Spheroidal-structure-based multi-qubit Toffoli gate via asymmetric Rydberg interaction

We propose an exotic multi-qubit Toffoli gate protocol via asymmetric Rydberg blockade, benefiting from the use of a spheroidal configuration to optimize the gate performance. The merit of a spheroidal structure lies in a well preservation of strong blocked energies between all control-target atom pairs within the sphere, which can persistently keep the blockade error at a low level. On the basis of optimization for three different types of $(2+1)$-$qubit$ gate units to minimize the antiblockade error, the gate fidelity of an optimal $(6+1)$-$qubit$ configuration can attain as high as $0.9841$ mainly contributed by the decay error. And the extension with much more control atoms is also discussed. Our findings may shed light on scalable neutral-atom quantum computation in special high-dimensional arrays.