# Quantum error correction and graph codes

I was reading combinatorial approach towards quantum correction. A lot of work in this is on finding diagonal distance of a graph. Let me add definition of diagonal distance so that this remains self-contained.

Given a labeling $$L$$ (a map where each vertex is is assigned 1 or 0) we define two operations on this:

1. $$X(v,L)$$: you flip labeling of vertex v that is if it was zero make it 1 if it was 1 make it 0.

2. $$Z(v,L)$$: you flip labeling of every neighbor of vertex v

Then diagonal distance is defined as length of minimal non-trivial sequence of operation so that $$L$$ is taken back to itself.

How is this exactly related to the quantum error correction property?

• This question has been answered on the quantum computing se. – smapers Aug 14 '20 at 7:03
• – D.W. Aug 14 '20 at 8:54
• @D.W. I waited for couple of weeks and it was not answered, so my understanding was that after clearly mentioning that it cross-posted one can do this. I think 2 weeks was good time for this. Let me know if there is a better way to do this. – Root Aug 14 '20 at 21:06