2
$\begingroup$

I've read a few papers regarding to Surface Code and its decoding algorithms. I've learned that a Union-Find decoder need up to $d$ measurement rounds to deal with measurement errors.

These measurement rounds yields a 3-D syndrome graph, like this: a 3D syndrome graph example

I tried to understand the way Union-Find Decoders deal with the 3D syndrome graphs but failed. I haven't found a paper or open-source implementation which clarify the foundamental steps of the decoder.

So here is my question:

  1. How to understand the way Union-Find Decoders deal with multiple measurement rounds and 3D syndrome graphs?
  2. Is there any papers or open-source implementations of this measurement-error-solvable decoder?

If you could provide any guidance or insights on this matter, I would be immensely grateful. Your expertise would be invaluable in helping me understand this topic. Thank you in advance for your time and knowledge.

$\endgroup$

1 Answer 1

1
$\begingroup$

It doesn't do anything special at all to deal with the measurement errors. The circuit noise problem is conceptually identical to the code capacity noise problem. Errors cause 2 or 1 detection events (defining the edges and boundary edges of a graph) and you match up the detection events by growing search regions on that graph. Literally the exact same code works when you add measurement errors.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.