Flag Fault-Tolerant Error Correction for any Stabilizer Code

Abstract

Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grow linearly with the code’s maximum stabilizer generator weight. For some common distance-three codes, the recent “flag paradigm” uses just two extra qubits. Chamberland and Beverland [Quantum 2, 53 (2018)] provide a framework for flag error correction of arbitrary-distance codes. However, their construction requires conditions that only some code families are known to satisfy. We give a flag error-correction scheme that works for any stabilizer code, unconditionally. With fast qubit measurement and reset, it uses ≤d+1 extra qubits for a distance-d code.