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arXiv:2304.03830

A programmable true random number generator using commercial quantum computers

Aviraj Sinha, Elena R. Henderson, Jessie M. Henderson, Eric C. Larson, Mitchell Aaron Thornton

Published Jun 13, 2023• 10 citations

Abstract

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.

DOI: 10.1117/12.2663497

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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.

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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.

True randomness is a basic necessity of secure cryptography. This secures the reliability of encryption keys, digital signatures and authentication mechanisms. Classical random number generators based on deterministic algorithms can introduce patterns and decrease reliability. This paper introduces a Quantum True Random Number Generator (QTRNG) takes advantage of the intrinsic unpredictability of quantum mechanics. The proposed quantum circuit uses

R Y(\pi / 2)

and

R Z(\pi / 2)

rotations to create superposition states like Hadamard operation. These gates control the phase and orientation of qubits on the Bloch sphere yields measurement outcomes are inherently random. The resulting distributions are unbiased and balanced offers a source of true randomness. The quality of the generated bitstrings is verified using statistical tests such as the NIST SP 800-22, SP 800-90 test suites and autocorrelation tests. The measurements show high entropy, uniform distribution and low bias satisfy the basic requirements for cryptographic security. Phase-based quantum operations provide an efficient for producing high-quality quantum randomness facilitates the construction of effective quantum-secure cryptographic systems.

Random numbers are used in various domains, including quantum communication and cryptography applications such as key generation and authentication. Quantum mechanics has the intrinsic ability to generate truly random numbers, making it an ideal alternative for scientific applications that require randomness. Quantum wireless communication is proposed as a new means of communication that is safe, secure, and efficient. The simplicity of our source rotation gate, combined with its independently verifiable solitary unpredictability, is essential to obtain quantum random number generators without spending any money. In this chapter, we explore and study the 24-qubit random number. The worst-case entropy value for such randomly produced integers is 0.999445, with the min-entropy of such numbers being 0.0008. Additionally, steering restart tests were used to validate later verification of true randomness, and the statistical characteristics of the True Random Number Generation (TRNG) were assessed using an autocorrelation study and the statistical test suites.

Random numbers are of vital importance in today’s world and used for example in many cryptographical protocols to secure the communication over the internet. The generators producing these numbers are Pseudo Random Number Generators (PRNGs) or True Random Number Generators (TRNGs). A subclass of TRNGs are the Quantum based Random Number Generators (QRNGs) whose generation processes are based on quantum phenomena. However, the achievable quality of the numbers generated from a practical implementation can differ from the theoretically possible. To ease this negative effect post-processing can be used, which contains the use of extractors. They extract as much entropy as possible from the original source and produce a new output with better properties. The quality and the different properties of a given output can be measured with the help of statistical tests. In our work we examined the effect of different extractors on two QRNG outputs and found that witg the right extractor we can improve their quality.