitrarily programmed without the need for any post-processing and that pass
all standard randomness tests of the NIST and Dieharder test suites without any
randomness extraction. Our method is based on measuring the arrival time of
single photons in shaped temporal modes that are tailored with an
electro-optical modulator. The advantages of our QRNs are shown via two
applications: simulation of a fractional Brownian motion, which is a
non-Markovian process, and option pricing under the fractional SABR model where
the stochastic volatility process is assumed to be driven by a fractional
Brownian motion. The results indicate that using the same number of random
units, our QRNs achieve greater accuracy than those produced by standard
pseudo-random number generators. Moreover, we demonstrate the advantages of our
method via an increase in computational speed, efficiency, and convergence.
