Quantum Systems for Monte Carlo Methods and Applications to Fractional Stochastic Processes

TL;DR

This paper presents a quantum random number generator based on photon arrival times that produces unbiased, programmable, and statistically validated random numbers, enhancing simulation accuracy and computational efficiency in fractional stochastic processes.

Contribution

The paper introduces a novel quantum random number generation method using shaped photon arrival times that requires no post-processing and passes all standard randomness tests.

Findings

Achieves higher accuracy than pseudo-random generators in simulations.

Increases computational speed and efficiency.

Demonstrates improved convergence in stochastic process applications.

Abstract

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.