  We model repetitive quantum error correction (QEC) with the
single-error-correcting five-qubit code on a network of individually-controlled
qubits with always-on Ising couplings, using our previously designed universal
set of quantum gates based on sequences of shaped decoupling pulses. In
addition to serving as accurate quantum gates, the sequences also provide
dynamical decoupling (DD) of low-frequency phase noise. The simulation involves
integrating unitary dynamics of six qubits over the duration of tens of
thousands of control pulses, using classical stochastic phase noise as a source
of decoherence. The combined DD/QEC protocol dramatically improves the
coherence, with the QEC alone responsible for more than an order of magnitude
infidelity reduction.
