An universal quantum computation scheme with low error diffusion property

Quantum concatenation code is an effective way to realize fault-tolerant universal quantum computing. Still, there are many non-fault-tolerant logical locations at its low encoding level, which thereby increases the probability of error multiplication and limits the ability that such code to realize a high-fidelity universal gate library. In this work, we propose a general framework based on machine learning technology for the decoder design of a segmented fault-tolerant quantum circuit. Then following this design principle, we adopt the neural network algorithm to give an optimized decoder for the such circuit. To assess the effectiveness of our new decoder, we apply it to the segmented fault-tolerant logical controlled-NOT gates, which act on the tensor composed of the Steane 7-qubit logical qubit and the Reed-Muller 15-qubit logical qubit. We simulate these gates under depolarizing noise environment and compare the gate error thresholds in contrast to the minimal-weight decoder. Finally, we provide a fault-tolerant universal gate library based on a 33-qubit non-uniform concatenated code. Furthermore, we offer several level-1 segmented fault-tolerant locations with optimized decoders to construct a non-Clifford gate on this code, which has less circuit depth than our existing work. Meanwhile, we analyze the pseudo-threshold of the universal scheme of this code.