An architecture for distributed fault tolerant quantum computing over a trapped-ion quantum network with finite resources

The development of large-scale quantum networks connecting quantum computers at distant nodes, capable of performing distributed fault-tolerant quantum computing, remains a highly sought-after area of research. We propose an architecture based on dual-species trapped-ion (DSTI) nodes for universal fault-tolerant quantum computation in the presence of loss errors in photonic interfacing and Pauli noise in the trapped ion qubits, using a hybrid approach that combines intra-nodal gate-based and inter-nodal measurement-based implementations. We conduct a detailed analysis of resources versus performance, pertaining to the cluster state generation between the distributed trapped-ion nodes. To enhance the probability of generating Bell pairs between distant nodes, we multiplex our attempts in both spatial and temporal domains. We demonstrate that the proposed architecture can be realized with finite layers of qubit memories by re-initializing the qubits after they have been measured.