We introduce the Extended Integrated Symmetry Algebra (EISA) as a phenomenological effective field theory (EFT) model for exploring the unification of quantum mechanics and general relativity, enhanced by the Recursive Info-Algebra (RIA) extension that integrates dynamic recursion via variational quantum circuits (VQCs) to minimize von Neumann entropy and fidelity losses. The EISA triple superalgebra AEISA = ASM ⊗ AGrav ⊗ AVac encodes Standard Model symmetries, gravitational norms, and vacuum fluctuations, while RIA optimizes information loops to drive emergent quantum field dynamics without invoking extra dimensions. Transient phenomena, such as virtual pair creation-annihilation, couple to a composite scalar ϕ in a modified Dirac equation, potentially sourcing spacetime curvature and phase transitions. Mathematical self-consistency is ensured through rigorous verification of super-Jacobi identities, guaranteeing algebraic closure across symmetry sectors. This framework synthesizes quantum information principles with algebraic structures, where recursive optimization generates physical laws from fundamental symmetries. The incorporation of VQCs offers a robust computational tool for investigating vacuum stability and entropy minimization in extended symmetry spaces. Within the EISA-RIA framework, numerical simulations incorporating 2025 data from NANOGrav gravitational wave observations and ATLAS t ¯t production analyses demonstrate consistency with the model’s predictions, such as modifications to the CMB power spectrum and a potential resolution to the Hubble tension, while highlighting prospects for ultraviolet completions via string theory, asymptotic safety, and holographic principles.