Rydberg excited atoms provide strong interactions suitable for high fidelity quantum gates. I will discuss theoretical bounds on the fidelity limit of coherent Rydberg gates, and describe progress towards demonstrating a multi-qubit quantum processor based on trapping ground state and Rydberg excited atoms. The finite lifetime of Rydberg states puts limits on the fidelity of Hamiltonian evolution. I will show how a dissipative approach can be used to create high fidelity entanglement, and simulate interacting spin systems.