Multiqubit Toffoli gates and optimal geometry with Rydberg atoms

Due to its potential for implementing a scalable quantum computer, multiqubit Toffoli gate lies in the heart of quantum information processing. In this article, we demonstrate a multiqubit blockade gate with atoms arranged in a three-dimension spheroidal array. The gate performance is greatly improved by the method of optimizing control-qubit distributions on the spherical surface via evolutionary algorithm, which leads to an enhanced asymmetric Rydberg blockade. This spheroidal configuration, not only arises a well preservation for the dipole blockade energy between arbitrary control-target pairs, which keeps the asymmetric blockade error at a very low level; but also manifests an unprecedented robustness to the spatial position variations, leading to a negligible position error. Taking account of intrinsic errors and with typical experimental parameters, we numerically show that a C$_6$NOT Rydberg gate can be created with a fidelity of 0.992 which is only limited by the Rydberg state decays.Our protocol opens up a new platform of higher-dimensional atomic arrays for achieving multiqubit neutral-atom quantum computation.