The first part of this talk will focus on our recently proposed ion-atom hybrid quantum computing architecture.  We demonstrate the universal two-qubit CNOT gate with 89.9% fidelity between an ionic and an atomic qubit relying on Rydberg excitation of the atom and the resulting phonon blockade in the motional states of the harmonically trapped ion [S. Mudli and B. Deb, https://arxiv.org/abs/2602.19222v1]. We also show a universal two-qubit gate operation with 97% fidelity between two neutral atom qubits based on ion-mediated interactions [S. Mudli et al. Phys. Rev. A 110, 062618 (2024)]. These demonstrations suggest that an ion-atom hybrid system can serve as a module of a quantum network for distributed quantum computing leveraging the best features of charged as well as neutral atom qubits. In the second part of the talk, we will focus on two- and three-qubit quantum gate operations in a neutral-atom architecture based on Rydberg blockade and dark state resonances [S. S. Rej and B. Deb New J. Phys.28 14513 (2026), S. S. Rej, S.  Ray and B.  Deb arxiv:2601.06665, S. S. Rej and B.  Deb arxiv:2507.02531]