We investigate anisotropic XXZ Heisenberg spin-1/2 chains with control ﬁelds acting on one of the end spins, with the aim of exploring local quantum control in arrays of interacting qubits. In this work, which uses a recent Lie-algebraic result on the local controllability of spin chains with “always-on” interactions, we determine piecewise-constant control pulses corresponding to optimal ﬁdelities for quantum gates such as spin-ﬂip (NOT), controlled-NOT (CNOT), and square-root-of-SWAP ( √ SWAP). We ﬁnd the minimal times for realizing different gates depending on the anisotropy parameter Δ of the model, showing that the shortest among these gate times are achieved for particular values of Δ larger than unity. To study the inﬂuence of possible imperfections in anticipated experimental realizations of qubit arrays, we analyze the robustness of the obtained results for the gate ﬁdelities to random variations in the control-ﬁeld amplitudes and ﬁnite rise time of the pulses. Finally, we discuss the implications of our study for superconducting charge-qubit arrays.