To realize universal fault-tolerant quantum computing, there is a need for circuit libraries of universal fault-tolerant quantum protocols that must be executable in terms of locality constraint that a quantum chip has and retain both the fault tolerance and the logic sequence of the protocol at the same time. Unlike topological codes that are fundamentally defined based on local operations, for concatenated codes, we must find such circuits separately. To date, a systematic method for such a task has never been reported, except for manually obtained circuits for small-sized codes. In this work, for the first time, a quantum circuit synthesis algorithm for universal fault-tolerant quantum computing based on concatenated codes has been proposed. We enumerate the requirements and present our approaches and how to implement them with the existing quantum circuit mapping heuristic algorithm. As examples, we show how to synthesize the circuit set of universal fault-tolerant quantum computing based on {{7, 1, 3}} Steane code and the circuit for the syndrome measurement of {{23, 1, 7}} Golay code.

 

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