Time fractional evolution of two superconducting charge qubits

We investigate the quantum correlation dynamics between two superconducting charge qubits (TSC-Q), governed by the time-fractional Schrödinger equation (TFSE), a framework incorporating non-Markovian memory effects arising from environmental interactions. By analyzing separable and partially entangled initial states, we highlight the central role of the fractional order τ, Josephson energies (EJ1, EJ2), and coupling strength (Em) in modulating concurrence, quantum steering asymmetry, and Bell nonlocality (via the CHSH inequality). Our results indicate that a decrease in the value of τ promotes a faster generation of quantum correlations for separable and partially entangled states, highlighting the dual role of τ as both a catalyst and a stabilizer of quantum resources. Furthermore, it is important to note that optimal behavior of quantum correlations is observed when the Josephson energies of the two qubits are close, i.e., when EJ2≈EJ1. In addition, a stronger coupling strength, denoted by Em, further enhances the generation of these correlations. The synergy among τ, EJ1, EJ2, and Em defines a tunable parameter space for engineering memory-driven correlations to mitigate decoherence. These results position the TFSE as a promising tool for modeling non-Markovian dynamics in superconducting architectures, paving the way for robust quantum platforms with enhanced correlations, suitable for scalable quantum computing and secure communication systems.