A Century of Quantum Mechanics: Mathematical Foundations and Computational Applications
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Physics".
Deadline for manuscript submissions: 30 November 2025 | Viewed by 35
Special Issue Editor
Interests: intelligent systems; quantum computing; quantum intelligent systems; evolutionary computation; fuzzy systems; neural networks; deep learning; computational intelligence
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
The year 2025 marks the centenary of quantum mechanics, a revolutionary scientific milestone that fundamentally reshaped our understanding of the physical world. From its mathematical formulation to its contemporary computational implementations, quantum theory continues to be a dynamic and evolving domain.
Over the past century, quantum theory has evolved from a foundational theory in physics to a cornerstone of modern technological innovation. In recent years, quantum computing has emerged as a disruptive paradigm, offering unprecedented capabilities for the solution of complex computational problems.
This Special Issue seeks to honor this monumental anniversary by gathering cutting-edge research that bridges foundational quantum theory with current advances in quantum computing, quantum machine learning, and hybrid quantum–classical intelligent systems. We welcome theoretical, algorithmic, and experimental contributions that reflect the evolution and transformative potential of quantum technologies.
Topics of interest include (but are not limited to) the following areas:
- Mathematical structures and formal foundations of quantum mechanics and computation: Hilbert spaces, operator theory, lie algebras, algebraic formulations, and topological or categorical frameworks supporting the mathematical modeling of quantum systems and algorithms.
- Quantum algorithms, complexity, and intelligent systems: foundational and applied quantum algorithms (e.g., Grover, Shor, HHL, QAOA, VQE), quantum complexity theory, quantum computational advantage, quantum artificial intelligence, machine learning, and hybrid quantum–classical models.
- Error correction, control, and simulation in quantum systems: quantum error correction codes, noise-resilient strategies, quantum control theory, optimal control methods, quantum circuit simulation, and the formal verification of quantum programs.
- Quantum-inspired computational techniques and soft computing paradigms:
quantum fuzzy logic, probabilistic reasoning, and optimization techniques derived from quantum principles. - Applications of quantum technologies: real-world implementations in cryptography, optimization, bioinformatics, robotics, and other domains where quantum systems offer novel capabilities.
- Historical and foundational perspectives: the theoretical and conceptual evolution of quantum mechanics and computation over the past century.
Prof. Dr. Oscar Montiel Ross
Guest Editor
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Keywords
- mathematical structures and formal foundations of quantum mechanics and computation
- quantum algorithms, complexity, and intelligent systems
- error correction, control, and simulation in quantum systems
- quantum-inspired computational techniques and soft computing paradigms
- applications of quantum technologies
- historical and foundational perspectives
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