Soleh Kh. Muminov, Evgeniy O. Kiktenko, Anastasiia S. Nikolaeva, Denis A. Drozhzhin, Sergey I. Matveenko, Aleksey K. Fedorov, Georgy V. Shlyapnikov

We propose a model of a scalable qudit-based quantum processor that uses rotational degrees of freedom of polar molecules. Entangling gates between qudits are implemented via moving molecule in optical traps by exploiting dipole-dipole interactions to mediate coherent coupling. We develop encoding schemes that map single qubits (d=2) into qudits of dimensions 2 <= d <= 5, and pairs of qubits into higher-dimensional qudits with d=4, 5. This approach enables the realization of a universal set of quantum gates. In particular, we exploit additional levels that are present in the d=3 and d=5 qudits, which allows one to simplify the decomposition of multiqubit gates. We then analyze the relevant experimental parameters to realize our schemes with SrF and 87Rb133Cs molecules. The proposed approach offers a promising route towards scalable and versatile quantum information processing with multilevel systems, which can be potentially realized using currently available experimental facilities.