Quantum Random Number Generator

Quantum Random Number Generator Jiapeng Zhao*,∗ Eneet Kaur, Michael Kilzer, Stephen DiAdamo, † Hassan Shapourian, Ramana Kompella, and Reza Nejabati Cisco Quantum Labs, 3232 Nebraska Ave, Santa Monica, CA, 90404 July 23, 2024 * [email protected] 
 † [email protected] ©Outshift by Cisco 2024 Quantum Random Number Generator 1

Introduction: Three Types of RNGs Random numbers are widely used in many aspects of modern technologies including scientific and engineering simulations [1], cryptography [2], artificial intelligence [3], gaming and finance. These tasks require random numbers that are truly unpredictable, which cannot be guaranteed in classical processes. The most widely used random number generators are pseudo-random number generators (PRNGs), which rely on mathematical algorithms and the presence of a secure seed. Even though some carefully designed PRNGs can pass statistical randomness tests, they are fundamentally predictable and deterministic. Therefore, once the seed is disclosed and computational power is strong, the random numbers generated by PRNGs are fully deterministic [1]. As such there is a need for a new type of random number generator capable of producing true random numbers. These type of true random number generators (TRNGs) utilise random physical processes to generate true random numbers. The random processes in TRNGs usually refer to classical physical processes like thermal noise and atmospheric turbulence [4]. Even though these TRNGs turn out to be more secure than PRNGs due to their inherent chaotic dynamics, the fundamental physics behind these classical processes is still deterministic while the unpredictability comes from the complexity of physical system [4]. Thanks to the inherent random nature of quantum mechanics, quantum random number generators (QRNGs) can, in principle, yield true random numbers which are mathematically unpredictable and nondeterministic without assumptions on devices, for example, QRNGs based on Bell tests [4, 5]. Compared to other quantum technologies, QRNGs are usually simpler and more mature, and are ready to be implemented to solve real-life challenges. FIG. 1. The Cisco QRNG architecture. The two-step randomness extraction implemented on the FPGA guarantees all classical correlations have been removed. ©Outshift by Cisco 2024 Quantum Random Number Generator 2

Cisco: QRNG Architecture Since quantum mechanics guarantees the inherent randomness of quantum phenomena, there are many possible quantum processes that can be leveraged as a source of randomness, and here, we choose the quantum vacuum noise as the randomness source [4, 5]. In classical physics, vacuum is defined as a state with no particles and energy. While in quantum physics, as shown in FIG. 1, the quantum vacuum state still has no particle but yields an energy fluctuation, which is called quantum vacuum noise. When representing quantum vacuum noise in phase space, we observe that both random variables of position and momentum, follow a Gaussian distribution. Therefore, when these two variables are measured, Gaussian distributed raw random numbers are obtained. In our QRNG system shown in FIG. 1, the quantum vacuum state can be prepared using a dark fiber or a blocked input at the interferometer, and the Gaussian distributed random variable is measured using homodyne detector. The analog signals from the homodyne detector are then sent to low-noise amplifiers (LNAs) for amplification before being sent to the AMD RFSoC for processing. The RFSoC made by AMD is a System-on-a-Chip platform which contains hard- core processors, FPGA fabric, and integrated ADCs and DACs, among other components. The ADCs in the RFSoC are responsible for converting the continuous, analog signals to discrete, digital values, which are raw bits containing both quantum vacuum noise and classical noise. Classical noise creates correlations in the experimental data that reduces its true randomness. To remove these correlations, we perform post-processing on the experimental data in a process referred to as randomness extraction [6]. The final data from the randomness extractor passes commonly used randomness testing software, such as NIST SP 800-22 and Dieharder. The randomness-extracted data is stored in memory in the RFSoC. From there, the random numbers can be transferred to an external computer via Ethernet for local use or uploaded to the cloud as a service. ©Outshift by Cisco 2024 Quantum Random Number Generator 3

