Nonadiabatic holonomic quantum computation in decoherence-free subspaces on Rydberg atoms

We propose a scheme for realizing nonadiabatic holonomic quantum computation within a decoherence-free subspace using Rydberg atoms. By employing large-detuned lasers and the Rydberg antiblockade condition, we construct an effective Hamiltonian that couples logical states in a three-atom decoherence-free subspace while ensuring that the Rydberg states remain unpopulated. This approach significantly suppresses decoherence caused by atomic spontaneous emission and mitigates the mechanical effects and sensitivity to interatomic distance variations associated with Rydberg excitations. We demonstrate the realization of both conventional and single-loop single-logical-qubit holonomic gates with high fidelity. Furthermore, by utilizing an asymmetric encoding method, in which the control logical qubits employ Rydberg-state encoding to provide the required conditional blockade, we extend the scheme to construct universal two- and three-logical-qubit holonomic gates, offering a robust and scalable approach for quantum information processing.