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NeuroQuantology

Quantum Walk Founds Over Dispersion of Field Random Number Generator Output: Mind Over Matter Through Quantum Processes

Takeshi Shimizu, Masato Ishikawa

Published Oct 16, 2015• 0 citations
Publisher

Abstract

Recent field RNG studies have reported that chi-square values of random number generator (RNG) outputs become highly significant when a large audience focuses on coherent events. Since the statistics are typically computed based on binomial distribution, RNG outputs are in a statistical state of over dispersion, lacking a framework for their interpretation. Notably, the Quantum Walk (QW) has the potential to detect such anomalies, since its distribution exhibits larger variances than binomial distribution. The current study focused on the distribution of QW and discusses several conditions. We assume that field consciousness unintentionally changes RNG output into chunks of Quanta that are mixed among the RNG output having its length. Using the concept of the quantum chunk, the proportions of test findings, which include the quantum chunk, are estimated. The current model estimates that about 1%-1.5% Qbits are mixed within a trial, based on results of previous significant field RNG experiments. Finally, several methodological tasks for the future are discussed.

DOI
10.14704/nq.2015.13.4.876

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Recent field RNG studies have reported that chi-square values of random number generator (RNG) outputs become highly significant when a large audience focuses on coherent events. Since the statistics are typically computed based on binomial distribution, RNG outputs are in a statistical state of over dispersion, lacking a framework for their interpretation. Notably, the Quantum Walk (QW) has the potential to detect such anomalies, since its distribution exhibits larger variances than binomial distribution. The current study focused on the distribution of QW and discusses several conditions. We assume that field consciousness unintentionally changes RNG output into chunks of Quanta that are mixed among the RNG output having its length. Using the concept of the quantum chunk, the proportions of test findings, which include the quantum chunk, are estimated. The current model estimates that about 1%-1.5% Qbits are mixed within a trial, based on results of previous significant field RNG experiments. Finally, several methodological tasks for the future are discussed.
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The generation of true randomness remains a significant challenge in computer science, particularly when relying solely on classical algorithms. Many current approaches employ pseudo-random number generators (PRNGs), which, despite their computational efficiency, are inherently predictable and lack genuine randomness. This paper proposes a novel method for algorithmic randomness generation leveraging the principles of quantum walks. We demonstrate that the inherent uncertainty and superposition properties of quantum systems provide a robust mechanism for generating truly random numbers. Specifically, we outline a framework for designing quantum walks on graphs, where the evolution of the walker's state is fundamentally probabilistic and unpredictable. The core of our approach resides in exploiting the quantum walk's non-deterministic nature to produce sequences of numbers that exhibit statistical properties consistent with true randomness. The theoretical framework is presented, including a detailed description of the mathematical formalism underlying the quantum walk and the probability distribution of the walker's positions. We highlight the potential advantages of this approach, particularly in scenarios demanding high-quality randomness for cryptographic applications or simulations. The key concept is to translate a classical problem into a quantum one, where the inherent probabilistic nature of quantum mechanics offers a superior solution to the problem of generating genuine randomness.
Even if the output of a Random Number Generator (RNG) is perfectly uniformly distributed, it may be correlated to pre-existing information and therefore be predictable. Statistical tests are thus not sufficient to guarantee that an RNG is usable for applications, e.g., in cryptography or gambling, where unpredictability is important. To enable such applications a stronger notion of randomness, termed "true randomness", is required, which includes independence from prior information. Quantum systems are particularly suitable for true randomness generation, as their unpredictability can be proved based on physical principles. Practical implementations of Quantum RNGs (QRNGs) are however always subject to noise, i.e., influences which are not fully controlled. This reduces the quality of the raw randomness generated by the device, making it necessary to post-process it. Here we provide a framework to analyse realistic QRNGs and to determine the post-processing that is necessary to turn their raw output into true randomness.
In experiments with physical noise generators based on electronic or photonic quantum events, significant deviations from random distributions have been repeatedly observed. To explain these effects, intention-based interactions between consciousness and mind with physical random processes have been suggested, either being caused by individual minds or by a proposed global mind. As these explanations involve physically undefined objects such as “mind” and “consciousness”, an explanatory model based on the concept of an information field is given herein, based on the concept of generalized quantum entanglement, including the entanglement of physical noise processes with information fields and an analogy to quantum teleportation. In addition, the non-random hypothesis of using such a physical noise generator in capturing qualitative characteristics of individuals is tested in a randomized controlled study with 100 participants.
The semi-source independent quantum walk random number generator (SI-QW-QRNG) is a cryptographic protocol that extracts a string of true random bits from a quantum random walk with an adversary controls a randomness source, but the dimension of the system is known. This paper analyzes SI-QW-QRNG protocols with a memory-based quantum walk state. The new protocol utilizes a generalized coin operator with various parameters to optimize the randomness of the quantum walk state. We focus on evaluations of the protocols in multiple scenarios and walk configurations. Moreover, we show some interesting behavior of the system depending on the size of the memory space and the number of quantum coins.
In this paper, we investigate the potential application of quantum computation for constructing pseudo-random number generators (PRNGs) and further construct a novel PRNG based on quantum random walks (QRWs), a famous quantum computation model. The PRNG merely relies on the equations used in the QRWs, and thus the generation algorithm is simple and the computation speed is fast. The proposed PRNG is subjected to statistical tests such as NIST and successfully passed the test. Compared with the representative PRNG based on quantum chaotic maps (QCM), the present QRWs-based PRNG has some advantages such as better statistical complexity and recurrence. For example, the normalized Shannon entropy and the statistical complexity of the QRWs-based PRNG are 0.999699456771172 and 1.799961178212329e-04 respectively given the number of 8 bits-words, say, 16Mbits. By contrast, the corresponding values of the QCM-based PRNG are 0.999448131481064 and 3.701210794388818e-04 respectively. Thus the statistical complexity and the normalized entropy of the QRWs-based PRNG are closer to 0 and 1 respectively than those of the QCM-based PRNG when the number of words of the analyzed sequence increases. It provides a new clue to construct PRNGs and also extends the applications of quantum computation.