Mathematics Methods in Quantum Physics and Its Applications

Dear Colleagues,

The year 2025 has been designated the Quantum Year, marking 100 years of significant advances in quantum science and technology. Worldwide celebrations highlight the profound impact of quantum theory on modern physics and emerging technologies. However, this brilliant progress would not have been possible without the essential foundation provided by mathematics. Key tools such as linear algebra, functional analysis, group theory, operator algebras, differential geometry, and complex analysis have enabled breakthroughs and continue to drive innovation. Overlooking the vital role of mathematics in this quantum revolution is a serious oversight. To acknowledge this, we are launching this Special Issue to celebrate and further explore the deep connection between mathematics and quantum physics.

This Special Issue invites high-quality submissions on developing, analyzing, and applying mathematical methods in quantum physics, including quantum computing and information theory. We aim to highlight theoretical insights and practical tools that enhance the understanding and control of quantum systems. We welcome original research, review papers, and methodological contributions from all areas of mathematical physics and quantum theory.

The topics include, but are not limited to:

1. Mathematical foundations of quantum mechanics: Hilbert space theory, operator algebras, spectral theory, and formal axiomatic approaches;
2. Quantum dynamics and open systems: Unitary and non-unitary evolution, Lindblad equations, decoherence, and quantum noise modeling;
3. Quantum estimation theory and metrology: Quantum Fisher information, Cramér–Rao bounds, optimal measurements, and multiparameter estimation;
4. Quantum control and optimization: Time-optimal control, variational control methods, control landscapes, and feedback systems;
5. Quantum optics: Field quantization and light–matter interaction;
6. Quantum thermodynamics: Quantum work and heat, fluctuation theorems, entropy production, and resource–theoretic approaches, quantum battery, and ergotropy;
7. Many-body quantum systems: Integrable models, tensor network methods, entanglement structure, and emergent phenomena;
8. Non-Hermitian and PT-symmetric quantum systems: Complex eigenvalue problems, exceptional points, and pseudo-Hermitian formulations;
9. Topological and geometrical methods: Berry phase, fiber bundles, topological order, and geometrical quantization;
10. Group theory and representation theory: Lie groups and algebras, symmetry classifications, and their applications in quantum theory;
11. Numerical and computational methods: Quantum simulation algorithms, matrix product states, spectral solvers, and numerical optimization;
12. Stochastic and probabilistic approaches: Quantum trajectories, path integral formulations, and noise-driven quantum systems;
13. Variational quantum algorithms and hybrid methods: VQE, QAOA, and variational principles applied to quantum simulation and optimization;
14. Quantum machine learning: Quantum neural networks, quantum kernel methods, generative models, and data-driven approaches to quantum systems;
15. Quantum information and computation: Entanglement theory, quantum circuits, quantum algorithms, error correction, and complexity theory.

Dr. Lebin Ho
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• mathematical methods in quantum physics
• quantum information theory
• quantum computing
• quantum control
• quantum estimation and metrology
• open quantum systems
• quantum thermodynamics
• quantum field theory
• many-body systems
• variational quantum algorithms
• quantum machine learning
• operator theory
• functional analysis
• group theory
• topological methods
• numerical methods