International Journal of Mathematical Education in Science and Technology

Random numbers and quantum computers

Mark McCartney, David H. Glass

Published Sep 1, 2002• 1 citation

Abstract

The topic of random numbers is investigated in such a way as to illustrate links between mathematics, physics and computer science. First, the generation of random numbers by a classical computer using the linear congruential generator and logistic map is considered. It is noted that these procedures yield only pseudo-random numbers since deterministic algorithms are used. The paper then discusses the strange behaviour of the quantum world and briefly describes how its properties could be exploited in a quantum computer to produce numbers that are genuinely random. The final section considers how different ways of looking at a problem can yield insights into the concept of randomness.

DOI: 10.1080/00207390210162421

Related papers

Testing Randomness in Quantum Mechanics

Aldo C. Martinez-Becerril, Aldo Solís, Rafael Díaz Hernández Rojas +3 more

Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.

arXiv:1810.08718Oct 20, 20183 citations

Quantum Computation and Quantum Information

Yazhen Wang

Quantum computation and quantum information are of great current interest in computer science, mathematics, physical sciences and engineering. They will likely lead to a new wave of technological innovations in communication, computation and cryptography. As the theory of quantum physics is fundamentally stochastic, randomness and uncertainty are deeply rooted in quantum computation, quantum simulation and quantum information. Consequently quantum algorithms are random in nature, and quantum simulation utilizes Monte Carlo techniques extensively. Thus statistics can play an important role in quantum computation and quantum simulation, which in turn offer great potential to revolutionize computational statistics. While only pseudo-random numbers can be generated by classical computers, quantum computers are able to produce genuine random numbers; quantum computers can exponentially or quadratically speed up median evaluation, Monte Carlo integration and Markov chain simulation. This paper gives a brief review on quantum computation, quantum simulation and quantum information. We introduce the basic concepts of quantum computation and quantum simulation and present quantum algorithms that are known to be much faster than the available classic algorithms. We provide a statistical framework for the analysis of quantum algorithms and quantum simulation.

Aug 17, 2016111 citations

Quantum Computation and Quantum Information

Yazhen Wang

arXiv:1210.0736Statistical ScienceAug 1, 201265 citations

Exploring quantum systems for pseudo-random number generation

Luis José Mantilla Santa Cruz, Luis Fernando Faina, João Henrique de Souza Pereira

Abstract Quantum realizations have opened a new ways for computer science. The new characteristics and phenomenons allow us to create new algorithms for general proposes. An interesting topic is random number generation. There are two perspectives for this proposes. True random numbers generator (TRN) and pseudo random numbers generator (PRNG). True Random Number Generators has four significant characteristics: randomness, long Period, insensitivity to seeds, repeatability. Additionally, Pseudo Random Number Generators is a fascinating topic that leverages the principles of computer science to craft deterministic algorithms, enabling the creation of a sequence of pseudo-random numbers. A crucial element in this process is the 'seed', which serves as the initial value to generate the entire sequence. This document proposes a algorithm based on a quantum system and the quasi-probability of its possible states to generate a long set of numbers which has pseudo random properties. The quantum system is compound by n qubits, its initial conditions and a small set of rotation gates with a fixed angle. The tests were realized using the battery test called NIST SP800-22, and alpha=0.01 as a threshold to ensures 99\% of precision. The results demonstrate that it is possible generate a long set of pseudo numbers with random characteristics using a quantum simple operation. However, the experiments reveal that a real world implementation require a quantum system with at least 10-9 precision order.

Quantum Studies Mathematics and FoundationsOct 4, 20242 citations

Quantum random walks - an introductory overview

Julia Kempe, Albert Einstein

This article aims to provide an introductory survey on quantum random walks. Starting from a physical effect to illustrate the main ideas we will introduce quantum random walks, review some of their properties and outline their striking differences to classical walks. We will touch upon both physical effects and computer science applications, introducing some of the main concepts and language of present day quantum information science in this context. We will mention recent developments in this new area and outline some open questions. 1. Overview Ever since the discovery of quantum mechanics people have been puzzled by the counter-intuitive character of the laws of nature. Over time we have learned to accept more and more effects that are unimaginable in a classical Newtonian world. Modern technology exploits quantum effects both to our benefit and detriment—among the memorable examples we should cite laser technology and not omit the atomic bomb. In recent years interest in quantum information theory has been generated by the prospect of employing its laws to design devices of surprising power [1]. New ideas include quantum cryptography [2, 3] and quantum computation. In 1994 Shor [4] discovered a quantum algorithm to factor numbers efficiently (that is in time that grows only polynomically with the length of the number to be factored). This has unleashed a wave of activity across a broad range of disciplines: physics, computer science, mathematics and engineering. This fruitful axis of research has uncovered many new effects that are strikingly different from their classical counterparts, both from the physical point of view as well as from a computer science and communication theory perspective. Over time these communities have gained a greater understanding of the concepts and notions of the other. The idea that information cannot be separated from

Jan 1, 2003920 citations

Quantum random number generators

Miguel Herrero-Collantes, Juan Carlos García-Escartín

In mathematics and computer science, random numbers have the role of a resource for assisting proofs, making cryptography secure, and enabling computational protocols. This role motivates efforts to produce random numbers as a physical process. Potential physical sources abound, but arguably the most fundamental are those based on elementary quantum mechanical processes. This review discusses the current status of devices that generate quantum random numbers.

arXiv:1604.03304Reviews of Modern PhysicsFeb 22, 2017801 citations