  Motivated by some recent results of quantum control theory, we discuss the
feasibility of local operator control in arrays of interacting qubits modeled
as isotropic Heisenberg spin chains. Acting on one of the end spins, we aim at
finding piecewise-constant control pulses that lead to optimal fidelities for a
chosen set of quantum gates. We analyze the robustness of the obtained results
f or the gate fidelities to random errors in the control fields, finding that
with faster switching between piecewise-constant controls the system is less
susceptible to these errors. The observed behavior falls into a generic class
of physical phenomena that are related to a competition between resonance- and
relaxation-type behavior, exemplified by motional narrowing in NMR experiments.
Finally, we discuss how the obtained optimal gate fidelities are altered when
the corresponding rapidly-varying piecewise-constant control fields are
smoothened through spectral filtering.
