Efficient Device Independent Quantum Number Generator Design and Analysis
By Max
Introduction
Monte Carlo simulations [Metropolis, 1949] are a powerful class of computational algorithms used to model and analyze complex systems or processes involving uncertainty. These simulations are widely used across various scientific and engineering domains, including physics, finance, and machine learning. A typical Monte Carlo simulation involves four main steps:
Model definition: Develop a mathematical or computational model of the system under investigation.
Randomization: Introduce random variables into the model to represent uncertain or variable inputs.
Sampling and simulation: Conduct a large number of simulation runs (often in the millions) by sampling from the input distributions and evaluating the model for each instance.
Statistical analysis: Aggregate the simulation outputs and compute statistical measures such as means, variances, percentiles, and probabilities.
Among these steps, Step 2 — randomization — is particularly critical. The quality of the random number generator (RNG) directly affects both the accuracy and reliability of the simulation. Poor-quality RNGs can introduce subtle biases, increase estimator variance, or compromise convergence, ultimately affecting the validity of the results.
Conventional pseudorandom number generators (PRNGs) rely on deterministic algorithms initialized with a finite seed, producing sequences that mimic randomness but are inherently predictable if the internal state is known. In contrast, quantum random number generators (QRNGs) exploit fundamental quantum mechanical phenomena — such as photon path selection or quantum phase noise — to generate intrinsically unpredictable sequences. Device-independent QRNGs (DI-QRNGs) further strengthen this unpredictability by avoiding reliance on assumptions about the internal workings of the device, instead using principles like Bell inequality violations to certify randomness.
The motivation for this work lies in understanding how the source of randomness influences the behavior and reliability of Monte Carlo simulations. While PRNGs are widely used and efficient, they may be inadequate in high-assurance applications such as cryptography, security-sensitive simulations, and quantum computing. QRNGs, particularly DI-QRNGs, offer a potential alternative with provable guarantees of randomness rooted in quantum physics.
Despite the theoretical advantages of QRNGs, there is limited practical analysis comparing their performance with PRNGs in computational settings. This work aims to bridge that gap by quantitatively evaluating how different RNG types impact key metrics in Monte Carlo simulations.
Intellectual Merit
We propose a new measure to compare two sampling algorithms, focusing on how each algorithm’s estimate of an extreme quantile (e.g., the 99.9th percentile) is affected by the use of imperfect random numbers in the simulation. More specifically, we propose a finite-sample, distribution-free quantile-error bound that explicitly trades RNG imperfection against sample size. If time permits, we also aim to propose a novel and efficient DI-QRNG design that works on IBM quantum computers.
Broader Impact
Monte Carlo simulations play a critical role in physics and mathematics, serving as essential tools for optimization, numerical integration, and generating draws from probability distributions. Examples include simulating fluid and cellular systems, engineering designs, and the stock market. Beyond Monte Carlo simulations, strong random number generation is crucial for any intentionally unpredictable process, including computer simulations, randomized design procedures, gambling, and cryptography.