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.