Topological One-Way Quantum Computation on Verified Logical Cluster States

We present a scheme to improve the noise threshold for the fault-tolerant topological one-way computation with a constant overhead. Certain cluster states of finite size, say star clusters, are constructed with logical qubits through an efficient verification process to achieve high fidelity. Then, the star clusters are connected near-deterministically with verification to form a three-dimensional cluster state to implement the topological one-way computation. The necessary postselection for verification is localized within the star clusters, ensuring the salability of computation. This scheme works with a high error rate $ \sim 1 % $ and reasonable resources comparable to or less than those for the other fault-tolerant schemes, suggesting potentially a noise threshold higher than 5%.