  We theoretically propose a quantum simulation scheme for the toric-code
Hamiltonian, the paradigmatic model of a quantum spin liquid, based on
time-periodic driving. We develop a hybrid continuous-digital strategy that
exploits the commutativity of different terms in the target Hamiltonian. It
allows one to realize the required four-body interactions in a nonperturbative
way, attaining strong coupling and the suppression of undesired processes. In
addition, we design an optimal protocol for preparing the topologically ordered
ground states with high fidelity. A proof-of-principle implementation of a
topological device and its use to simulate the topological phase transition are
also discussed. The proposed scheme finds natural implementation in
architectures of superconducting qubits with tuneable couplings.
