This study investigates how qubits of modern quantum annealers (QA) such as D-Wave can be applied for generating truly random numbers. We show how a QA can be initialised and how the annealing schedule can be set so that after the annealing, thousands of truly random binary numbers are measured in parallel. Those can then be converted to uniformly distributed natural or real numbers in desired ranges, either biased or unbiased. We discuss the observed qubits’ properties and their influence on the random number generation and consider various physical factors that influence the performance of our generator, i.e., digital-to-analogue quantisation errors, flux errors, temperature errors and spin bath polarisation. The numbers generated by the proposed algorithm successfully pass various tests on randomness from the NIST test suite. Our source code and large sets of truly random numbers are publicly available on our project web pagehttps://4dqv.mpi-inf.mpg.de/QRNG/.
This study investigates how qubits of modern quantum annealers (QA) such as D-Wave can be applied for generating truly random numbers. We show how a QA can be initialised and how the annealing schedule can be set so that after the annealing, thousands of truly random binary numbers are measured in parallel. Those can then be converted to uniformly distributed natural or real numbers in desired ranges, either biased or unbiased. We discuss the observed qubits’ properties and their influence on the random number generation and consider various physical factors that influence the performance of our generator, i.e., digital-to-analogue quantisation errors, flux errors, temperature errors and spin bath polarisation. The numbers generated by the proposed algorithm successfully pass various tests on randomness from the NIST test suite. Our source code and large sets of truly random numbers are publicly available on our project web pagehttps://4dqv.mpi-inf.mpg.de/QRNG/.
Quantum devices offer a highly useful function - that is generating random numbers in a non-deterministic way since the measurement of a quantum state is not deterministic. This means that quantum devices can be constructed that generate qubits in a uniform superposition and then measure the state of those qubits. If the preparation of the qubits in a uniform superposition is unbiased, then quantum computers can be used to create high entropy, secure random numbers. Typically, preparing and measuring such quantum systems requires more time compared to classical pseudo random number generators (PRNGs) which are inherently deterministic algorithms. Therefore, the typical use of quantum random number generators (QRNGs) is to provide high entropy secure seeds for PRNGs. Quantum annealing (QA) is a type of analog quantum computation that is a relaxed form of adiabatic quantum computation and uses quantum fluctuations in order to search for ground state solutions of a programmable Ising model. Here we present extensive experimental random number results from a D-Wave 2000Q quantum annealer, totaling over 20 billion bits of QA measurements, which is significantly larger than previous D-Wave QA random number generator studies. Current quantum annealers are susceptible to noise from environmental sources and calibration errors, and are not in general unbiased samplers. Therefore, it is of interest to quantify whether noisy quantum annealers can effectively function as an unbiased QRNG. The amount of data that was collected from the quantum annealer allows a comprehensive analysis of the random bits to be performed using the NIST SP 800-22 Rev 1a testsuite, as well as min-entropy estimates from NIST SP 800-90B. The randomness tests show that the generated random bits from the D-Wave 2000Q are biased, and not unpredictable random bit sequences. With no server-side sampling post-processing, the 1 microsecond annealing time measurements had a min-entropy of 0.824.
Generation of random numbers is a central problem for many applications in the field of information processing, including, e.g., cryptography, in classical and quantum regime, but also mathematical modeling, Monte Carlo methods, gambling and many others. Both, the quality of the randomness and efficiency of the random numbers generation process are crucial for the most of these applications. Software produced pseudorandom bit sequences, though sufficiently quick, do not fulfill required randomness quality demands. Hence, the physical hardware methods are intensively developed to generate truly random number sequences for information processing and electronic security application. In the present paper we discuss the idea of the quantum random number generators. We also present a variety of tests utilized to assess the quality of randomness of generated bit sequences. In the experimental part we apply such tests to assess and compare two quantum random number generators, PQ4000KSI (of company ComScire US) and JUR01 (constructed in Wroclaw University of Science and Technology upon the project of The National Center for Research and Development) as well as a pseudorandom generator from the Mathematica Wolfram package. Finally, we present our new prototype of fully operative miniaturized quantum random generator JUR02 producing a random bit sequence with velocity of 1 Mb/s, which successfully passed standard tests of randomness quality (like NIST and Dieharder tests). We also shortly discuss our former concept of an entanglement-based quantum random number generator protocol with unconditionally secure public randomness verification.
