Exploring quantum systems for pseudo-random number generation

Quantum realizations have opened new ways for computer science. The integration of quantum characteristics and phenomena allows us to create new algorithms. An interesting topic is random number generation. There are two main perspectives for random numbers generators: True Random Number Generators (TRNGs) and Pseudo-Random Number Generators (PRNGs). TRNGs typically harness physical mechanisms to capture environmental information, generating truly random numbers. Conversely, PRNGs employ deterministic algorithms to generate sequences of numbers that appear random. They boast four key attributes: randomness, long period, insensitivity to seeds, and repeatability. This fascinating field harnesses principles of computer science to craft deterministic algorithms, enabling the generation of sequences of pseudo-random numbers. This paper introduces a pseudo-random generator based on deterministic algorithms, leveraging a set of quantum systems and their associated quasi-probabilities to generate a long sequence of numbers with pseudo-random characteristics. The quantum system consists of three qubits, initial conditions called seed, and a small set of rotation gates with a fixed angle. The tests were realized using the battery test called NIST SP800-22, and \(\alpha =0.01\) $\alpha =0.01$ as a threshold to ensure 99% of precision. The results demonstrate the ability to generate numbers exhibiting random characteristics. However, experimental findings suggest that real-world implementation necessitates a quantum system with precision on the order of \( 10^{-9} \) ${10}^{-9}$ .