A Research of the Influence of Quantum Annealing Parameters on the Quality of the Solution of the Number Factorization Problem

Abstract

Introduction. Modern information security systems use methods of asymmetric cryptography to transfer encryption keys, which are based on the high computational complexity of factorization of large numbers. Quantum computers (QCs) theoretically make it possible to accelerate the solution of the problem of factorization of numbers in comparison with classical computers and pose a potential threat to information security systems. However, real QCs have a limited number of connections between them and problems with preserving a stable low temperature, which reduces the probability of detecting a global minimum. The joint use of QCs with classical computers based on hybrid cloud services is advisable when the search for the optimal solution by direct methods is a complex problem both in the theoretical sense and in the sense of the required amount of calculations for tasks with specific data. The article proposes a method for improving the accuracy of solving the factorization problem based on multiple minimum search by the method of hardware reverse quantum annealing with a variation of its parameters. The results of numerical experiments for two different QC processors and a hybrid quantum-classical computer by D-Wave are presented, it is shown that the maximum number that can be factorized exclusively by direct annealing is 143, and with a combination of direct and reverse annealing 255. The purpose. Examination of the influence of the parameters of quantum annealing and the corresponding solutions for the adiabatic CC, developed by D-Wave, on the quality of the solution of the factorization problem. To give recommendations for improving the accuracy of solving the factorization problem and increasing the statistical frequency of the appearance of correct pairs of multipliers. Results. Numerical experiments have shown that for the problem of factorization of numbers, the successive application of direct and reverse annealing makes it possible to improve the probability of obtaining the correct pair of multipliers and to more than double the statistical frequency of its occurrence. Quantum annealing modes: pause and quenching reduce the probability of obtaining the correct solution and worsen the statistical frequency of the appearance of correct pairs of multipliers. Conclusions. The use of direct and reverse annealing makes it possible to increase the probability of obtaining the correct solution of the factorization problem for the adiabatic QC of D-Wave. Increasing the calculation time of the problem is justified, since it allows increasing the probability of a correct solution. The use of hybrid quantum-classical computing and cloud services allows factorization for numbers with a bit depth of up to twenty-two bits. Keywords: quantum annealing, factorization of natural numbers, asymmetric shifts, hardening, reverse annealing, combinatorial optimization.