Zhang Xiangqian's Unified Field Theory: From State Vectors to Quantum Control and Correction, Then to the Unified Geometric Theory of Antigravitational Waves

Under the core paradigm of "physics is geometry" in Zhang Xiangqian's Unified Field Theory (UFT), this paper systematically completes the full geometric reconstruction from non-relativistic quantum mechanics, open quantum systems, quantum information theory to quantum control and error correction.All derivations logically originate from three core postulates—spacetime light-speed cylindrical spiral motion, the light-speed constraint equation, and the geometrization postulate—thoroughly reducing the entire mathematical structure of quantum mechanics to the geometric properties of spacetime vibration modes. Key achievements include: 1) Interpreting state vectors, superposition principle, coherence, density matrix, and decoherence as inevitable manifestations of spatiotemporal vibration modes, amplitude-coherent superposition, geometric phase locking, vibrational ensemble statistics, and geometric phase dispersion, respectively. Deriving the decoherence rate , where represents the geometric phase coupling strength; 2) Established geometric interpretations for trace, purity, norm coherence, and relative entropy coherence, directly relating them to the total number of vibrational units, coherence strength, and non-diagonal long-range phase correlations, while providing the geometric origin of typical two-level system Hamiltonians; 3) Rigorously derives the Liouville–von Neumann equation, Lindblad principal equation, and Bloch equation from UFT geometric dynamics, expressing relaxation rates and decoherence times as functions of the fluctuation spectral density of environmental geometric parameters; 4) Unifies the interpretation of light-matter interactions, superconducting macroscopic coherence, and spin dynamics as outcomes of spacetime flexural fields, phase-locked collective modes, and geometric coupling, deriving UFT geometric formulations for the Jaynes–Cummings model, London equation, Josephson relations, and NMR Bloch equations; 5) Reveals the geometric essence of spin echo and CPMG sequences—temporal inversion of geometric phase and frequency-domain windowing—providing the frequency-domain convolution relationship between decoherence factors and environmental spectra; 6) Interpreted the logical subspace of stabilizer codes as a geometric constrained subspace of vibrational modes, revealing the error correction process as a three-step operation of geometric projection, geometric classification, and geometric relocking, and provided the geometric meaning of the fault tolerance threshold . 7) Finally, the theory is extended to the active regulation and long-range propagation mechanisms of anti-gravitational fields. Based on the geometric chirality principle of UFT, five theoretical pathways for achieving long-range propagation of anti-gravitational waves are systematically evaluated, providing a clear theoretical blueprint for gravitational engineering, space propulsion, and gravitational wave communication. All derivations undergo rigorous dimensional consistency verification, forming a logical closed loop with prior UFT achievements (mass-frequency equivalence, geometric expression of the fine-structure constant, system, electromagnetic-gravitational unified theory, etc.), while smoothly converging to existing quantum theories under corresponding limits.This work signifies that the UFT paradigm of "physics as geometry" has extended from classical physics, electromagnetism, and relativistic quantum mechanics to the core domains of quantum information and quantum engineering. It provides a robust first-principles geometric foundation for understanding the essence of quantum mechanics and actively safeguarding quantum technologies. This record is formatted and submitted by Lynn Lou Beran on behalf of the author. The author is solely responsible for the content.