Fault-tolerant logical state construction based on cavity-QED network

Exploring an efficient and scalable architecture of fault-tolerant quantum computing (FTQC) is vital for demonstrating useful quantum computing. Here, we propose and evaluate a scalable and practical architecture with a cavity-quantum-electrodynamics (CQED) network. Our architecture takes advantage of the stability of neutral atoms and the flexibility of a CQED network. We show a concrete framework for implementing surface codes and numerically analyze the logical error rate and threshold values beyond the simplified circuit-level noise model on several network structures. Although the requirement of CQED parameters is demanding given the current performance of experimental systems, we show that an error-decoding algorithm tailored to our proposed architecture, where the loss information of ancillary photons is utilized, greatly improves the error threshold. For example, the internal cooperativity, a good figure of merit of the cavity performance for quantum computing, required for FTQC is relaxed to 1/5 compared to the normal error-decoding for the surface code. Since our proposal and results can be extended to other LDPC codes straightforwardly, our approach will lead to achieve more reliable FTQC using CQED.