arXiv:1912.09549 · PRX Quantum

Flag Fault-Tolerant Error Correction for any Stabilizer Code

Rui Chao, Ben W. Reichardt

Published Sep 3, 2020• 94 citations

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.

DOI: 10.1103/prxquantum.1.010302

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