Major Advantages of Cisco QRNG There are several technological alternatives based on different quantum mechanics properties that can be used for random number generation. Table I summarizes some of the major technological alternatives for QRNG. A typical QRNG systems consists of source and detector, which can be either trusted or not trusted. As shown in Table I, the device-independent QRNG based on Bell tests, does not rely on the assumption of trusted sources and detectors. However, this type of QRNG usually has a very low data rate. Most QRNGs are device-dependent QRNGs, and both source and detectors to be trusted. This applies to our approach as well, as from an engineering perspective, a high data rate and a streamlined hardware system are desirable. In QRNG solutions, the primary challenge in engineering security lies in implementing trusted sources and detectors. In our approach, the source of randomness—the quantum vacuum state—requires no special preparation, making it inherently trustworthy from an engineering security standpoint. Consequently, the vacuum noise method simplifies the engineering security process and reduces associated costs. Regarding the data rate, our approach uses passive quantum vacuum noise as the source of randomness, eliminating the need for slow quantum detectors. The only limiting factors are the bandwidth of the homodyne detector and the transimpedance amplifier (TIA). By employing a low- noise, high-speed homodyne detector and TIA, an ultrafast vacuum-based QRNG with a data rate of 100 Gbps can be achieved [7]. Source of randomness Quantum source Quantum detector Trusted source Trusted detector Data rate N N Y Y 100 Gbps Vacuum noise Photon number N Y Y Y 200 Mbps ASE N N Y Y 80 Gbps Spatial mode N Y Y Y 10 Mbps Time of arrival N Y Y Y 130 Mbps SRS N Y Y Y 10 Mbps Bell tests Y Y N N 10 Kbps TABLE I. Comparison of different types of QRNGs in terms of the requirement of dedicated quantum source, dedicated quantum detector, trusted device, as well as the best reported data rate (ASE is amplified spontaneous emission, SRS is spontaneous Raman scattering). In terms of the technology maturity of high speed homodyne detectors and TIA, Cisco has successfully commercialized high performance coherent transceivers for optical telecommunications at various speeds up to 60G baud rate. Inside each transceiver, homodyne detectors with TIA at the corresponding speeds can be found. Therefore, high speed homodyne detectors and TIA with low noise levels are mature technology at Cisco. These characteristics make Cisco QRNG a suitable candidate for commercial production. ©Outshift by Cisco 2024 Quantum Random Number Generator 4

Example Use Cases and Applications of QRNG QRNG has the potential to become the de facto hardware-based random number generator for a wide range of applications, digital services, and devices used in our daily lives. QRNG for cryptography: Cryptographic protocols and algorithms rely on random numbers, and QRNG can provide a trusted source of true random numbers. This makes QRNG crucial for enabling trusted authentication and encryption, enhancing the security of our information, apps, and services. Therefore QRNG hardware can potentially become an integrated part of all our digital devices. QRNG for gaming and lottery: The gaming and lottery industries can immensely benefit from a true random number generator. The true randomness of QRNG is a crucial feature required by any gaming or lottery application to eliminate bias and prevent users from increasing their chances of winning by predicting biased outcomes. This guarantees fairness that is not possible for players to manipulate. QRNG for Monte Carlo simulations: Monte Carlo simulations provide a robust method for predicting outcomes and making informed decisions in complex systems. They have applications in a wide range of areas, including economics, finance, energy, and manufacturing. Monte Carlo simulations rely on random number generators, and the quality of the generated random numbers can significantly impact the accuracy and runtime of simulations. Therefore, QRNGs are valuable assets for implementing practical, useful, and accurate Monte Carlo simulations. ËÙ J. E. Gentle, Random number generation and Monte Carlo methods, Vol. 381 (Springer, 2003).ô ÕÙ N. Ferguson and B. Schneier, Practical cryptography, Vol. 141 (Wiley New York, 2003)Ù ÃÙ V. Vovk, A. Gammerman, and G. Shafer, Algorithmic learning in a random world, Vol. 29 (Springer, 2005)Ù ÐÙ X. Ma, X. Yuan, Z. Cao, B. Qi, and Z. Zhang, Quantum random number generation, npj Quantum Information 2, 1 (2016)Ù »Ù M. Herrero-Collantes and J. C. Garcia-Escartin, Quantum random number generators, Reviews of Modern Physics 89, 015004 (2017)Ù æÙ X. Ma, F. Xu, H. Xu, X. Tan, B. Qi, and H.-K. Lo, Postprocessing for quantum random- number generators: Entropy evaluation and randomness extraction, Physical Review A 87, 062327 (2013)Ù ³Ù C. Bruynsteen, T. Gehring, C. Lupo, J. Bauwelinck, and X. Yin, 100-gbit/s integrated quantum random number generator based on vacuum fluctuations, PRX quantum 4, 010330 (2023). ©Outshift by Cisco 2024 Quantum Random Number Generator 5