Pieceable fault-tolerant conversion between Steane and Reed-Muller quantum codes with neural network decoders.

Designing efficient fault-tolerant circuits for converting between two quantum codes is an effective way to realize universal fault-tolerant quantum computing. In this work, we adopt the round-robin circuit construction to design a conversion circuit between CSS 7-qubit error-correcting code and Reed-Muller 15-qubit code. We take the pieceable fault-tolerant protocol to guarantee the fault tolerance of our conversion circuit. A neural network decoding scheme is proposed to suppress the propagation of quantum errors. Our decoding scheme can effectively reduce the damaging effects of imperfect syndrome extraction operations and predict possible logical errors that occurred after the error correction process. We provide a detailed description of our syndrome data model and analyze the depolarizing noise threshold of our conversion circuit through numerical simulations of the stabilizer circuit.

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