Phenomenological Loop-Entropy Cosmology: Numerical Simulations and Quantum-Circuit Benchmarks

We investigate a phenomenological extension of Loop Quantum Cosmology (LQC) incorporating quantum entropy measurements from IBM Quantum hardware. The model explores statistical correlations between measured circuit entropy and effective cosmological dynamics near the quantum bounce. A multiplicative entropy correction to the Friedmann equation is introduced as a heuristic ansatz. The model is intended as a correlation study rather than a fundamental derivation. The coupling parameter β is restricted by theoretical consistency conditions of the effective model (positivity of H²≥0, nonsingular bounce preservation) and numerical stability of the RK4 integrator, yielding a numerically resolved window β∈[0.01,0.1] under the present integration setup, with the upper bound set by perturbativity. The model is calibrated against numerical simulations and tested for internal consistency on 14 quantum circuit experiments (up to 8192 shots on ibm_marrakesh, with cross-backend comparison to ibm_fez providing partial bounds on systematic errors). A robustness analysis demonstrates that the bounce dynamics and coupling bounds are insensitive to the precise functional form of the entropy profile S(a). Connections to the emergent entropy-gravity programme are discussed.