Qudit encoding in Rydberg blockaded arrays of atoms

We propose a protocol to realize arbitrary state synthesis and unitary operations on a qudit encoded in the collective dressed states of a Rydberg-blockaded array of three-level atoms. This system is isomorphic to the Jaynes-Cummings model and acts as a multilevel Rydberg superatom whose nonlinear spectrum can be precisely controlled through the parameters of the laser driving the intermediate-to-Rydberg transition. Control of the qudit state is possible through pulse sequences of the laser driving the ground-to-intermediate transition. The dimension of the qudit Hilbert space is scalable by adjusting the number of atoms involved in the Rydberg-blockaded array. We estimate the fidelity of our protocol for realizing arbitrary unitaries and discuss the influence of the finite lifetime of the Rydberg state. Our work paves the way for processing quantum information with Rydberg blockaded arrays of atoms as an alternative to atom qubit arrays.