  We investigate the feasibility of single-shot Toffoli- and Fredkin-gate
realizations in qubit arrays with Heisenberg-type exchange interactions between
adjacent qubits. As follows from the Lie-algebraic criteria of controllability,
such an array is rendered completely controllable -- equivalent to allowing
universal quantum computation -- by a Zeeman-like control field with two
orthogonal components acting on a single "actuator" qubit. Adopting this
local-control setting, we start our analysis with piecewise-constant control
fields and determine the global maxima of the relevant figure of merit
(target-gate fidelity) by combining the multistart-based clustering algorithm
and quasi-Newton type local optimization. We subsequently introduce important
practical considerations, such as finite frequency bandwidth of realistic
fields and their leakage away from the actuator. We find the shortest times
required for high-fidelity Toffoli- and Fredkin-gate realizations and provide
comparisons to their respective two-qubit counterparts -- controlled-NOT and
exponential-SWAP. In particular, the Toffoli-gate time compares much more
favorably to that of controlled-NOT than in the standard decomposition-based
approach. This study indicates that the use of the single-shot approach can
alleviate the burden on control-generating hardware in future experimental
realizations of multi-qubit gates.
