Random number generators (RNGs) are critical for problems involving security and cryptography. Much work has been done with true random number generators (TRNGs) that utilize quantum mechanical phenomena as sources of entropy to generate numbers according to some distribution without any underlying deterministic component. While qubit-based quantum computers can serve as high-quality sources of randomness, their effectiveness is limited by constraints due to their physical construction (e.g. not being feasible at room temperatures) and by the number of qubits that are necessary for fine-grained distributions (the number of bins scale as 2n for a n-qubit implementation). Continuous variable photonic quantum computers offer promising scalability, both from their experimental realization and from the use of linear optical components and photon number resolving detectors to generate varied distributions. We demonstrate that boson-sampling-based approaches realized with photonic quantum computers like the Xanadu X8 machine can be used to generate random numbers in diffuse, hard-to-predict distributions and they can be optimized for transformation to a uniform distribution. Specifically, boson sampling can act as a high-quality source of entropy and we introduce a strategy for scaling our TRNG with further experimental development (both in terms of the number of qumodes available and improvements for photonic components). We compare our results to the performance of qubit-based TRNGs and discuss experimental realizations.
Random number generators (RNGs) are critical for problems involving security and cryptography. Much work has been done with true random number generators (TRNGs) that utilize quantum mechanical phenomena as sources of entropy to generate numbers according to some distribution without any underlying deterministic component. While qubit-based quantum computers can serve as high-quality sources of randomness, their effectiveness is limited by constraints due to their physical construction (e.g. not being feasible at room temperatures) and by the number of qubits that are necessary for fine-grained distributions (the number of bins scale as 2n for a n-qubit implementation). Continuous variable photonic quantum computers offer promising scalability, both from their experimental realization and from the use of linear optical components and photon number resolving detectors to generate varied distributions. We demonstrate that boson-sampling-based approaches realized with photonic quantum computers like the Xanadu X8 machine can be used to generate random numbers in diffuse, hard-to-predict distributions and they can be optimized for transformation to a uniform distribution. Specifically, boson sampling can act as a high-quality source of entropy and we introduce a strategy for scaling our TRNG with further experimental development (both in terms of the number of qumodes available and improvements for photonic components). We compare our results to the performance of qubit-based TRNGs and discuss experimental realizations.
Random number generators (RNG) are essential elements in many cryptographic systems. True random number generators (TRNG) rely upon sources of randomness from natural processes such as those arising from quantum mechanics phenomena. We demonstrate that a quantum computer can serve as a high-quality, weakly random source for a generalized user-defined probability mass function (PMF). Specifically, QC measurement implements the process of variate sampling according to a user-specified PMF resulting in a word comprised of electronic bits that can then be processed by an extractor function to address inaccuracies due to non-ideal quantum gate operations and other system biases. We introduce an automated and flexible method for implementing a TRNG as a programmed quantum circuit that executes on commercially-available, gate-model quantum computers. The user specifies the desired word size as the number of qubits and a definition of the desired PMF. Based upon the user specification of the PMF, our compilation tool automatically synthesizes the desired TRNG as a structural OpenQASM file containing native gate operations that are optimized to reduce the circuit’s quantum depth. The resulting TRNG provides multiple bits of randomness for each execution/measurement cycle; thus, the number of random bits produced in each execution is limited only by the size of the QC. We provide experimental results to illustrate the viability of this approach.
Abstract It is proven that Boson sampling is a much promising model of optical quantum computation, which is applied to designing quantum computer successfully, such as “Jiuzhang” . However, the meaningful randomness of Boson sampling results has not been utilized or exploited. In this research, Boson sampling is applied to design a quantum random number generator (QRNG) by fully exploiting the randomness of Boson sampling results, and its prototype system is constructed with the programmable silicon photonic processor, which can generate unbiased random sequences and overcome the shortcomings of the existing discrete QRNGs such as source‐restricted, high demand for the photon number resolution capability of detector and slow self‐detection generator speed. Boson sampling is implemented as a random entropy source, and random bit strings with satisfactory randomness and uniformity can be obtained after post‐processing the sampling results. It is the first approach for applying the randomness of Boson sampling results to develop a practical prototype system for actual tasks, and the experiment results demonstrate that the designed Boson sampling‐based QRNG prototype system passes 15 tests of the NIST SP 800‐22 statistical test component, which proves that Boson sampling has great potential for practical applications with desirable performance besides quantum advantage.
