Geometrical Optimization of Spin Clusters for the Preservation of Quantum Coherence

Abstract

We investigate the influence of geometry on the preservation of quantum coherence in spin clusters subjected a thermal environment. Assuming weak interspin coupling, we explore the various buffer network configura yons that can be embedded in a plane. Our findings reveal that the connectivity of the buffer network is crucial indetermining 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 #umber of buffer spins. Employing a quantum master equation in our simulations, we further demonstrate that a Cetrahedral geometry comprising a four-spin buffer network provides optimal protection against environmental Tects.