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Научное мнение

THE CONTENT OF STEM TRAINING IN THE CONSTRUCTION OF CLASSICAL DECOMPOSITIONS OF QUANTUM GATES

Tatiana S. Smirnova, Mikhail V. Shvetskiy

Published Mar 28, 2025• 0 citations
Publisher

Abstract

The article clarifies the content of training in the construction of controlled quantum gates using twelve decompositions of single-qubit quantum gates (Z-Y, Z-X, X-Y, Y-Z, X-Z, Y-X; Z-Y-X, Z-X-Y, X-Y-Z, X-Z-Y, Y-X-Z, Y-Z-X), consisting in a detailed proof of two theorems that make it possible to construct these decompositions much faster. The obtained results are used in the process of teaching the section “Quantum Computing and Big Data” of the “Big Data” course to students of the Institute of Information Systems and Telecommunications (3rd year, Herzen State Pedagogical University).

DOI
10.25807/22224378_2025_3_36

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The article clarifies the content of training in the construction of controlled quantum gates using twelve decompositions of single-qubit quantum gates (Z-Y, Z-X, X-Y, Y-Z, X-Z, Y-X; Z-Y-X, Z-X-Y, X-Y-Z, X-Z-Y, Y-X-Z, Y-Z-X), consisting in a detailed proof of two theorems that make it possible to construct these decompositions much faster. The obtained results are used in the process of teaching the section “Quantum Computing and Big Data” of the “Big Data” course to students of the Institute of Information Systems and Telecommunications (3rd year, Herzen State Pedagogical University).
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The article is devoted to the actual problem of teaching methods of the subjects of the educational process of modern information and computer science. The contribution of Ukrainian scientists to the development of electronic computing machines, their programming and teaching methods, prospects for further research are briefly considered. In the natural sciences, elementary units are widely used for various measurements. In particular, Planck’s constant is the smallest portion, quantum of energy, quantum of action, which is used in quantum mechanics. It is also known from the course of physics that the smallest portion of energy in classical mechanics is the energy per one degree of freedom. Logically created mathematical models and theories describing the relevant properties of matter using the specified units. Similarly, emphasis is placed on clarifying the difference between a classical computer and quantum units of information. The concepts of bit of information, qubit and trit are revealed, and depending on the defined units of information, types of computers are distinguished: classical and quantum. The concepts of qubit and trit are considered mainly as a mathematical entity, and attention is not focused on the content of the physics of quantum objects, a comparison of the indicated units of quantum information with a traditional bit of information in the quantum world is given. A historical-genetic analysis of the registers of elementary logic systems, a theoretical study of the principles of superposition and interaction between quantum states, and experimental methods of implementing qubits and their connections have been carried out. An important field for the use of quantum computers is cryptology, for solving the problems of which Grover’s method has already been created. With Grover’s quantum algorithm, it is possible to quickly search for the necessary element in an unsorted database with 2nN (n is the length of the search space of the quantum register - the number of qubits in it; N is the size of the search space). However, although the quantum simulator gives a high probability of the correct result, experimental studies also show large discrepancies. Therefore, there is a problem for further research. Quantum computers can influence each other through the phenomenon of entanglement.
Multi-controlled unitary gates have been a subject of interest in quantum computing since its inception, and are widely used in quantum algorithms. The current state-of-the-art approach to implementing n-qubit multi-controlled gates involves the use of a quadratic number of single-qubit and CNOT gates. However, linear solutions are possible for the case where the controlled gate is a special unitary SU(2). The most widely-used decomposition of an n-qubit multi-controlled SU(2) gate requires a circuit with a number of CNOT gates proportional to 28n. In this work, we present a new decomposition of n-qubit multi-controlled SU(2) gates that requires a circuit with a number of CNOT gates proportional to 20n, and proportional to 16n if the SU(2) gate has at least one real-valued diagonal. This new approach significantly improves the existing algorithm by reducing the number of CNOT gates and the overall circuit depth. As an application, we show the use of this decomposition for sparse quantum state preparation. Our results are further validated by demonstrating a proof of principle on a quantum device accessed through quantum cloud services.