  We describe how a universal set of dynamically-corrected quantum gates can be
implemented using sequences of shaped decoupling pulses on any qubit network
forming a sparse bipartite graph with always-on Ising interactions. These
interactions are constantly decoupled except when they are needed for two-qubit
gates. We analytically study the error operators associated with the
constructed gates up to third order in the Magnus expansion, analyze these
errors numerically in the unitary time evolution of small qubit clusters, and
give a bound on high-order errors for qubits on a large square lattice. We
prove that with a large enough toric code the present gate set can be used to
implement a fault-tolerant quantum memory.
