Published November 18, 2020 | Version v1
Dataset Open

Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators

  • 1. University of Portland


This upload contains the data and code used in the following paper:

J. T. Kavulich, B. P. Van Deren, and M. Schlosshauer, “Searching for evidence of algorithmic randomness and incomputability in the output of quantum random number generators,” Phys. Lett. A 388, 127032 (2021),

The contents of the data set are as follows:

1) Random strings for two QRNGs and four PRNGs. For each RNG, a zip archive provides 100 strings containing 25 x 226 = 1,677,721,600 bits each.

2) C++ code for the Chaitin–Schwartz–Solovay–Strassen (CSSS) and Borel-normality tests (, 13 KB).

The bulk of this code is not ours, but was written and made publicly available at this link by the authors of the following paper:

A. A. Abbott, C. S. Calude, M. J. Dinneen, and N. Huang, Phys. Scri. 94 (2019) 045103, doi:10.1088/1402-4896/aaf36a

We have made just a few small modifications to their original code:

  • For the CSSS tests, a text file containing the Carmichael numbers (for tests 1–3) and odd composites up to 100 (for test 4) is read in and used to perform the tests. (Note: The set of Carmichael numbers used in the tests was generously provided to us by R. G. E. Pinch. Reference: R. G. E. Pinch, The Carmichael numbers up to 1021, in: A.-M. Ernvall-Hytönen (Ed.), Proceedings of Conference on Algorithmic Number Theory, Vol. 46, Turku Centre for Computer Science, Turku, Finland, 2007, pp. 129–131.)
  • We combined the first and second CSSS tests into a single program.
  • We reformatted the display of the output, and included a VERBOSE flag for additional status output.

3) Results from CSSS and Borel-normality tests in Python format (, 22 KB). This archive also contains a Python script ( that reads the result files, carries out the statistical analysis, and displays the plots.


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