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Simulating decoherence of two coupled spins using the generalized cluster correlation expansion

We simulate the coherence of two coupled electron spins interacting with a bath of nuclei using the generalized cluster correlation expansion (gCCE) method. An exchange interaction between the electrons facilitates a family of entangling gates that can be spoiled by nuclear-induced dephasing. Consequently, we study the dephasing of the coherent two-electron system by characterizing the $T_2$ and $T_2^*$ of the two-electron reduced density matrix for various system parameters in the range mimicking magnetic molecules, including magnetic field strength and orientation, exchange interaction strength, distance between the two spins, minimum distance between electron and nuclei and between nuclei, and nuclei density. We find the optimal regime for each parameter in which the coherence time is maximized and provide a physical understanding of it.