Cosmology from Two Axioms 5, Duality between Quantum Computational Complexity and Spacetime Geometry

Based on the twofundamental axioms of “Information Conservation” and “Computability”, this paper proposes a theoretical framework that uses the quantumcomputational complexity gradient (∇C) as the core order parameter to connectspacetime geometry with quantum entanglement evolution. Research shows that ina closed system satisfying information conservation, the growth of computationalcomplexity necessarily drives the evolution of spacetime curvature, leading to aduality relation between the Einstein field equations and the quantum complexityaction. Based on this dynamical mechanism, the theory predicts three classes ofphenomena that can be experimentally tested: correlation signals simulating wormhole geometry in quantum processors, oscillatory features in the primordial gravitational wave power spectrum within specific frequency bands, and the residualentanglement entropy corresponding to the saturation of computational complexityat the late stage of black hole evaporation. These predictions are expected to beindependently tested within five years through superconducting quantum simulations, space-based gravitational wave detectors (such as LISA), and next-generationEvent Horizon Telescopes (ngEHT).