Feasibility of single-shot realizations of conditional three-qubit gates in exchange-coupled qubit arrays with local control

Abstract: 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.