  We construct a universal set of high fidelity quantum gates to be used on a
sparse bipartite lattice with always-on Ising couplings. The gates are based on
dynamical decoupling sequences using shaped pulses, they protect against
low-frequency phase noise, and can be run in parallel on non-neighboring
qubits. This makes them suitable for implementing quantum error correction with
low-density parity check codes like the surface codes and their finite-rate
generalizations. We illustrate the construction by simulating quantum Zeno
effect with the $[[4,2,2]]$ toric code on a spin chain.
