QUANTUM SUPERPOSITION AND MULTIDIMENSIONAL GILBERT SPACES: PHYSICAL FOUNDATIONS OF MODERN QUANTUM COMPUTERS

Abstract

This article is devoted to the analysis of the physical foundations of quantum computers, in particular the role of quantum superposition and multidimensional Hilbert spaces in quantum computation. Quantum superposition—the ability of a quantum system to exist in multiple states simultaneously—forms the basis of quantum parallelism. Multidimensional Hilbert spaces are realized through qudits (d-level quantum systems), providing higher information capacity and improved error resistance compared to qubits. The article reviews theoretical foundations of superposition based on scientific works indexed in the Scopus database from 2020–2024, as well as its implementation in physical systems such as trapped ions, superconducting circuits, photonic systems, and neutral atom systems. In addition, issues of coherence and quantum error correction are discussed. In conclusion, quantum superposition and multidimensional spaces are fundamental physical principles of future quantum computers, and their development depends on solving decoherence and error correction problems.