  We investigate the influence of geometry on the preservation of quantum
coherence in spin clusters subjected to a thermal environment. Assuming weak
inter-spin coupling, we explore the various buffer network configurations that
can be embedded in a plane. Our findings reveal that the connectivity of the
buffer network is crucial in determining the preservation duration of quantum
coherence in an individual central spin. Specifically, we observe that the
maximal planar graph yields the longest preservation time for a given number of
buffer spins. Interestingly, our results demonstrate that the preservation time
does not consistently increase with an increasing number of buffer spins.
Employing a quantum master equation in our simulations, we further demonstrate
that a tetrahedral geometry comprising a four-spin buffer network provides
optimal protection against environmental effects.
