Abstract
With the aim of exploring local quantum control in arrays of interacting qubits, we study anisotropic XXZ Heisenberg spin-1/2 chains with control fields acting on one of the end spins. In this work, which hinges on a recent Lie-algebraic result pertaining to 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, controlled-NOT, and square-root-of-SWAP. We find the minimal times for realizing different gates depending on the anisotropy parameter of the model, showing that the shortest gate times are reached for particular values of this parameter larger than unity. To study the influence of possible imperfections in anticipated implementations of qubit arrays, we analyse the robustness of the obtained gate fidelities to random variations in the control-field amplitudes and finite rise time of the pulses. Finally, we discuss the implications of our findings for superconducting charge-qubit arrays.
