  We investigate the impact of different connectivities on the decoherence time
in quantum systems under quasi-static Heisenberg noise. We considered three
types of elementary units, including node, stick and triangle and connect them
into ring, chain, and tree configurations. We find that rings exhibit greater
stability compared to chains, contrary to the expectation that higher average
connectivity leads to decreased stability. Additionally, the stick
configuration is more stable than the triangle configuration. We also observe
similar trends in entanglement entropy and return probability, indicating their
potential use in characterizing decoherence time. Our findings provide insights
into the interplay between connectivity and stability in quantum systems, with
implications for the design of robust quantum technologies and quantum error
correction strategies.
