Comparing pseudo- and quantum-random number generators with Monte Carlo simulations
David Cirauqui, Miguel Ángel García-March, Guillem Guigó i Corominas, Tobias Graß, Przemysław R. Grzybowski, Gorka Muñoz-Gil, J. R. M. Saavedra, Maciej Lewenstein
We study how the Monte Carlo simulations of the critical dynamics of two-dimensional Ising lattices are affected by the quality (as compared to true randomness) of the pseudo-randomness used in them by computing an observable known to be sensitive to it: the dynamic critical exponent z. To this end, we first present a review of the literature and then perform the same simulations with different pseudo-randomness sources. We control the quality of the random streams by physically reseeding the generators and observe that while the mean value of the measured observable is slightly affected by the correlations within them, its variance does get a severe impact. By studying this affectation and how such pseudo-random streams perform under standard randomness tests based on statistical analysis, we conclude that the new protocol is able to detect other types of correlations and can thus be used as an additional test. On the other hand, we present the first (to the best of our knowledge) computation of the dynamic critical exponent with a perfectly random quantum random number generator (QRNG) and hypothesize that the presented strategy may point toward a route to establish quantum advantage based on the quality of results as complementary to those strategies based on the speed of the computational task.
We study how the Monte Carlo simulations of the critical dynamics of two-dimensional Ising lattices are affected by the quality (as compared to true randomness) of the pseudo-randomness used in them by computing an observable known to be sensitive to it: the dynamic critical exponent z. To this end, we first present a review of the literature and then perform the same simulations with different pseudo-randomness sources. We control the quality of the random streams by physically reseeding the generators and observe that while the mean value of the measured observable is slightly affected by the correlations within them, its variance does get a severe impact. By studying this affectation and how such pseudo-random streams perform under standard randomness tests based on statistical analysis, we conclude that the new protocol is able to detect other types of correlations and can thus be used as an additional test. On the other hand, we present the first (to the best of our knowledge) computation of the dynamic critical exponent with a perfectly random quantum random number generator (QRNG) and hypothesize that the presented strategy may point toward a route to establish quantum advantage based on the quality of results as complementary to those strategies based on the speed of the computational task.
We discuss the current state of the art of Quantum Random Number Generators (QRNG) and their possible applications in the search for quantum advantages. To this aim, we first discuss a possible way of benchmarking QRNG by applying them to the computation of complicated and hard to realize classical simulations, such as critical dynamics in two-dimensional Ising lattices. These are performed with the help of computing devices based on field-programmable gate arrays (FPGAs) or graphic processing units (GPUs). The results obtained for QRNG are compared with those obtained by classical pseudo-random number generators (PRNG) of various qualities. Monte Carlo simulations of critical dynamics in moderate lattice sizes (128$\times$128) start to be sensitive to the correlations present in pseudo-random numbers sequences, allowing us to detect them. By comparing our analysis with that of Ref. [PRE {\bf 93}, 022113 (2016)], we estimate the requirements for QRNGs in terms of speed, rapidity of access, and efficiency to achieve the objective of quantum advantage with respect to the best PRNGs. We discuss the technical challenges associated with this objective.
We study the importance of the quality of random numbers in Monte Carlo simulations of 2D Ising systems. Simulations are carried out at critical temperature to find the dynamic scaling law of the linear relaxation time. Our aim is to show that statistical correlations that appear in large Ising simulations performed with pseudorandom numbers can be corrected using a quantum random number generator (QRNG). To achieve high speeds and large systems, Ising lattices are simulated on a field programmable gate array (FPGA) with an optical QRNG.
Abstract The advantages of quantum random number generators (QRNGs) over pseudo-random number generators (PRNGs) are normally attributed to the nature of quantum measurements. This is often seen as implying the superiority of the sequences of bits themselves generated by QRNGs, despite the absence of empirical tests supporting this. Nonetheless, one may expect sequences of bits generated by QRNGs to have properties that pseudo-random sequences do not; indeed, pseudo-random sequences are necessarily computable, a highly nontypical property of sequences. In this paper, we discuss the differences between QRNGs and PRNGs and the challenges involved in certifying the quality of QRNGs theoretically and testing their output experimentally. While QRNGs are often tested with standard suites of statistical tests, such tests are designed for PRNGs and only verify statistical properties of a QRNG, but are insensitive to many supposed advantages of QRNGs. We discuss the ability to test the incomputability and algorithmic complexity of QRNGs. While such properties cannot be directly verified with certainty, we show how one can construct indirect tests that may provide evidence for the incomputability of QRNGs. We use these tests to compare various PRNGs to a QRNG, based on superconducting transmon qutrits and certified by the Kochen–Specker theorem, to see whether such evidence can be found in practice. While our tests fail to observe a strong advantage of the quantum random sequences due to algorithmic properties, the results are nonetheless informative: some of the test results are ambiguous and require further study, while others highlight difficulties that can guide the development of future tests of algorithmic randomness and incomputability.
