how are redundant stabilisers handled when measuring sydrome?

Question

I'm reading this old post surface code and the second answer under error detection and correction it talks about measuring "every stabilizer". It is known that of the $d^2$ $X$ stabilisers only $d^2-1$ are independent (same for $Z$ stabilisers). Do you measure all $d^2$ or just $d^2-1$? If it's the latter then this seems to break the geometric symmetry of the stabilizers : one would need to be skipped (for example the one in the bottom left corner...). What if one of the anyon pairs land on that omitted site?

Answer 1

It really doesn't matter. It might be that something in your implementation makes the symmetric implementation easier, or you may just prefer to minimise the total number of operations.

If one anyon from a pair lands on the unmeasured stabilizer, you know it: there must always be an even number of anyons, so if you see an odd number, you know there's one on the region you didn't look at.