Quantum Information Field Theory (QIFT) proposes a novel unification of quantum mechanics and gravity based on the concept of infons—discrete, quantized units of relational information. In this theory, matter fields and spacetime geometry emerge from the distribution and dynamics of infons. QIFT models spacetime curvature as a coarse-grained metric on infon density, enabling a unified framework that connects thermodynamics, quantum field theory, and general relativity. This paper presents the first complete theoretical exposition of QIFT, including mathematical formulations, governing equations, and simulated applications. We explore the feasibility of gravitational propulsion using engineered Quantum Metric Resonators (QMRs)—toroidal cavities embedded in phononic meta-shells storing squeezed-vacuum energy. Simulations indicate that a tri-cavity QMR system can yield measurable non-Newtonian thrust, providing a falsifiable prediction using current atom interferometry and superconducting technologies. This paper also gives a comprehensive review of related literature, including warp metrics, negative-mass metamaterials, and entanglement entropy in emergent gravity. This positions QIFT as a testable, information-theoretic bridge between quantum foundations and next-generation propulsion systems. Keywords: quantum information, infon, emergent spacetime, gravitational propulsion, negative energy, quantum gravity, field theory, Casimir effect, metamaterials, QIFT