Flag fault-tolerant error correction for arbitrary stabilizer codes

Presenting Author: Rui Chao, University of Southern California
Contributing Author(s): Ben Reichardt

Quantum fault tolerance generally incurs a large qubit overhead. Conventional fault-tolerant error-correction schemes based on ancilla verification or decoding tricks needs as many ancillas as the maximum stabilizer generator weight, whereas a scheme using the flag paradigm requires only two ancillas for common distance-three codes. Recently, Chamberland and Beverland (Quantum 2, 53 (2018)) have provided a framework for flag error correction of arbitrary-distance codes. However, their construction requires certain conditions, which only a few code families are known to satisfy. In this paper, we describe a detailed flag fault-tolerant error-correction scheme that applies unconditionally to arbitrary stabilizer codes. In particular, the circuit construction and correction procedure only depend on the code distance and the weights of the stabilizers. For a code with distance d, it uses d+1 ancilla qubits.

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