We demonstrate a viable source of unbiased quantum random numbers whose statistical properties can be arbitrarily programmed without the need for any postprocessing such as randomness distillation or distribution transformation. It is based on measuring the arrival time of single photons in shaped temporal modes that are tailored with an electro-optical modulator. We show that quantum random numbers can be created directly in customized probability distributions and pass all randomness tests of the NIST and Dieharder test suites without any randomness extraction. The min-entropies of such generated random numbers are measured close to the theoretical limits, indicating their near-ideal statistics and ultrahigh purity. Easy to implement and arbitrarily programmable, this technique can find versatile uses in a multitude of data analysis areas.
Randomness property is an essential component in fields of cryptography, scientific simulations, secure communications and randomized algorithms. In this study, the reason for pseudo random generators were analyzed and illustrated for which are being slowly replaced by quantum random number generators. Quantum mechanics has emerged as a domain with extreme potential, however, the biggest challenge being faced towards practical utilization is that of scalability. This study proposes a method for Truly Random Bit Sequence (TRBS) generation also determining the most suitable physical implementation of qubits in the process for application in domains of data security, integrity and authentication as a precursor to secure communications. Illustration of the proposed method reaffirms that the probabilistic nature of quantum measurement and inherent randomness being used for the sequence generation lead to a truly random sequence which is also validated through NIST testing suite results.
In this thesis we study the generation of randomness from quantum mechanical sources: quantum random number generators (QRNGs). Such devices are thought to provide a better quality of randomness than is possible with classical devices, but the issue is in need of more rigorous study. In Chapter 1 we provide the necessary background for the thesis from both computability and probability theory. We then present and extend some recent results providing a more theoretical grounding for the indeterminism in quantum mechanics. In particular, we show that sequences of quantum random bits are incomputable in the strongest sense: no bit can be provably computed in advance. In Chapter 2 we study in detail the use of von Neumann normalisation for QRNGs producing both finite strings and infinite sequences of bits; such normalisation methods are necessary in order to counter for experimental imperfections. We show that, in the case of a constantly biased source, this normalisation gives the desired uniform distribution. The effect of this normalisation on the (in)computability of the generated sequences is studied, and it is shown that algorithmic randomness and Borel normality are preserved, but e-randomness (and thus incomputability) is, in general, not. Experimental bounds for the extent of departure from the uniform distribution in the non-ideal case of a slowly drifting bias are derived. In Chapter 3 we propose a new QRNG which uses entangled photon pairs and is certified to produce incomputable bits by value indefiniteness; this is the first QRNG with explicit certification by a physical principle. The effects of various experimental imperfections are discussed in detail, and care is taken to make the proposed QRNG as robust as is possible to these. A robust method based on XORing the produced bitstrings together is proposed to further improve the quality of the distribution produced by the QRNG. Various improvements and optimisations to this scheme are discussed.
ABSTRACT Quantum random number generator (QRNG) platforms use principles of quantum mechanics to create truly random numbers. Traditional pseudo-random number generators (PRNGs) generate numbers based on deterministic formulas. QRNG's use of the principles of superposition and measurement can provide numbers that cannot be predicted or replicated; therefore, they have been used as a source of randomness in various fields. In this research project, an experimental QRNG was designed and built using Qiskit simulations. Each experiment consisted of a series of two-qubit circuits. The circuits were created to place both qubits into an equal probability state. This was done by applying a pair of Hadamard gates (Hadamard gate applies a rotation operator of π/2 radians). Then each circuit was measured. For each measurement, there would be one output from each qubit. Since the Hadamard gate creates an equal-probability superposition, the combination of each qubit will either add up to 1 or subtract from -1. These combinations will be recorded and processed through several methods to evaluate their quality. Those methods include: Shannon Entropy Analysis, Frequency Distribution Analysis and Chi-Square Uniformity Testing. Keywords: Quantum Random Number Generator, Quantum Computing, Quantum Measurement, Cryptography, Secure Randomness, Qiskit Simulation