Random numbers are fundamental elements in different fields of science and technology such as computer simulation like Monte Carlo-method simulation, statistical sampling, cryptography, games and gambling, and other areas where unpredictable results are necessary. Random number generators (RNG) are generally classified as “pseudo”-random number generators (PRNG) and "truly" random number generators (TRNG). Pseudo random numbers are generated by computer algorithms with a (random) seed and a specific formula. The random numbers produced in this way (with a small degree of unpredictability) are good enough for some applications such as computer simulation. However, for some other applications like cryptography they are not completely reliable. When the seed is revealed, the entire sequence of numbers can be produced. The periodicity is also an undesirable property of PRNGs that can be disregarded for most practical purposes if the sequence recurs after a very long period. However, the predictability still remains a tremendous disadvantage of this type of generators. Truly random numbers, on the other hand, can be generated through physical sources of randomness like flipping a coin. However, the approaches exploiting classical motion and classical physics to generate random numbers possess a deterministic nature that is transferred to the generated random numbers. The best solution is to benefit from the assets of indeterminacy and randomness in quantum physics. Based on the quantum theory, the properties of a particle cannot be determined with arbitrary precision until a measurement is carried out. The result of a measurement, therefore, remains unpredictable and random. Optical phenomena including photons as the quanta of light have various random, non-deterministic properties. These properties include the polarization of the photons, the exact number of photons impinging a detector and the photon arrival times. Such intrinsically random properties can be exploited to generate truly random numbers. Silicon (Si) is considered as an interesting material in integrated optics. Microelectronic chips made from Si are cheap and easy to mass-fabricate, and can be densely integrated. Si integrated optical chips, that can generate, modulate, process and detect light signals, exploit the benefits of Si while also being fully compatible with electronic. Since many electronic components can be integrated into a single chip, Si is an ideal candidate for the production of small, powerful devices. By complementary metal-oxide-semiconductor (CMOS) technology, the fabrication of compact and mass manufacturable devices with integrated components on the Si platform is achievable. In this thesis we aim to model, study and fabricate a compact photonic quantum random number generator (QRNG) on the Si platform that is able to generate high quality, "truly" random numbers. The proposed QRNG is based on a Si light source (LED) coupled with a Si single photon avalanche diode (SPAD) or an array of SPADs which is called Si photomultiplier (SiPM). Various implementations of QRNG have been developed reaching an ultimate geometry where both the source and the SPAD are integrated on the same chip and fabricated by the same process. This activity was performed within the project SiQuro—on Si chip quantum optics for quantum computing and secure communications—which aims to bring the quantum world into integrated photonics. By using the same successful paradigm of microelectronics—the study and design of very small electronic devices typically made from semiconductor materials—, the vision is to have low cost and mass manufacturable integrated quantum photonic circuits for a variety of different applications in quantum computing, measure, sensing, secure communications and services. The Si platform permits, in a natural way, the integration of quantum photonics with electronics. Two methodologies are presented to generate random numbers: one is based on photon counting measurements and another one is based on photon arrival time measurements. The latter is robust, masks all the drawbacks of afterpulsing, dead time and jitter of the Si SPAD and is effectively insensitive to ageing of the LED and to its emission drifts related to temperature variations. The raw data pass all the statistical tests in national institute of standards and technology (NIST) tests suite and TestU01 Alphabit battery without a post processing algorithm. The maximum demonstrated bit rate is 1.68 Mbps with the efficiency of 4-bits per detected photon. In order to realize a small, portable QRNG, we have produced a compact configuration consisting of a Si nanocrystals (Si-NCs) LED and a SiPM. All the statistical test in the NIST tests suite pass for the raw data with the maximum bit rate of 0.5 Mbps. We also prepared and studied a compact chip consisting of a Si-NCs LED and an array of detectors. An integrated chip, composed of Si p+/n junction working in avalanche region and a Si SPAD, was produced as well. High quality random numbers are produced through our robust methodology at the highest speed of 100 kcps. Integration of the source of entropy and the detector on a single chip is an efficient way to produce a compact RNG. A small RNG is an essential element to guarantee the security of our everyday life. It can be readily implemented into electronic devices for data encryption. The idea of "utmost security" would no longer be limited to particular organs owning sensitive information. It would be accessible to every one in everyday life.
Random number generators (RNG) are an important resource in many areas: cryptography (both quantum and classical), probabilistic computation (Monte Carlo methods), numerical simulations, industrial testing and labeling, hazard games, scientific research, etc. Because today's computers are deterministic, they can not create random numbers unless complemented with a RNG. Randomness of a RNG can be precisely, scientifically characterized and measured. Especially valuable is the information-theoretic provable RNG (True RNG - TRNG) which, at state of the art, seem to be possible only by use of physical randomness inherent to certain (simple) quantum systems. On the other hand, current industry standard dictates use of RNG's based on free running oscillators (FRO) whose randomness is derived from electronics noise present in logic circuits and which cannot be strictly proven. This approach is currently used in 3-rd and 4-th generation FPGA and ASIC hardware, unsuitable for realization of quantum TRNG. We compare weak and strong aspects of the two approaches and discuss possibility of building quantum TRNG in the recently appeared Mixed Signal FPGA technology. Finally, we discuss several examples where use of a TRNG is critical and show how it can significantly improve security of cryptographic systems.
Quantum computer (QC) can be used as a true random number generator (TRNG). However, various noise sources introduce a bias in the generated number which affects the randomness. In this work, we analyze the impact of noise sources e.g., gate error, decoherence, and readout error in QC-based TRNG by running a set of error calibration and quantum tomography experiments. We employ a hybrid quantum-classical gate parameter optimization routine to find an optimal gate parameter. The optimal parameter compensates for error-induced bias and improves the quality of the random number by exploiting even the worst quality qubits. However, searching the optimal parameter in a hybrid setup requires time-consuming iterations between classical and quantum machines. We propose a machine learning model to predict optimal quantum gate parameters based on the qubit error specifications. We validate our approach using experimental results from IBM's publicly accessible quantum computers and the NIST statistical test suite. The proposed method can correct bias in any worst-case qubit by up to 88.57% in real quantum hardware.
Quantum mechanics offers a fundamentally unpredictable entropy source due to the intrinsic probabilistic nature of quantum measurements, making it attractive for secure random number generation. This paper explores the practicality of generating random numbers from two quantum platforms: gate-based circuits on IBM Quantum and (Gaussian) boson sampling with Xanadu Borealis. We implement simple post-processing methods, including the classic Von Neumann extractor and two tailored variants designed to address the correlated structure of boson sampling outputs. We evaluate debiased output from real quantum hardware using the NIST SP800-22r1a test suite and measure the extraction efficiency of each debiasing method. Results show that, while unbiased bitstreams can be achieved on both platforms, throughput remains low and cost per random bit is high compared to specialized QRNG devices.