Advances in Quantum Information Geometry: Mathematical Methods, Quantum States, and Emerging Applications
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".
Deadline for manuscript submissions: 20 January 2027 | Viewed by 326
Editors
Interests: quantum geometry; gravity
Special Issue Information
Dear Colleagues,
Quantum information geometry (QIG) represents one of the most profound mathematical developments in quantum theory, providing geometric insight into the structure of quantum mechanics itself. By endowing spaces of quantum states with Riemannian metrics, connections, and curvature, this field reveals deep mathematical relationships between quantum phenomena and classical geometric concepts.
Building on these foundations, key geometric tools have emerged that connect theory with concrete physical applications. The quantum Fisher information metric enables optimal parameter estimation in quantum metrology, while the Bures metric and Fubini–Study metric characterize distances between quantum states crucial for quantum algorithm design and error correction. The quantum geometric tensor reveals topological properties essential for understanding quantum materials and many-body systems.
This Special Issue focuses on the mathematical foundations and practical applications of QIG in current and emerging quantum technologies. We seek contributions that demonstrate how geometric methods can solve real-world problems in quantum computing, enhance quantum sensing protocols, optimize quantum communication systems, and advance our understanding of quantum materials. Furthermore, we look for contributions that advance the mathematical foundations of quantum information geometry, develop novel computational methods, establish new theoretical connections, and explore applications to fundamental problems in quantum mechanics and related mathematical fields.
Dr. Diego Gonzalez
Dr. José David Vergara
Guest Editors
Manuscript Submission Information
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Keywords
- quantum geometry
- quantum geometric tensor
- quantum metric tensor
- Berry curvature
- quantum metrology
- quantum phase transitions
- condensed matter theory
- topological phases
- geometric phases
- quantum entanglement
- holonomic quantum computation
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