The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information science. In spite of its significance, a thorough exposition of such a procedure is lacking in the literature. In this article we present relevant details concerning the numerical implementation and applicability of what we call the iid, normalization, and trigonometric methods for generating an unbiased probability vector $\mathbf{p}=(p_{1},\cdots,p_{d})$. An immediate application of these results regarding the generation of pseudo-random pure quantum states is also described.
The generation of pseudo-random discrete probability distributions is of paramount importance for a wide range of stochastic simulations spanning from Monte Carlo methods to the random sampling of quantum states for investigations in quantum information science. In spite of its significance, a thorough exposition of such a procedure is lacking in the literature. In this article we present relevant details concerning the numerical implementation and applicability of what we call the iid, normalization, and trigonometric methods for generating an unbiased probability vector p=(p1,⋯,pd). An immediate application of these results regarding the generation of pseudo-random pure quantum states is also described.
Pseudo‐random operators consist of sets of operators that exhibit important statistical features of uniformly distributed operators although their parametrization and generation requires exponentially fewer resources. Pseudo‐random operators can be applied for quantum communication tasks such as data‐hiding and super‐dense coding of quantum states, and enable efficient stochastic methods for noise estimation on prototype quantum processors. This paper summarizes published work by Emerson et al. [Science 302:2098 (2003)] demonstrating a random circuit method for the implementation of pseudo‐random unitary operators on a quantum processor and some more recent related results.
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered in experimental implementations and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.
Pseudo-random number generators are widely used in many branches of science, mainly in applications related to Monte Carlo methods, although they are deterministic in design and, therefore, unsuitable for tackling fundamental problems in security and cryptography. The natural laws of the microscopic realm provide a fairly simple method to generate non-deterministic sequences of random numbers, based on measurements of quantum states. In practice, however, the experimental devices on which quantum random number generators are based are often unable to pass some tests of randomness. In this review, we briefly discuss two such tests, point out the challenges that we have encountered and finally present a fairly simple method that successfully generates non-deterministic maximally random sequences.
Quantum algorithms for Monte Carlo integration (QMCI), which are based on quantum amplitude estimation (QAE), provide quadratic speed-up compared with classical counterparts, and are therefore widely investigated, along with applications to industries such as finance. One typical feature of problems in finance is high dimensionality, or, in other words, the necessity to create numerous random numbers (RNs) to calculate the integrand. In such a situation, the original implementation of QMCI, in which states encoding the probability distributions of the RNs are generated on different quantum registers, requires a large number of qubits. In this poster, we propose an implementation of QMCI, in which pseudo-random numbers (PRNs) are sequentially generated on one register, and therefore the qubit number is tremendously reduced. Moreover, we show that, when the integrand has the form such that contributions from different RNs are separable into different terms, we can also achieve time complexity reduction with respect to the number of dimensions by combining the nested QAE and use of PRNs.
Randomness is widely used in various fields, including encryption, statistical analysis, and numerical simulations. Randomness is also a fundamental resource in science and engineering. For such applications, we usually need to provide unbiased and independent random bits. This raises the issue of where to get these supposed random bits. Quantum random number generators (QRNGs) generate real random numbers based on the inherent randomness of quantum measurements. In practice, unfortunately, quantum randomness is inevitably mixed with classical randomness due to classical noise. Also, randomness is often correlated and biased. It is necessary to process the resulting raw bits sequence and convert them to good-quality output values that are as close to uniform distribution as possible. Random extractors are required for this. We analyze the randomness obtained by quantum random number generators as well as various examples of post-processing. We discuss the types of randomness extractors. Also, we use information-theoretically secure extractors and present improved novel randomness extraction.
Abstract Quantum realizations have opened a new ways for computer science. The new characteristics and phenomenons allow us to create new algorithms for general proposes. An interesting topic is random number generation. There are two perspectives for this proposes. True random numbers generator (TRN) and pseudo random numbers generator (PRNG). True Random Number Generators has four significant characteristics: randomness, long Period, insensitivity to seeds, repeatability. Additionally, Pseudo Random Number Generators is a fascinating topic that leverages the principles of computer science to craft deterministic algorithms, enabling the creation of a sequence of pseudo-random numbers. A crucial element in this process is the 'seed', which serves as the initial value to generate the entire sequence. This document proposes a algorithm based on a quantum system and the quasi-probability of its possible states to generate a long set of numbers which has pseudo random properties. The quantum system is compound by n qubits, its initial conditions 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 as a threshold to ensures 99\% of precision. The results demonstrate that it is possible generate a long set of pseudo numbers with random characteristics using a quantum simple operation. However, the experiments reveal that a real world implementation require a quantum system with at least 10-9 precision order.