<p>I was reading <a href="https://arxiv.org/abs/1304.6743" rel="nofollow noreferrer">combinatorial approach towards quantum correction</a>. 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.</p>

<p>Given a labeling <span class="math-container">$L$</span> (a map where each vertex is is assigned 1 or 0) we define two operations on this: </p>

<ol>
<li><p><span class="math-container">$X(v,L)$</span>: you flip labeling of vertex v that is if it was zero make it 1 if it was 1 make it 0.</p></li>
<li><p><span class="math-container">$Z(v,L)$</span>: you flip labeling of every neighbor of vertex v</p></li>
</ol>

<p>Then diagonal distance is defined as length of minimal non-trivial sequence of operation so that <span class="math-container">$L$</span> is taken back to itself. </p>

<p>How is this exactly related to the quantum error correction property?  </p>

CC BY-SA 4.0
2020-08-14T07:03:13.840Z
This question has been answered on the [quantum computing se](https://quantumcomputing.stackexchange.com/questions/12793/quantum-error-correcting-codes-and-graphs).
smapers
CC BY-SA 4.0
2020-08-14T08:54:39.310Z
Cross-posted: https://cstheory.stackexchange.com/q/47049/5038, https://quantumcomputing.stackexchange.com/q/12793/510.  Please [do not post the same question on multiple sites](https://meta.stackexchange.com/q/64068).
D.W.
CC BY-SA 4.0
2020-08-14T21:06:31.540Z
@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
<graph-theory><co.combinatorics><quantum-computing><coding-theory><combinatorics>
Quantum error correction and graph codes
Root
# Quantum error correction and graph codes

(Asked by: username_0 on 2020-06-16)

I was reading [combinatorial approach towards quantum correction](https://arxiv.org/abs/1304.6743). 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?

**Tags:** graph-theory, co.combinatorics, quantum-computing, coding-theory, combinatorics
> **Comments:**
> **username_1**: This question has been answered on the [quantum computing se](https://quantumcomputing.stackexchange.com/questions/12793/quantum-error-correcting-codes-and-graphs).  
> **username_2**: Cross-posted: https://cstheory.stackexchange.com/q/47049/5038, https://quantumcomputing.stackexchange.com/q/12793/510.  Please [do not post the same question on multiple sites](https://meta.stackexchange.com/q/64068).  
> **username_0**: @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.  

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## 0 answers

