Prospects, problems and development of quantum technologies

G. G. Malinetskiy, T. S. Akhromeeva, S. A. Toropygina


Abstract: This review examines the prospects for using quantum technologies, closely related to problems in applied mathematics.
The first part of the paper demonstrates the fundamental challenges currently facing the quantum-mechanical description of reality. While at the beginning of the 20th century, quantum mechanics was treated as a statistical theory, experiments in recent decades have made it possible to work with individual microparticles, changing our perspective on the fundamental problems that preoccupied the founders of quantum mechanics. Interpretations of quantum mechanics, previously viewed as philosophical problems, can now be viewed from a different perspective, and the concepts predicted within them can be used to create new technologies.
The second part of the paper analyzes the dynamics of the development of quantum technologies and their connections to problems in applied mathematics. If the creation of quantum theory in the 1920s is considered the first quantum revolution, then a second quantum revolution is currently underway. It is already significantly changing the mathematical foundations of cryptography, related to the use of complex problems in various protocols. One of the most daring areas of modern technology development is quantum technology. Its development is linked to the second quantum revolution—an important area of modern physics. While in other fields it is possible to predict the level of advancement in the coming decades, here the uncertainty is much greater. Key economic, telecommunications, and military applications are linked to new information security systems, mathematical modeling, new generations of sensors, and quantum computers.
Currently, a number of countries, with quantum technologies in mind, are considering how to reach a new level of information security. One area is developing existing approaches to mathematical cryptography. This is post-quantum security, which utilizes complex problems inaccessible even to quantum computers, which may be created in the foreseeable future. The second area is related to quantum key exchange technologies used in traditional cryptographic systems. The prospects for applying quantum approaches here appear vast and very exciting.
The development of new technologies is often paradoxical. What was once on the fringes of scientific and technological developments may, after a certain time, become a key area.

Keywords: problems of quantum mechanics, Bell's inequality, interpretations of quantum mechanics, first quantum revolution, complex problems, mathematical cryptography, quantum teleportation, prospects for using quantum technologies in various fields, emerging breakthrough technologies, second quantum revolution, new communication systems, mathematical modeling of quantum systems, quantum computers, qubits.