Related papers: Random Numbers in Scientific Computing: An Introdu…
We review and extend, in a self-contained way, the mathematical foundations of numerical simulation methods that are based on the use of random states. The power and versatility of this simulation technology is illustrated by calculations…
Monte Carlo simulations are widely used in many areas including particle accelerators. In this lecture, after a short introduction and reviewing of some statistical backgrounds, we will discuss methods such as direct inversion, rejection…
We discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations and rigorous results. We also make various speculations about computation in a broader sense.
When permutation methods are used in practice, often a limited number of random permutations are used to decrease the computational burden. However, most theoretical literature assumes that the whole permutation group is used, and methods…
General wisdom is, mathematical operation is needed to generate number by numbers. It is pointed out that without any mathematical operation true random numbers can be generated by numbers through algorithmic process. It implies that human…
We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and…
We describe an embarrassingly parallel, anytime Monte Carlo method for likelihood-free models. The algorithm starts with the view that the stochasticity of the pseudo-samples generated by the simulator can be controlled externally by a…
Quantum Random Number Generators (QRNGs) emerged as a promising solution for generating truly random numbers. In the present article, we give an overview of QRNGs highlighting the merits and demerits of various strategies briefly. Then…
Random numbers form an intrinsic part of modern day computing with applications in a wide variety of fields. But due to their limitations, the use of pseudo random number generators (PRNGs) is certainly not desirable for sensitive…
Shower Monte Carlo event generators have played an important role in particle physics. Modern experiments would hardly be possible without them. In this talk I discuss how QCD physics is incorporated into the mathematical structure of these…
The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits…
Quantum advantage is notoriously hard to find and even harder to prove. For example the class of functions computable with classical physics actually exactly coincides with the class computable quantum-mechanically. It is strongly believed,…
We question the commonly accepted statement that random numbers certified by Bell's theorem carry some special sort of randomness, so to say, quantum randomness or intrinsic randomness. We show that such numbers can be easily generated by…
Random projections offer an appealing and flexible approach to a wide range of large-scale statistical problems. They are particularly useful in high-dimensional settings, where we have many covariates recorded for each observation. In…
Quantum information processing shows advantages in many tasks, including quantum communication and computation, comparing to its classical counterpart. The essence of quantum processing lies on the fundamental difference between classical…
This is the documentation for generating random samples from the quantum state space in accordance with a specified distribution, associated with this webpage: http://tinyurl.com/QSampling . Ready-made samples (each with at least a million…
We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is…
This work considers the notion of random tensors and reviews some fundamental concepts in statistics when applied to a tensor based data or signal. In several engineering fields such as Communications, Signal Processing, Machine learning,…
Many random processes can be simulated as the output of a deterministic model accepting random inputs. Such a model usually describes a complex mathematical or physical stochastic system and the randomness is introduced in the input…
Quantum random number generation is a technique to generate random numbers by extracting randomness from specific quantum processes. As for practical random number generators, they are required not only to have no information leakage but…