Multiqudit interactions in molecular spins

12 pags., 7 figs., 3 apps.
We study photon-mediated interactions between molecular spin qudits in the dispersive regime of operation. We derive from a microscopic model the effective interaction between molecular spins, including their crystal field anisotropy (i.e., the presence of nonlinear spin terms) and their multilevel structure. Finally, we calculate the long-time dynamics for a pair of interacting molecular spins using the method of multiple-scale analysis. This allows us to find a set of two-qudit gates that can be realized for a specific choice of molecular spins and to determine the time required for their implementation. Our results are relevant for the implementation of logical gates in general systems of qudits with unequally spaced levels or to determine an adequate computational subspace to encode and process the information.
We acknowledge funding from the Spanish MICIN Grant No. PCI2018-093116 (MCIU/AEI/FEDER, UE) and the CSIC Interdisciplinary Thematic Platform (PTI+) on Quantum Technologies (PTI-QTEP+).