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I am studying quantum decoding, especially for minimum weight perfect matching. I wonder after finding perfect matching (syndrome graph referred by sparse Blossom), why do we need to select minimum weight? Is there any specific reason for selecting minimum weight?

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More weight corresponds to less probability. You're trying to guess the most likely error (max probability, min weight) so you want the min weight matching.

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  • $\begingroup$ Would you please explain more ? Why more weigth corresponds to less probability? $\endgroup$
    – 김동민
    Feb 14 at 0:29
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    $\begingroup$ @김동민 because w = -log(p / (1 - p)). When p is near 0, w increases as p decreases. $\endgroup$ Feb 14 at 0:40
  • $\begingroup$ Where does the equation come from? paper? thesis? $\endgroup$
    – 김동민
    Feb 14 at 0:42
  • $\begingroup$ I am sorry, what is p also? $\endgroup$
    – 김동민
    Feb 14 at 0:47
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    $\begingroup$ @김동민 probability of error $\endgroup$ Feb 14 at 1:15

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