Investigating the Geometry of Quantum Complexity in Open Systems

Konstantin A. Makarov, Eduard Tsekanovskiı̆

Halil Özbil

The Law of Geometric Consistency (LGC) is introduced as a proposed theoretical framework investigating whether physically realizable states require compatibility with underlying geometric and structural constraints.This work explores the possibility that not every mathematically allowed configuration corresponds to a physically admissible state. A geometric mapping perspective is developed to study relationships between quantum states, spacetime structure, information geometry, and complex physical systems.The framework discusses:geometric consistency as a possible state-selection principle,structural constraints in physical theories,connections with quantum foundations and measurement problems,potential applications in information geometry and complex systems.LGC is presented as an open research proposal requiring further mathematical formalization, independent validation, and experimental investigation.This work is part of the Structure-Sensitive Science Research Program (2026–2035).

Jincheng Zhang

Quantum entanglement, a cornerstone of quantum mechanics, presents unique challenges in computational modeling and analysis. This paper investigates the intersection of quantum entanglement and non-classical geometry, proposing a novel topological geometry model leveraging entanglement's inherent asymmetry to facilitate the computation and representation of quantum systems. We explore how this approach provides a framework for dynamic and complex topological structures, offering enhanced capabilities for ultra-high-density quantum computing and secure information protocols. The study demonstrates the potential of this methodology to refine existing topological computation techniques and opens avenues for novel quantum algorithms.

裕樹 真島

Jincheng Zhang

This paper investigates the potential of quantum entanglement to enable adaptive geometric transformation and optimization within a system. We introduce a novel mechanism leveraging quantum entanglement to dynamically adjust the geometry of a system, offering a potentially transformative approach to geometric manipulation and optimization. The core claim is that a system capable of exploiting quantum entanglement can achieve more effective geometric transformations and optimization compared to conventional methods. This work explores the principles of entanglement-based geometry and proposes a framework for utilizing this phenomenon to guide the evolution of complex systems. The theoretical foundation rests on a simplified model of geometric transformations and explores the implications of quantum entanglement on these transformations. This research addresses a long-standing challenge in computational geometry, potentially opening avenues for advanced optimization and control within various fields.

Ishaun Datta, Adam Bouland, Ellen Vitercik +3 more