Robust segmented entangling gates with pulse gradient and power optimization using a hypersurface-tangent method

To implement a scalable and fault-tolerant programmable quantum computing architecture, the realization of high-fidelity, robust, and efficient quantum entangling gates in a multiqubit system is an essential requirement. In this paper, we consider the optimization of the segmented amplitude-modulated entangling gates realized by applying spin-dependent forces to a chain of ions trapped in a hybrid quadratic and quartic potential. We propose a geometrical hypersurface-tangent method to optimize the laser power and the pulse gradient, carefully considering the experimental feasibility in realizing the effective Rabi frequency and its change between adjacent pulse segments. In addition, our method allows us to optimize the solution for the case of a few segments by constructing an approximated null space through trading a negligible amount of gate fidelity. Finally, we show that the present scheme can provide a unified framework to improve the robustness to an arbitrary order against random static drifts of the motional frequencies, the gate duration errors, the laser detuning drifts, and their simultaneous drifts.