Long-range Rydberg-blockade entangling gate mediated by auxiliary atoms

Arrays of qubits encoded in the ground state manifold of trapped neutral atoms appear as a promising platform for the realisation of a scalable quantum computer. Indeed, such physical qubits have a long coherence time and allow for high-fidelity single-qubit operations [1]. In such a platform, entangling two-qubit gates can be implemented by exploiting the Rydberg-blockade mechanism to produce a phase shift or a flip of the state of a target atom conditioned on the state of a control atom [2]. However, because dipole-dipole interactions fall off rapidly with the interatomic distance, such entangling gates based on Rydberg-blockade are impractical between distant qubits. In this work, we propose a protocol to implement long-range Rydberg-blockade gates (CZ or CNot) using auxillary non-coding atoms to transfer the Rydberg excitation from the control to the target qubit. The dependence of the fidelity on the number of auxillary atoms, the blockade strength and the decay rates of the Rydberg states are determined. When compared to a sequential application of nearest neighbours entangling gates, our protocol leads to a larger fidelity and a reduction of the overall gate duration (which scales linearly with the number of auxillary atoms).

[1] M. Saffman, J. Phys. B: At. Mol. Opt. Phys. 49, 202001 (2016). [2] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Phys. Rev. Lett. 85, 2208 (2000).