Measurement-Based Fault-Tolerant Quantum Computation on High-Connectivity Devices: A Resource-Efficient Approach toward Early FTQC

We propose a measurement-based FTQC (MB-FTQC) architecture for high-connectivity platforms such as trapped ions and neutral atoms. The key idea is to use verified logical ancillas combined with Knill's error-correcting teleportation, eliminating repeated syndrome measurements and simplifying decoding to logical Pauli corrections, thus keeping classical overhead low. To align with near-term device scales, we present two implementations benchmarked under circuit-level depolarizing noise: (i) a Steane-code version that uses analog R_Z(θ) rotations, akin to the STAR architecture [Akahoshi et al., PRX Quantum 5, 010337], aiming for the megaquop regime $sim 10⁶$ $T$ gates on devices with thousands of qubits; and (ii) a Golay-code version with higher-order zero-level magic-state distillation, targeting the gigaquop regime $sim 10⁹$ $T$ gates on devices with tens of thousands of qubits. At a physical error rate p=10^-4, the Steane path supports 5times 10⁴ logical R_Z(θ) rotations, corresponding to sim 2.4times 10⁶ T gates and enabling megaquop-scale computation. With about 2{,}240 physical qubits, it achieves log₂QV=64. The Golay path supports more than 2times 10⁹ T gates, enabling gigaquop-scale computation. These results suggest that our architecture can deliver practical large-scale quantum computation on near-term high-connectivity hardware without relying on resource-intensive surface codes or complex code concatenation.