Flag fault-tolerant error correction for any stabilizer code

TL;DR

This paper introduces a universal flag fault-tolerant error correction scheme for any stabilizer code, requiring only a small number of extra qubits and working unconditionally, thus improving efficiency in quantum error correction.

Contribution

It provides a new flag error correction method applicable to all stabilizer codes, overcoming previous limitations and requiring minimal additional qubits.

Findings

Works for any stabilizer code with unconditionally guaranteed fault tolerance.

Uses only d+1 extra qubits for a distance-d code with fast measurement.

Reduces qubit overhead compared to traditional schemes.

Abstract

Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows 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 (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.