Dynamical automorphism (DA) code[1,2] 

Classification of stabilizers by masking

There exists an efficient classical algorithm that tracks information learned by syndrome extraction at each step [4]. The algorithm performs the following classification of stabilizers into unmasked, temporarily masked, and permanently unmasked stabilizers.

An unmasked stabilizer is a stabilizer whose outcome can be obtained by measurements. In general, it is not obvious to determine if a stabilizer can be unmasked as its eigenvalue may only be revealed indirectly as a product of several measurements. A temporarily masked stabilizer is a stabilizer whose syndrome can not be obtained by the given sequence but could possibly be obtained with future measurements. A permanently masked stabilizer is a stabilizer whose outcome is irreversibly lost by the given sequence.

For a masked stabilizer code with a set \(U\) of \(l\) masked stabilizers, its masked distance is given by: \begin{equation} d_{\mathrm{u}} = \min\:\text{wt}\{ \mathsf{N}(U)\backslash \mathsf{G}\}~. \tag*{(1)}\end{equation} Above, \(\mathsf{G}\) is a gauge group defined from the algorithm that depends partly on the freedom in the choice of destabilizerss for the temporarily masked stabilizers, and partly on the measurement sequence which fixes the destabilizerss for the permanently masked stabilizers.