measure the stabilizers) which, if satisfied, can be used for flag error correction. We are primarily concerned with extending the lifetime of encoded information using fault-tolerant error correction and defer the study of implementing gates fault-tolerantly to future work. Our approach can be applied to a broad class of codes (including but not limited to surface codes, color codes and quantum Reed-Muller codes). Of the three general schemes described above, flag EC has most in common with Shor EC. Further, flag EC does not require verified state preparation, and for all codes considered to date, requires fewer ancilla qubits. Lastly, we note that in order to satisfy the fault-tolerant error correction definition presented in \[subsec:Section0\], our protocol applied to distance-three codes differs from [@CR17v1].

We foresee a number of potential applications of these results. Firstly we believe it is advantageous to have new EC schemes with different properties that can be used in various settings. Secondly, flag EC involves small qubit overhead, hence possibly the schemes presented here and in other flag approaches [@CR17v1; @CR17v2; @Yoder2017surfacecodetwist] will find applications in early qubit-limited experiments. Thirdly, we expect the flag EC protocol presented here could potentially be useful for LDPC codes as 