Employing online quantum random number generators for generating truly random quantum states in Mathematica

Abstract

The presented package for the Mathematica computing system allows the harnessing of quantum random number generators (QRNG) for investigating the statistical properties of quantum states. The described package implements a number of functions for generating random states. The new version of the package adds the ability to use the on-line quantum random number generator service and implements new functions for retrieving lists of random numbers. Thanks to the introduced improvements, the new version provides faster access to high-quality sources of random numbers and can be used in simulations requiring large amount of random data. New version program summaryProgram title: TRQSCatalogue identifier: AEKA_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEKA_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.htmlNo. of lines in distributed program, including test data, etc.: 18134No. of bytes in distributed program, including test data, etc.: 252049Distribution format: tar.gzProgramming language: Mathematica, C.Computer: Any supporting Mathematica in version 7 or higher.Operating system: Any platform supporting Mathematica; tested with GNU/Linux (32 and 64 bit).RAM: Case-dependentSupplementary material: Fig. 1 mentioned below can be downloaded.Classification: 4.15.External routines: Quantis software library (http://www.idquantique.com/support/quantis-trng.html)Catalogue identifier of previous version: AEKA_v1_0Journal reference of previous version: Comput. Phys. Comm. 183(2012)118Does the new version supersede the previous version?: YesNature of problem:Generation of random density matrices and utilization of high-quality random numbers for the purpose of computer simulation.Solution method:Use of a physical quantum random number generator and an on-line service providing access to the source of true random numbers generated by quantum real number generator.Reasons for new version:Added support for the high-speed on-line quantum random number generator and improved methods for retrieving lists of random numbers.Summary of revisions:The presented version provides two signicant improvements. The first one is the ability to use the on-line Quantum Random Number Generation service developed by PicoQuant GmbH and the Nano-Optics groups at the Department of Physics of Humboldt University. The on-line service supported in the version 2.0 of the TRQS package provides faster access to true randomness sources constructed using the laws of quantum physics. The service is freely available at https://qrng.physik.hu-berlin.de/. The use of this service allows using the presented package with the need of a physical quantum random number generator.The second improvement introduced in this version is the ability to retrieve arrays of random data directly for the used source. This increases the speed of the random number generation, especially in the case of an on-line service, where it reduces the time necessary to establish the connection. Thanks to the speed improvement of the presented version, the package can now be used in simulations requiring larger amounts of random data. Moreover, the functions for generating random numbers provided by the current version of the package more closely follow the pattern of functions for generating pseudo- random numbers provided in Mathematica.Additional comments:Speed comparison: The implementation of the support for the QRNG on-line service provides a noticeable improvement in the speed of random number generation. For the samples of real numbers of size 101; 102,…,107 the times required to generate these samples using Quantis USB device and QRNG service are compared in Fig. 1. The presented results show that the use of the on-line service provides faster access to random numbers. One should note, however, that the speed gain can increase or decrease depending on the connection speed between the computer and the server providing random numbers.Running time:Depends on the used source of randomness and the amount of random data used in the experiment.