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

Geometrical optimization of spin clusters for the preservation of quantum coherence