Cluster-based architecture for fault-tolerant quantum computation

We present a detailed description of an architecture for fault-tolerant quantum computation, which is based on the cluster model of encoded qubits. In this cluster-based architecture, concatenated computation is implemented in a quite different way from the usual circuit-based architecture where physical gates are recursively replaced by logical gates with error-correction gadgets. Instead, some relevant cluster states, say fundamental clusters, are recursively constructed through verification and postselection in advance for the higher-level one-way computation, which namely provides error-precorrection of gate operations. A suitable code such as the Steane seven-qubit code is adopted for transversal operations. This concatenated construction of verified fundamental clusters has a simple transversal structure of logical errors, and achieves a high noise threshold $~3%$ for computation by using appropriate verification procedures. Since the postselection is localized within each fundamental cluster with the help of deterministic bare controlled-Z gates without verification, divergence of resources is restrained, which reconciles postselection with scalability.