Efficient Decoding Scheme of Non-Uniform Concatenation Quantum Code with Deep Neural Network

How to design a universal fault-tolerant quantum computation protocol with high fidelity and low resource consumption is a hot topic in the field of quantum computing research. By reducing the effective code distance, the design of a universal fault-tolerant gate set based on concatenation code has been proposed. The auxiliary state required by the error correction of code must be verified before it can be used, so as to avoid the errors spread from the auxiliary state to the data state. But the qubit consumption can be very large due to multiple verification processes for the ancillary block. In this work, we analyze the ancillary consumption of two different verification schemes used in the Steane’s error correction process. We take the basic state preparation of a 25-qubit 2-level concatenation code as an example, adopt a simpler verification circuit in its error correction process, and design an efficient decoding strategy by using deep neural network algorithm. Numerical simulations are also performed to analyze our low qubit resource overhead error correction scheme.