This dissertation uses the hierarchical q-state Potts model at the critical point to develop a new random number generator test. We start with an exposition of renormalization group approach by means of which one can numerically exactly compute the free energy, specific heat and susceptibility of large, but finite lattices. We then show that generalization of these standard techniques allows one to also compute probability distributions related to the energy and the order parameter. The various computed quantities can be compared with Monte Carlo estimates of the same quantities. We demonstrate that the structure of the hierarchical lattices used allows one to perform the Monte Carlo calculations by direct sampling. This avoids the usual critical slowing down that plagues Monte Carlo calculations at the critical point. As is well known, critical behavior is highly susceptible to perturbations. We expect that flaws of the pseudo random number generator, such as correlations, will cause statistically significant discrepancies between the results of the simulations and the numerically exactly computed results. Details of the computer code generated for these tests are included.
The subject matter of the article is pseudo-random number generators. Random numbers play the important role in cryptography. Using not secure pseudo-random number generators is a very common weakness. It is also a fundamental resource in science and engineering. There are algorithmically generated numbers that are similar to random distributions but are not random, called pseudo-random number generators. In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo-random number generators, true randomness is required. In such situations, we use real random number generators whose source of randomness is unpredictable random events. Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. The goal is to develop a mathematical model of the generator, which generates fast random numbers at a lower cost. At the same time, a high level of randomness is essential. Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols. It is essential to trust cryptographic random number generators to generate only true random numbers. This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated. The goal of the research is also to develop the model of a hybrid semi self-testing certification method for quantum random number generators (QRNG). The tasks to be solved are to create the mathematical model of a random number generator, which generates the fast random numbers at a lower cost. To create the mathematical model of a hybrid semi self-testing certification method for quantum random number generators. To integrate a hybrid semi self-testing certification method to the hybrid random number generator. the methods used are mathematical optimization and simulation. The following results were obtained: we present the improved hybrid quantum random number generator, which is based on QRNG, which uses the time of arrival of photons. The model of a hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper. This method combines different types of certification approaches and is rather secure and efficient. Finally, the hybrid certification method is integrated into the model of the new quantum random number generator. Conclusions. The scientific novelty of the results obtained is as follows: 1. The hybrid quantum random number generator is offered, which is based on QRNG, which uses the time of the arrival of photons. It uses the simple version of the detectors with few requirements. The hybrid QRNG produces more than one random bit per the detection of each photon. It is rather efficient and has a high level of randomness. 2. The hybrid semi self-testing certification method for quantum random number generators (QRNG) is offered. The Self-testing, as well as device-independent quantum random number generation methods, are analyzed. The advantages and disadvantages of both methods are identified. Based on the result the hybrid method is offered. 3. The hybrid semi self-testing certification method for quantum random number generators is integrated into the offered model of the quantum random number generator. The paper analyzes its security and efficiency. The paper offers to use the new random number generator in the crypto-schemes.
Random numbers play an important role in many areas, for example, encryption, cryptography, static analysis, simulations.It is also a fundamental resource in science and engineering.There are algorithmically generated numbers that are similar to random distributions, but are not actually random, called pseudo random number generators.In many cases the tasks to be solved are based on the unpredictability of random numbers, which cannot be guaranteed in the case of pseudo random number generators, true randomness is required.In such situations, we use real random number generators whose source of randomness is unpredictable random events.Quantum Random Number Generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements.Our goal is to generate fast random numbers at a lower cost.At the same time, a high level of randomness is essential.Through quantum mechanics, we can obtain true numbers using the unpredictable behavior of a photon, which is the basis of many modern cryptographic protocols.It is essential to trust cryptographic random number generators to generate only true random numbers.This is why certification methods are needed which will check both the operation of the device and the quality of the random bits generated.We present the improved novel quantum random number generator, which is based the on time of arrival QRNG.It uses the simple version of the detectors with few requirements.The novel QRNG produces more than one random bit per each photon detection.It is rather efficient and has a high level of randomness.Self-testing as well as device independent quantum random number generation methods are analyzed.The advantages and disadvantages of both methods are identified.The model of a novel semi self-testing certification method for quantum random number generators (QRNG) is offered in the paper.This method combines different types of certification approaches and is rather secure and efficient.Finally, the novel certification method is integrated into the model of the new quantum random number generator.The paper analyzes its security and efficiency.