3

Suppose I know a set of stabilizer generators of a qubit quantum code. Is there a systematic (and possibly efficient) way to transform this set of generators to a different set (generating the same code) with lowest possible weights? I suspect that there is no efficient way, because this problem looks very similar to the shortest basis problem of lattices which is conjectured to be very hard.

user1677907
  • 63
  • 3
  • I guess a first and easier question is whether you can do this for parity checks of classical codes. – smapers Mar 11 '20 at 16:06
  • there will be a systematic way of doing it using, for example, binary programming. As for efficient? I don't really know, but intuition suggests not. Binary programming iteself is NP-complete and I'd guess you can encode hard instances within this specfic problem. But that's hardly a rigorous aswer ;) – DaftWullie Mar 12 '20 at 09:03
  • Computing the distance (weight of lowest weight check) of a linear code is NP-hard. Even approximating it is hard (https://doi.org/10.1109/SFFCS.1999.814620). – Tushant Mittal Jan 10 '24 at 22:45

0 Answers0