Analysis of the limitations of quantum computing in cryptoanalysis problems

Abstract

The NISQ era is a transitional phase in the development of quantum computing with a limited number of qubits and high noise levels. In response to the limitations, specialized algorithms have been developed, such as the variational quantum eigenvalue algorithm (VQE) for modeling molecular structures, and QAOA for solving combinatorial optimization problems. To reduce the impact of noise on the calculations, effective strategies are used: randomized compilation (RC) and zero-noise extrapolation (ZNE). Hybrid quantum-classical approaches are also being developed that combine quantum generation with classical optimization and processing methods. Potential areas of application of NISQ technologies include the optimization of logistics problems, financial modeling, and supply chain optimization. In cryptography, NISQ devices stimulate the development of quantum-resistant encryption algorithms. The main challenges remain the limited scalability of systems and the problem of noise in quantum computing. The search for new architectures, including topological qubits and "glass" chips for a more stable environment, continues. An important trend is the gradual transition to the era of fully fault-tolerant quantum computers (FTQC), expected in the period 2025-2029. Unlike NISQ, which focuses on noise reduction methods, FTQC implements full quantum error correction (QEC). Quantum computing has transformed from an academic discipline into a field with a clear commercial strategy. Despite current limitations, existing achievements open up real opportunities for the applied use of quantum computing in cryptography. The analysis of mathematical criteria of different eras of quantum computing development has implications for solving cryptanalytic problems, transforming the understanding of the time frames and methodological approaches to overcoming cryptographic protection of classical cryptosystems.