Simulation Of Quantum Spin Systems For Qubit Applications

Abstract

This study presents a numerical investigation of the dynamics of two coupled spin-1/2 quantum systems with emphasis on entanglement, quantum coherence, and state fidelity. The system is described by an isotropic Heisenberg Hamiltonian and investigated for exchange-coupling strengths J=−1, −0.5, 0, 0.5, and 11. Four representative initial states, comprising the Bell state, a partially entangled state with initial concurrence C (0) =0.8, and the separable states ∣01⟩and ∣++⟩are considered. Closed-system evolution is obtained using the unitary propagator, while environmental effects are modelled through a Lindblad master equation with local Markovian pure-dephasing channels for γ=0,0.1,0.5, and 11. The results show that the Bell state maintains maximal concurrence under closed Heisenberg evolution, while the partially entangled state retains its initial concurrence of 0.8 for all tested exchange couplings. In contrast, the initially separable ∣01⟩state develops strong transient entanglement through exchange interaction, reaching concurrence values essentially equal to unity for ∣J∣=0.5 and 11, whereas the ∣++⟩state remains separable to numerical precision. Under pure dephasing, concurrence and coherence decay progressively with increasing dephasing strength, while fidelity decreases toward its asymptotic value. The numerical calculations were further validated through normalization and Hermiticity checks, analytical dephasing benchmarks, and step-refinement convergence tests, with discrepancies remaining at machine-precision levels. The findings demonstrate that the preservation and generation of quantum correlations depend strongly on the initial state, exchange interaction, and environmental decoherence, providing validated numerical benchmarks for the study of coupled qubit dynamics.